As example of a single-gap fixed frequency cavity, a longitudinal section of the CERN PS 80 MHz cavity is sketched in Fig. 8.21. The gap on the left can be opened and closed by a pneumatically operated mechanical short-circuit, which allows to make the cavity "invisible" to the beam. Piston tuners entering from the left allow to set the fundamental mode resonance frequency to the operation frequency. The cavity is fabricated from stainless steel, galvanically copper plated on the inside, leading to a *Q* of 22,600. The *R*/*Q* of this cavity is 56 . Figure 8.22 shows the cavity in the RF power test-stand. The final amplifier (visible in the foreground) is strongly coupled to the cavity, which allows the rapid filling of the cavity [39].

It is also part of a fast feed-back loop, which allows making the cavity almost invisible to the beam if the gap is mechanically open. This works as follows: the voltage present in the cavity is constantly monitored by a pick-up, the signal of which is fed into the amplifier chain with the proper phase. If the set-point value of the accelerating voltage is zero but the beam induces a voltage in the cavity

**Fig. 8.21** CERN PS 80 MHz cavity, assembly drawing

(current source on the right in Fig. 8.15), the pick-up will detect this induced voltage and the feedback loop creates an equal voltage with opposite phase, such that the beam induced voltage is exactly compensated. The fast RF feedback loops in the PS 40 MHz and 80 MHz systems have a loop gain in excess of 40 dB, thus reducing the beam induced voltage by more than a factor 100. The loop also stabilizes the voltage precisely around any other set-point value.

# *8.2.6 Multi-Gap Cavities*

In a normal-conducting, single-gap vacuum cavity, there exists a maximum value for the shunt impedance that can be obtained after full optimisation of the cavity. This value is in the order of a few M, the exact value will depend on the frequency range. Limited by the available RF power and the cavity, this sets a upper limit to the accelerating voltage; for larger voltages one has to increase the number of RF systems and the power accordingly.

**Fig. 8.22** CERN PS 80 MHz cavity in the RF test bunker. The final amplifier is visible in the foreground

**Fig. 8.23** Distributing a given power *P* to *n* cavities

To introduce multi-gap cavities let us see what happens if one just increases the number of gaps, keeping the total power constant: consider *n* single-gap cavities with a shunt impedance *R*, as sketched in Fig. 8.23. The available power is split in equal parts and evenly distributed to the *n* cavities. According to Eq. (8.19), each cavity will produce an accelerating voltage of √2*R (P/n)*, so with the correct phasing of the RF the total voltage will be just the sum, *V*acc = √2*(nR)P*. If we now consider the assembly consisting of the *n* original cavities and the power splitter as a single cavity with *n* gaps, we notice that this new cavity has the shunt impedance *nR*; this is a significant increase. Consequently by just multiplying the number of gaps one can make much more efficient use of the available RF power to generate very large accelerating voltages.

Instead of using *n* individual power couplers and a large power splitter, much more elegant ways of distributing the available RF power to many gaps have been invented—one can combine the individual gaps in one vacuum vessel and one can in fact use this vacuum vessel itself as a distributed power splitter, which leads to standing wave or travelling wave cavities. In a travelling wave structure (Sect. 7.5.1), the RF power is fed via a power coupler into one end of the cavity, flowing

**Fig. 8.24** A view inside the CERN SPS 200 MHz travelling wave cavity

(travelling) through the cavity, typically in the same direction as the beam, creating an accelerating voltage at every gap. An output coupler at the far end of the cavity is connected to a matched power load. By design it is assured that the phase velocity of the travelling wave is equal to the speed of the particles, i.e. the phase advance over a cell of length *d* is equal to 2*πd*/*λ* for particles travelling with the speed of light. If this condition is satisfied, one can imagine the particles "surfing" on this forward travelling wave.

As an example for a travelling wave structure, Fig. 8.24 shows a view inside one of the 4 SPS 200 MHz travelling wave cavities [40] with the end covers removed. The phase advance per cell is *π*/2, corresponding to a regular gap distances of 375 mm. The presently operating 4 SPS travelling wave cavities produce an unloaded accelerating voltage of 12 MV with a total power of about 4 MW at 200 MHz, but in the framework of the LHC injector upgrade project, the cavities will be shortened to allow for higher beam current and their number will be increased from 4 to 6.

Vacuum cavities can reach significantly higher voltages than cavities with a ceramic gap, which has a maximum hold-off voltage smaller than vacuum. Multigap accelerating structures, both travelling wave and standing wave, allow in addition to effectively convert available RF power to acceleration. For these reasons, multi-gap vacuum cavities are used where very large accelerating gradients are required, like in a future linear collider projects. Section 7.5 above is dedicated to the design of high gradient accelerating cavities for linear colliders.

# *8.2.7 Superconducting Cavities*

Superconductivity denotes the effect of vanishing electrical resistivity in some materials at cryogenic temperatures. Superconductivity is applied in many present day high energy accelerators in coils to create very large (DC) magnetic fields (Sect. 8.1.3). If also the RF resistance were zero, one would be able to establish RF fields as cavity mode in a superconducting cavity without feeding any RF power, i.e. the shunt impedance would become infinite. The RF surface resistance is not exactly zero though, but it still can be made small enough to reach *Q* values in the order of 1010, which makes RF superconductivity still extremely attractive.

It should be noted that even if the power lost in a superconducting cavity is much smaller than in normal-conducting cavities, this power has to be cooled at cryogenic temperatures, which is much less efficient. As a rule of thumb, an AC power for the refrigerator plant of about 1 kW is necessary to cool a lost RF power of 1 W lost at 2 K (Sect. 8.3.5).

The more serious limitation for superconducting RF cavities is however the maximum possible accelerating field: the RF magnetic field at the cavity surface of the accelerating mode is equal to a surface current density, which must stay below a critical value. For niobium, the best RF superconductor known today, this effect limits the accelerating gradient to below 50 MV/m. But already accelerating gradients above of 5 MV/m require extraordinary care, since also other effects like field emissions from impurities on the surface or multipactor induced quenches have to be dealt with. In order to obtain very large accelerating fields, a very complex technology has been developed over the last decades, primarily driven by the TESLA collaboration (and later the ILC Global Design Effort) with the aim to develop cavities for a linear collider. This R&D allowed pushing the practical values for reliably obtained accelerating gradients from a few MV/m to levels close to the above mentioned limit; the accelerating gradient considered practical for the ILC is 31.5 MV/m. Also the European XFEL, now under construction near Hamburg, uses this technology. The developed technology includes the forming and welding of niobium sheets, different abrasive and non-abrasive, chemical and electrochemical cleaning processes, a special technique with ultra-pure water applied under high pressure, and the strict application of clean-room methods.

Since Sect. 7.5.2 above is dedicated to superconducting accelerating structures for linacs, we will here give an example of a superconducting cavity using a different technology, which has been initially developed for LEP at CERN and is now also used for LHC. The cavities are fabricated from sheet metal copper—a process well understood—and eventually sputtered from the inside with a thin layer of Nb. The advantage of this technique is that the good thermal conductivity of copper will

**Fig. 8.25** Longitudinal section of LHC 400 MHz cryostat containing 4 single-cell cavities

rapidly equalize the temperature distribution if local heating occurs caused by a surface defect or an impurity; this retards the onset of a quench significantly and thus reduces the sensitivity to impurities. Due to the significant cost of niobium, this technique can also be very cost effective. The maximum accelerating fields however are still in the order of 10 MV/m today, well below what has been obtained with bulk Niobium cavities, which makes this technology less attractive for linacs, but very attractive for large synchrotrons.

The LHC 400 MHz cavities [41], sketched in Fig. 8.25 in a longitudinal section, are fabricated using this technique. One cryostat contains 4 individual cavities, each equipped with its helium tank, tuner, HOM dampers and variable power coupler. A total of 16 cavities (4 cryostats) are installed in LHC, 8 for each beam. They are operated at the relatively modest accelerating gradient of 5.5 MV/m resulting in a total accelerating voltage of 2 MV per cavity or 16 MV per beam.

# *8.2.8 RF Cavities for Special Applications*

The use of RF cavities is not limited to particle acceleration in the direction of their motion. Cavities with longitudinal fields are also used for bunching, de-bunching and deceleration. Radio frequency quadrupoles (RFQ's), for example, serve at the same time transverse focussing, bunching and acceleration in a very effective way; most modern ion injectors make use of RFQ's.

Three examples for deceleration shall be mentioned here: antiprotons are decelerated for example in the CERN AD facility to enable studies of antiprotons at rest or for the creation of antimatter. Decelerating cavities knows as PETS (for Power Extraction and Transfer Structure) are used to slow down the CLIC drive beam in order to extract its kinetic energy as high frequency electromagnetic energy (12 GHz in the case of CLIC), which allows to use the drive beam as a high efficiency, high power microwave source [42]. And finally in energy recovery linacs (ERLs), one and the same cavity is used for both acceleration and deceleration to recover the beam energy (Sect. 7.9).

# *8.2.9 Deflecting Cavities: Crab Cavities*

Another class of RF cavities employ the transverse, not the longitudinal component of the force to kick particles sideways. If a beam bunched at a frequency *f* travels through a deflecting cavity oscillating at a frequency *f* /2, every even bunch will be kicked in one direction, every odd bunched in the other. This can be used to separate the beam in two beams bunched at half the frequency. It can equally be used to combine two beams, interleaving the bunches and thus creating one beam with twice the current and bunched at double the frequency. This scheme is a basic building block of the drive beam recombination scheme in CLIC (see Sect. 7.4.3 above) and has been thoroughly tested in the CTF3 facility.

Probably the most important application of deflecting cavities is their use as socalled *crab cavities*. In a high energy collider like the LHC, very small bunches of counter-running beams are colliding in the interaction points. The beams are normally not colliding exactly head on, but with a small crossing angle in order to minimize long-range beam-beam effects. Due to this non-vanishing crossing angle, only some particles of one bunch will collide with some particles of the oncoming bunch (see Fig. 8.26, top). If the head and the tail of the bunches are kicked sideways in opposite directions in the plane of the collision, the bunches become tilted after some drift—they start to move sideways like crabs. If this tilt is equal to half the crossing angle at the interaction point, the bunches are again oriented exactly as in a head-on collision and the geometrical loss of luminosity is compensated (Fig. 8.26, bottom).

The plan to upgrade the LHC to reach larger luminosity contains a number of important elements: In addition to increasing the bunch intensity by an upgrade of the LHC injector chain, stronger final focus magnets (the inner triplet) are planned with larger apertures. These will allow working with smaller beam sizes at collision and larger crossing angles. In order to take full advantage of this upgrade, crab cavities are essential [43]. An important additional feature of the operation with crab cavities is the possibility to change the crab cavity voltage during the coast to compensate for the loss of particles (luminosity levelling).

For the construction of crab cavities for the LHC, RF engineers were confronted with an additional difficulty resulting from the proximity of the two beam pipes, which in most of the machine are spaced by only 194 mm. Conventional, elliptically shaped RF cavities have a radius of roughly half a wavelength, which in the case of LHC is not consistent at a frequency of 400 MHz. A special straight section near point 4 is provided for the 400 MHz accelerating cavities described in Sect. 8.2.7 above, but it is desirable that the crab cavities are located upstream and downstream of the high luminosity collision points.

In a rigorous R&D program over recent years, a collaboration between CERN, FNAL, JLAB, BNL, LBNL and ODU in the US, the STFC in the UK, KEK in Japan and industry has successfully designed, prototyped, fabricated and tested crab cavities compact enough to meet the demanding LHC constraints and specifications. The "Double Quarter-Wave" (DQW) cavity was optimized for vertical crossing; its inside geometry is sketched in Fig. 8.27a, indicating also the location of the second beam pipe. The "RF Dipole" (RFD) cavity with similar topology but different coupling for both fundamental and higher-order modes, was optimized for horizontal crossing and is sketched in Fig. 8.27b. Both designs are needed since the LHC high-luminosity interaction points IP1 (ATLAS) and IP5 (CMS) utilize different crossing planes. Each cavity produces a transverse kick voltage in the order of 4 MV; two cavities will be assembled in one cryomodule. A total of 16 cavities (8 cryomodules) will initially be installed in the LHC, two per beam per side and per IP.

Figure 8.27c shows a cut-open view of a 2-cavity cryomodule (illustrated by means of the DQW cavities). The cavities are located in individual helium vessels and equipped with tuners, power couplers and HOM couplers. The cryomodules are equipped equally with thermal and magnetic shields. A large cryogenic line (2 K) connected to a cryogenic service box can be seen on the left. The fundamental mode couplers are connected to two 400 MHz waveguides on the top. The beam tube for the second LHC beam passes through the cryomodule. The cryomodule shown was

**Fig. 8.27** Conceptual cross section of the DQW crab cavity, indicating the crossing plane and the second beam tube (**a**). Conceptual cross section of the RFD crab cavity indicating the crossing plane and the HOM couplers (**b**). Cut-open view of the 2-cavity cryomodule equipped with DQW cavities (**c**)

built for the test of the LHC crab cavities in the SPS for full validation in 2018, but it is conceptually compatible with the LHC requirements.

# **8.3 Cryogenics**

Ph. Lebrun · L. Tavian

# *8.3.1 Introduction*

Cryogenics has become a key technology for particle accelerators, primarily as ancillary to the developing use of superconducting magnets and RF cavities [44, 45]. In this class of applications, the superconductor must operate at a fraction of its critical temperature in order to preserve current-carrying capability at high field (magnets) or to limit a.c. losses (RF cavities), thus imposing the use of helium in the case of low-temperature superconductors. Additional important benefits of operating the accelerator beam pipes at low temperature are the achievement of high vacuum through cryo-pumping of all residual gas species except helium, and the reduction of wall resistance which controls image-current losses and transverse impedance. Following pioneering work at the TeVatron and first large-scale applications (HERA, LEP2), accelerators at the energy frontier (RHIC, LHC) use superconducting magnets, while high-intensity proton accelerators (SNS, ESS) and high-energy electron linacs (European X-FEL, ILC) are based on superconducting RF cavities, all requiring large helium cryogenic systems. A recent example of such a system is sorely described in [46]. On a smaller scale, cryogenics is also at work cooling compact superconducting cyclotrons for radionuclide production or particle therapy, as well as compact synchrotron sources for X-ray lithography.

# *8.3.2 Cryogenic Fluids*

### **<IP_ADDRESS> Thermophysical Properties**

The simplest way of cooling equipment with a cryogenic fluid is to make use of its latent heat of vaporization, e.g. by immersion in a bath of boiling liquid. As a consequence, the useful temperature range of cryogenic fluids [47–49] is that in which there exists latent heat of vaporization, i.e. between the triple point and the critical point, with a particular interest in the normal boiling point, i.e. the saturation temperature at atmospheric pressure. This data are given in Table 8.8. In the following, we will concentrate on two cryogens: helium which is the only liquid at very low temperature and thus the coolant of low-temperature superconducting

**Table 8.8** Characteristic temperature [K] of cryogenic fluids

aλ point

**Table 8.9** Properties of helium and nitrogen compared to water

aAt normal boiling point

devices [50, 51], and nitrogen for its wide availability and ease of use for pre-cooling equipment and for thermal shielding.

To develop a feeling about properties of these cryogenic fluids, it is instructive to compare them with those of water (Table 8.9). In both cases, but particularly with helium, applications operate much closer to the critical point, i.e. in a domain where the difference between the liquid and vapour phases is much less marked: the ratio of liquid to vapour densities and the latent heat associated with the change of phase are much smaller. Due to the low values of its critical pressure and temperature, helium can also be used as a cryogenic coolant beyond the critical point, in the supercritical state. It is also interesting to note that, while liquid nitrogen resembles water as concerns density and viscosity, liquid helium is much lighter and less viscous. This latter property makes it a medium of choice for permeating small channels inside magnet windings and thus stabilizing the superconductor.

### **<IP_ADDRESS> Liquid Boil-off**

The factor of ten in latent heat of vaporization between helium and nitrogen, combined with the lower density of the former, induces a large difference in vaporization rates under the same applied heat load (Table 8.10). This illustrates the need for implementing much better insulation techniques in liquid helium vessels to achieve comparable holding times. Vaporization flow measurements during steady-

state boil-off constitute a practical method for assessing the heat load of a cryostat holding a saturated cryogen bath.

### **<IP_ADDRESS> Cryogen Usage for Equipment Cooldown**

For both fluids, the specific heat of the vapour over the temperature range from liquid saturation to ambient is comparable to or larger than the latent heat of vaporization. This provides a valuable cooling potential at intermediate temperature, which can be used for thermal shielding or for pre-cooling of equipment from room temperature. The heat balance equation for cooling a mass of, say iron *m*Fe of specific heat *C*Fe(*T*) at temperature *T* by vaporizing a mass d*m* of cryogenic liquid at saturation temperature *Tv*, latent heat of vaporization *Lv* and vapour specific heat *Cp* (taken as constant), is assuming perfect heat exchange with the liquid and the vapour:

$$\operatorname{Im}\_{\text{Fe}}\mathcal{C}\_{\text{Fe}}(T)\mathbf{d}T = \left[L\_v + C\_p\left(T - T\_v\right)\right]\mathbf{d}m.\tag{8.21}$$

Hence the specific liquid cryogen requirement for cool-down from temperature *T*0:

$$\frac{m}{m\_{\rm Fe}} = \int\_{-T\_0}^{T} \frac{C\_{Fe}(T) \mathrm{d}T}{L\_v + C\_p \left(T - T\_v\right)}.\tag{8.22}$$

Calculated values of specific liquid cryogen requirements for iron are given in Table 8.11, clearly demonstrating the interest of making use of the specific heat of helium vapour, as well as that of pre-cooling equipment with liquid nitrogen.

### **<IP_ADDRESS> Phase Domain**

Typical operating domains with cryogenic helium and nitrogen are shown in Figs. 8.28 and 8.29, superimposed on the phase diagrams of the substances. While

Using Latent heat only Latent heat and specific heat of vapour Liquid helium from 290 K to 4.2 K 29*.*5 0.75 Liquid helium from 77 K to 4.2 K 1*.*46 0.12 Liquid nitrogen from 290 K to 77 K 0*.*45 0.29

**Table 8.11** Volume [l] of liquid cryogens required to cool down 1 kg of iron

nitrogen shows a classical phase diagram, that of helium shows several peculiarities. The solid phase of helium only exists under pressure and the normal liquid He I undergoes below 2.2 K a transition to another liquid phase, He II, instead of solidifying. There is no latent heat associated with this phase transition, but a peak in the specific heat, the shape of which gave the name "λ-line" to the phase boundary. He II exhibits superfluidity, a macroscopic quantum behaviour entailing very high thermal conductivity and very low viscosity which make it a coolant of choice for advanced superconducting devices [52, 53]. Besides the thermodynamic penalty of lower temperature, the use of He II imposes that at least part of the cryogenic circuits operate at sub-atmospheric pressure, thus requiring efficient compression of lowpressure vapour and creating risks of dielectric breakdown and contamination by air in-leaks.

While saturated He I provides fixed (saturation) temperature and high boiling heat transfer at moderate heat flux, it may develop instabilities in two-phase flow and is prone to boiling crisis above the peak nucleate boiling flux (about 1 W/cm2). The use of mono-phase supercritical helium in forced-flow systems avoids the problems of two-phase flow. However, the strongly varying properties of the fluid in the vicinity of the critical point may create other issues, such as density wave oscillations. More fundamentally, supercritical helium exhibits no latent heat, so that applied heat loads result in temperature increases which must be contained by high flow-rate or periodic re-cooling in extended systems.

# *8.3.3 Materials at Low Temperatures*

Designing and building cryogenic apparatus require good knowledge of material properties at low temperatures [54–56], some of which may vary by orders of magnitude between ambient and cryogenic conditions, or even exhibit discontinuous behaviour. Of particular concern is the ductile-to-brittle transition undergone by metals and alloys of body-centered cubic and to a lesser extent, hexagonal close-packed structures: these materials should always be used above their ductileto-brittle transition temperature.

Thermal contraction, shown in Fig. 8.30 for selected materials, range from very low to a few per mille (metals and alloys) up to a few percent (polymers). For practical purposes, it is important to note that most of the contraction occurs between ambient and 80 K.

Specific heat of materials always shows a marked drop at low temperatures, asymptotic to zero as one approaches absolute zero (Fig. 8.31). Solid state physics describes specific heat as the sum of several terms due to the contributions from:

Specific heat of compounds can be approximately predicted by the Kopp-Neumann additivity principle: the molar heat capacity of a compound is equal to the sum of the atomic heat capacities of its constituents. To be noted that, at liquid helium temperature, the specific heat of the fluid is several orders of magnitude higher than that of solid materials.

The thermal conductivity of technical materials spans across several orders of magnitude, from high-purity metals down to insulators (Fig. 8.32). The bulk thermal conductivity results from two basic mechanisms, namely:

It must be noted that, for pure metals, low temperature thermal conductivity is strongly influenced by the impurity level and microstructure (e.g. cold work).

Electrical resistivity at low temperatures is a most interesting property both for engineering applications, assessment of material purity and microstructure, and understanding of its solid-state physics. Low temperature resistivity spans across several orders of magnitude, depending upon the type of material, degree of alloying and purity (Fig. 8.33). In all cases, the decrease of electrical resistivity upon cooldown shows a plateau, corresponding to a residual value *ρ*0. Matthiessen's rule expresses total resistivity *ρ*(*T*) as the sum of two terms,

$$
\rho(T) = \rho\_0 + \rho\_l(T), \tag{8.23}
$$

where *ρ*0 is the residual resistivity due to electron scattering by impurities and lattice imperfections, and *ρi*(*T*) is the intrinsic resistivity due to electron scattering by phonons, strongly temperature dependent.

A convenient way to characterize a pure metal or dilute alloy is to measure its residual resistivity ratio *RRR*:

$$RRR = \rho \left( 273 \text{ K} \right) / \rho \left( 4 \text{ K} \right) . \tag{8.24}$$

### **Fig. 8.33** Electrical resistivity of selected materials at low temperature

# *8.3.4 Heat Transfer and Thermal Design*

With the exception of superfluid helium, the heat transfer processes at work in cryogenics are basically the same as for any engineering temperature range. The strong variation of thermal properties of materials and fluids at low temperature however has two consequences: the relative and absolute magnitudes of the processes may be very different from those at room temperature, and the equations become nonlinear, thus requiring numerical integration. Cryogenic thermal design is the art of using these processes adequately, either for achieving thermal insulation (cryostats, transfer lines) or for improving thermal coupling between equipment and coolant (cool-down & warm-up, thermal stabilization, thermometry) [57, 58]. The diversity and complexity of convection processes cannot be treated here. Fortunately, in the majority of cases, the correlations established for fluids at higher temperature are fully applicable to the cryogenic domain [59], and reference is made to the abundant technical literature on the subject.

### **<IP_ADDRESS> Solid Conduction**

Heat conduction in solids is represented by Fourier's law, expressing proportionality of heat flux with thermal gradient

$$\mathcal{Q} = k(T)\mathcal{S}\mathbf{d}T/\mathbf{dx}.\tag{8.25}$$

This equation also defines the thermal conductivity *k*(*T*) of the material, which varies with temperature. Conduction along a solid rod of length *L*, cross section *S* spanning a temperature range [*T*1, *T*2], e.g. the support strut of a cryogenic vessel, is then given by the integral form

$$\mathcal{Q} = \frac{\mathcal{S}}{L} \int\_{-T\_1}^{T\_2} k(T) \mathrm{d}T,\tag{8.26}$$

where *T*2 *T*1 *k(T )*d*T* is called the thermal conductivity integral.

Thermal conductivity integrals of standard materials are tabulated in the literature [54]. A few examples are given in Table 8.12, showing the large differences between good and bad thermal conducting materials, the strong decrease of conductivity at low temperatures, particularly for pure metals, and the interest of thermal interception to reduce conductive heat in-leak in supports. As an example, the thermal conductivity integral of austenitic stainless steel from 80 K to vanishingly low temperature is nine times smaller than from 290 K, hence the benefit of providing a liquid nitrogen cooled heat sink on the supports of a liquid helium vessel.

### **<IP_ADDRESS> Radiation**

Blackbody radiation strongly and only depends on the temperature of the emitting body, with the maximum of the power spectrum given by Wien's law

$$
\lambda\_{\max} T = 2898 \text{ [}\mu\text{m}\text{- K]},\tag{8.27}
$$

**Table 8.12** Thermal conductivity integrals [W/m] of selected materials

and the total power radiated by an surface area *A* given by Stefan-Boltzmann's law

$$
\mathcal{Q} = \sigma \, A \, T^4,\tag{8.28}
$$

with Stefan-Boltzmann's constant *σ* 5.67 10−8 W m−2 K−4. The dependence of the radiative heat flux on the fourth power of temperature makes a strong plea for radiation shielding of low-temperature vessels with one or several shields cooled by liquid nitrogen or cold helium vapour. Technical radiating surfaces are usually described as "gray" bodies, characterized by an emissivity *ε* smaller than 1:

$$
\mathcal{Q} = \varepsilon \,\,\sigma \,\, A \,\, T^4 \,\,. \tag{8.29}
$$

The emissivity *ε* strictly depends on the material, surface finish, radiation wavelength and angle of incidence. For materials of technical interest, measured average values are found in the literature [60], a subset of which is given in Table 8.13. As a general rule, emissivity decreases at low temperature, for good electrical conductors and for polished surfaces. As Table 8.13 shows, a simple way to obtain this combination of properties is to wrap cold equipment with aluminium foil. Conversely, radiative thermal coupling requires emissivity as close as possible to that of a blackbody, which can be achieved in practice by special paint or adequate surface treatment, e.g. anodizing of aluminium.

The net heat flux between two "gray" surfaces at temperature *T*1 and *T*2 is similarly given by

$$\mathcal{Q} = E \,\sigma \, A \left( T\_2^{\,4} - T\_1^{\,4} \right), \tag{8.30}$$

with the emissivity factor *E* being a function of the emissivities *ε*1 and *ε*2 of the surfaces, of the geometrical configuration and of the type of reflection (specular or

Radiation from 290 K, surface at 77 K Radiation from 77 K, surface at 4.2 K Stainless steel, as found 0.34 0.12 Stainless steel, mechanically polished 0.12 0.07 Stainless steel, electro-polished 0.10 0.07 Stainless steel + aluminium foil 0.05 0.01 Aluminium, black anodized 0.95 0.75 Aluminium, as found 0.12 0.07 Aluminium, mechanically polished 0.10 0.06 Aluminium, electro-polished 0.08 0.04 Copper, as found 0.12 0.06 Copper, mechanically polished 0.06 0.02

**Table 8.13** Emissivity of some technical materials at low temperature

diffuse) between the surfaces. Its precise determination can be quite tedious, apart from the few simple geometrical cases of flat plates, nested cylinders and nested spheres.

### **<IP_ADDRESS> Gas Conduction**

Since J. Dewar's invention (1898) of the cryogenic vessel which bears his name, evacuated envelopes provide the best insulation against heat transport in gaseous media. At low pressure, convection becomes negligible and only residual gas conduction is at work. This process operates in two distinct regimes, depending upon the value of the mean free path of gas molecules relative to the typical distance *d* between the cold and warm surfaces.

The mean free path of gas molecules, as predicted by kinetic theory, scales with the square root of temperature and inversely with pressure and the square root of molar mass. It therefore becomes large at low pressure, high temperature and for light gas species.

When is much less than *d* corresponding to higher pressure, the probability of interaction of a given molecule with others before it travels distance *d* is high (viscous regime), and heat diffuses as in any continuous medium:

$$
\mathcal{Q} = k(T) A \text{d}T/\text{d}x.\tag{8.31}
$$

Note that the thermal conductivity *k*(*T*) of the gas is independent of pressure.

When is much greater than *d* at low pressure, the molecular regime prevails and the heat transfer between two surfaces at temperatures *T*1 and *T*2 is given by Kennard's law:

$$\mathcal{Q} = A \,\, \alpha(T) \,\, \Omega \,\, P \,\, \left(T\_2 - T\_1\right),\tag{8.32}$$

where *Ω* is a parameter depending upon the gas species, and *α* is the "accommodation coefficient" representing the thermalization of molecules on the surfaces; its value depends on *T*1, *T*2, the gas species and the geometry of the facing surfaces. Note that the conductive heat flux in molecular regime is proportional to pressure *P* and independent of the spacing between the surfaces (and therefore not amenable to the concept of thermal conductivity). Typical values of heat flux by gas conduction at cryogenic temperature are given in Table 8.14.

### **<IP_ADDRESS> Multilayer Insulation**

Multi-layer insulation (MLI) is based on *n* multiple reflecting shields wrapped around the cryogenic piece of equipment to be insulated, with the aim of benefiting from the *n* + 1 reduction factor in radiative heat in-leak. In practice, this is implemented in the form of aluminium or aluminized polymer films, with low

packing density achieved by crinkling or by insertion of a net-type spacer between layers. The wrapping can be made by winding the layers and spacer in situ, or by pre-fabricated blankets installed and held in place by insulating fasteners.

In all cases, MLI is a complex thermal system, involving the combination of radiation, solid-contact conduction, and residual-gas conduction between layers. As a result, increasing the number of layers, while beneficial for cutting radiation, usually results in increased packing with more contacts and trapped residual gas between layers, two effects which increase heat transfer. In view of the nonlinearity of these elementary processes, thermal optimization requires layer-to-layer modelling and efficient control of the critical parameters. In practice, performance is measured on test samples and measured data is available from an abundant literature. Typical values for some practical MLI systems are given in Table 8.14.

Of particular interest is the case of operation in degraded vacuum, where the heat in-leak by molecular conduction is directly proportional to the residual pressure. The presence of a multilayer system which segments the insulation space into many cells thermally in series, significantly contains the increase in heat in-leak to the lowtemperature surface (Table 8.14). In this respect, the multilayer system is no longer used for its radiative properties, but for the reduction of molecular gas conduction. In the extreme case of complete loss of vacuum in a liquid helium vessel, MLI also efficiently limits the heat flux which would otherwise become very high due to condensation of air on the cold wall, thus alleviating the requirements for emergency discharge systems.

### **<IP_ADDRESS> Vapour-Cooling of Necks and Supports**

The enthalpy of cryogen vapour escaping from a liquid bath can be used to continuously intercept conduction heat along solid supports and necks connecting the cryogenic bath with the room temperature environment (Fig. 8.34).

Assuming perfect heat exchange between the escaping vapour and the solid, the energy balance equation reads

$$k(T)\text{Sdf}/\text{dx} = \mathcal{Q}\_{\text{U}} + \dot{m}\,\,\mathcal{C}\_{P}(T)\,\,(T - T\_{\text{U}})\,,\tag{8.33}$$

where *Qv* is the heat reaching the liquid bath and *m*˙ is the vapour mass flow-rate. In the particular case of self-sustained vapour cooling, i.e. when the vapour mass flow-rate *m*˙ precisely equals the boil-off from the liquid bath,

$$\mathcal{Q}\_v = L\_v \,\,\dot{m} \tag{8.34}$$

Combining Eqs. (8.32) and (8.33) and integrating yields the value of *Qv*

$$\mathcal{Q}\_{v} = \frac{S}{L} \int\_{-T\_{v}}^{T\_{0}} \frac{k(T)}{1 + (T - T\_{v})\frac{C\_{\rho}}{L\_{v}}} \mathrm{d}T \tag{8.35}$$

The denominator of the integrand clearly acts as an attenuation term for the conduction integral. Numerical results for helium and a few materials of technical interest appear in Table 8.15. If properly used, the cooling power of the vapour brings an attenuation of one to two orders of magnitude in the conductive heat inleak.

Vapour cooling can also be used for continuous interception of other heat loads than solid conduction. In cryogenic storage and transport vessels with vapour-cooled shields, it lowers shield temperature and thus reduces radiative heat in-leak to the

**Table 8.15** Heat conduction attenuation between 290 K and 4 K by self-sustained helium cooling

liquid bath. In vapour-cooled current leads, a large fraction of the resistive power dissipation by Joule heating is taken by the vapour flow, in order to minimize the residual heat reaching the liquid bath [61, 62].

Worked-out example of how these diverse thermal insulation techniques are implemented in real designs are given in [63–65].

# *8.3.5 Refrigeration and Liquefaction*

Refrigeration and liquefaction of gases are historically at the root of cryogenics, as they constitute the enabling technology which gave access to the low-temperature domain. They have developed over the years along several lines, to become a specialized subject which would deserve a thorough presentation. In the following, we shall briefly describe the basic thermodynamics, the cooling processes at work and the corresponding equipment in the case of helium. For more complete reviews, see [66, 67].

### **<IP_ADDRESS> Thermodynamics of Refrigeration**

A refrigerator is a machine raising heat *Qi* from a low-temperature source *Ti* to a higher-temperature sink (usually room temperature) *T*0, by absorbing mechanical work *Wi*; doing so, it rejects heat *Q*0 (see Fig. 8.35). These quantities are related through the application of the first (Joule) and second (Clausius) principles of thermodynamics:

$$
\mathcal{Q}\_0 = \mathcal{Q}\_l + W\_l,\tag{8.36}
$$

$$
\mathcal{Q}\_0/T\_0 \ge \mathcal{Q}\_l/T\_l.\tag{8.37}
$$

In Eq. (8.36), the equality applies to the case of a reversible process. From the above

$$W\_l \ge T\_0 Q\_l / T\_l - Q\_l. \tag{8.38}$$

This expression can be written in three different ways. Introducing the reversible entropy variation *ΔSi* = *Qi*/*Ti*:

$$W\_l \ge T\_0 \Delta S\_l - \mathcal{Q}\_l.\tag{8.39}$$

Another form isolates the group *Qi*(*T*0/*Ti* − 1) as the proportionality factor between *Qi* and *Wi*, i.e. the minimum specific refrigeration work,

$$W\_l \ge \mathcal{Q}\_l \left( T\_0 / T\_l - 1 \right). \tag{8.40}$$

As Carnot has shown in 1824 [68], the minimum work can only be achieved through a cycle constituted of two isothermal and two adiabatic transforms (Carnot cycle). All other thermodynamic cycles entail higher refrigeration work for the same refrigeration duty.

A third form of Eq. (8.37) is

$$W\_l \ge \Delta E\_l.\tag{8.41}$$

This introduces the variation of "exergy" *ΔEi* = *Qi*(*T*0/*Ti* − 1), a thermodynamic function representing the maximum mechanical work content (Gouy's "énergie utilisable") of a heat quantity *Qi* at temperature *Ti*, given an environment at temperature *T*0 [69].

Equation (8.39) enables to calculate the minimum mechanical power needed to extract 1 W at 4.5 K (saturated liquid helium temperature at 1.3 bar pressure, i.e. slightly above atmospheric) and reject it at 300 K (room temperature), yielding a value of 65.7 W. This is the power that would be absorbed by a refrigerator operating on a Carnot cycle between 4.5 K and 300 K. In practice, the best practical cryogenic helium refrigerators have an efficiency of about 30% with respect to a Carnot refrigerator, hence a specific refrigeration work of about 220 W/W.

Cryogenic refrigerators are often required to provide cooling duties at several temperatures or in several temperature ranges, e.g. for thermal shields or continuous heat interception. Equation (8.39) can then be applied to the cooling duty at every temperature and every elementary mechanical power *Wi* summed or integrated in the case of continuous cooling. This also allows comparison of different cooling duties in terms of required mechanical work.

### **<IP_ADDRESS> Helium Refrigerators vs. Liquefiers**

A 4.5 K helium refrigerator absorbs heat isothermally at this temperature, by recondensing the cold helium vaporized at saturation (saturation pressure 1.3 bar). A liquefier also eventually condenses cold helium vapour at saturation, but starting from gaseous helium at 300 K which it must first pre-cool to 4.5 K (Fig. 8.36). From

**Fig. 8.36** A helium refrigerator (**a**) performs the duty by condensing cold helium vapour (red area). A helium liquefier (**b**) additionally needs to precool helium gas from room temperature (green area)

Eq. (8.38), the minimum mechanical power *W*liq for helium liquefaction is:

$$W\_{\rm liq} = W\_{\rm condens} + W\_{\rm precool},\tag{8.42}$$

$$W\_{\rm liq} = T\_0 \Delta S\_{\rm condens} - Q\_{\rm condensates} + T\_0 \Delta S\_{\rm precool} - Q\_{\rm precool}.\tag{8.43}$$

The heat quantities *Q*condens and *Q*precool exchanged at constant pressure are by definition—equal to the enthalpy variations *H*condens and *H*precool. With *T*0 = 300 K and the entropy and enthalpy differences taken from thermodynamic tables, one finds *W*liq = 6628 W per g/s of helium liquefied. Given the minimum specific mechanical work of 65.7 at 4.5 K, this yields an approximate equivalence of about 100 W at 4.5 K for 1 g/s liquefaction. More precisely, a liquefier producing 1 g/s liquid helium at 4.5 K will absorb the same power (and thus have similar size) as a refrigerator extracting about 100 W at 4.5 K, provided they both have the same efficiency with respect to the Carnot cycle. For machines with mixed refrigeration and liquefaction duties, this equivalence can be approximately verified by trading some liquefaction against refrigeration around the design point and *vice versa*. An example is given in reference [70].

### **<IP_ADDRESS> Real Cycles and Refrigeration Equipment**

So far we have only addressed cryogenic refrigeration and liquefaction through thermodynamics, i.e. through the exchanges of mass, heat and work at the boundaries of machines seen as "black boxes". We will now consider cycles, cooling methods and equipment of real refrigerators.

In order to minimize the specific mechanical work requirement (and hence the size and power consumption), an efficient refrigerator should try to approximate the Carnot cycle, which is represented by a rectangle on the temperature-entropy diagram: the two isotherms are horizontal lines, while the two isentropic transforms are vertical lines. To liquefy helium, the base of the rectangle should intercept the liquid-vapour dome (Fig. 8.37).

However, superimposing this cycle on the temperature-entropy diagram of helium shows that one should operate at a high pressure of about 613 kbar (!), with a first isentropic compression from 1.3 bar to 82 kbar (!), followed by an isothermal compression. This is clearly impractical, and real helium cycles are elongated along isobar (or isochoric) lines, thus involving transforms which require heat exchange between the high- and low-pressure streams. This heat exchange can be performed in recuperative or regenerative heat exchangers, respectively for continuous or alternating flows. In the following, we focus on the continuous-flow cycles using recuperative heat exchangers which constitute the operating principles of large-capacity helium refrigerators and liquefiers.

Practical elementary cooling processes are shown on the temperature-entropy diagram in Fig. 8.38. Apart from the quasi-isobar cooling of the gas stream in a heat exchanger (segment AB1), refrigeration can be produced by adiabatic (paraisentropic) expansion with extraction of mechanical work, usually in a gas turbine (segment AB2 ), and isenthalpic Joule-Thomson expansion in a valve or restriction (segment AB3).

This latter process does not produce any cooling for ideal gases, the enthalpy of which is a sole function of temperature. For real gases, however, enthalpy depends both on temperature and pressure, so that isenthalpic expansion can produce warming or cooling, depending upon the slope of the isenthalps on the diagram in the region of interest. In order to cool the gas stream, Joule-Thomson expansion must start below a limit called the inversion temperature. The values of inversion temperature for cryogenic fluids (Table 8.16) show that while air can be cooled from room temperature by Joule-Thomson expansion (the risk of freezing the pressure reducer on the air bottle is well known to scuba divers), helium must first be precooled down to below its inversion temperature of 43 K. The moderate downward slope of isenthalps on the temperature-entropy diagram indicates that in any case, Joule-Thomson expansion generates substantial entropy. Its relative inefficiency with respect to adiabatic expansion is however accepted in view of the simplicity of its implementation, particularly when it results in partial condensation of the

**Fig. 8.39** Schematic example of two-pressure, two-stage Claude cycle: flow scheme (left) and T-S diagram (right)

stream entailing two-phase flow conditions which would be difficult to handle in an expansion turbine.

These elementary cooling processes are combined in practical cycles, a common example for helium refrigeration is provided by the Claude cycle and its refinements. A schematic two-pressure, two-stage Claude cycle is shown in Fig. 8.39: gaseous helium, compressed to high pressure (HP) in a lubricated screw compressor, is recooled to room temperature in water-coolers, dried and purified from oil aerosols down to the ppm level, before being sent to the HP side of the heat exchange line (HX1 to HX5) where it is refrigerated by heat exchange with the counter-flow of cold gas returning on the low pressure (LP) side. Part of the flow is tapped from the HP line and expanded in the turbines before escaping to the LP line. At the bottom of the heat exchange line, the remaining HP flow is expanded in a Joule-Thomson valve and partially liquefied.

Large-capacity helium refrigerators and liquefiers operate under this principle, however with many refinements aiming at meeting specific cooling duties and improving efficiency and flexibility of operation, such as three- and sometimes four-pressure cycles, liquid nitrogen pre-cooling of the helium stream, numerous heat exchangers, many turbines in series or parallel arrangements, Joule-Thomson expansion replaced by adiabatic expansion in a "wet" turbine, cold compressors to lower the refrigeration temperature below 4.5 K.

The capital cost of these complex machines is high, but scales less than linearly with refrigeration power, which favours large units. Operating costs are dominated by that of electrical energy, typically amounting to about ten percent of the capital cost per year in case of quasi-continuous operation. For overall economy, it is therefore very important to seek high efficiency, which is also easier to achieve on large units. For a review of these aspects, see [70].

# **8.4 High Precision Power Converters for Particle Accelerators**

F. Bordry · J. P. Burnet · M. Cerqueira Bastos

# *8.4.1 Introduction to Magnet Power Converters*

The trend in power electronics is evolving rapidly, mainly due to progress in power semiconductors. Since the nineties, the IGBT (Insulated Gate Bipolar Transistor) took the leadership in medium and large power, with the development of new converter topologies called switch-mode power converters [71, 72]. With the progress of electronics (analogue and digital) and measurement systems, the performance of the power converters made a step forward in precision and stability. This chapter will give an overview of the state of the art for high precision power converters for particle accelerators (conventional and superconducting magnet, RF klystrons, solenoids, *...*).

# *8.4.2 Main Parameters of Magnet Power Converters*

The powering of particle accelerator magnets are mainly DC power converters and in most cases, the feedback control system regulates the magnet current. The choice of the power converter topology and thus the technology will be defined by the required performance, translated into a precise specification. First of all, the peak and the rms ratings of the current and voltage to power the magnet should be

**Fig. 8.40** Definition of the 4-quadrant operation

defined. Then, the operation in different quadrants has to be identified: shall the power converter be bipolar in current and/or in voltage? Shall the power converter operate as a generator and/or as a receptor? Figure 8.40 defines the 4-quadrants of operation of a power converter.

In quadrant 1 and 3, the power converter operates as a generator. In quadrant 2 and 4, the power converter operates as a receptor. In this mode, the magnet is giving back its stored energy during the ramping down of the current. The power converter can dissipate this energy, give it back to the mains, or store it locally making it available for the next cycle. The power converters can be classified in 3 categories: one-quadrant power converter; unipolar in current and voltage, twoquadrant power converter; unipolar in current but bipolar in voltage, and 4-quadrant power converter; bipolar in current and voltage.

The power converter can be controlled with different strategies: steady DC current control, variable current reference, or pulsed current.

Another important parameter for the design of the power converters is the voltage and current ripple. The power converter topology and the performance of the inner control loops define the voltage ripple. The current ripple is defined by the load transfer function (cables, magnet inductance *...*). To get good current ripple estimation, a good identification of the converter load is required.

To identify the optimal topology of the power converter, a complete list of parameters has to be reviewed between the accelerator physicists, the magnet designers and the power converter designers.

# *8.4.3 Power Converter Topologies*

Three main families of power converters are used for particle accelerators: Thyristor-controlled rectifier, switch-mode power converter and discharged power converter. Each type will be described in the following paragraphs.

### **<IP_ADDRESS> Thyristor Controlled Rectifier**

The thyristor-controlled rectifier was the main topology used from the seventies up to the nineties. Many different topologies can be implemented with thyristor devices, but only the three main types will be described here. First, the simplest one is the 6-pulse thyristor rectifier with freewheeling diode, see Fig. 8.41.

The topology includes a transformer, a 6-pulse thyristor bridge with a freewheeling diode and an output filter. The output voltage is controlled by the firing angle of the thyristor bridge. Due to the free-wheeling diode, the output voltage can only be positive, as well as the current. This topology is a one quadrant power converter. Second, the most used is the 12-pulse rectifier. This topology includes a transformer with two secondaries with a phase shift of ±15◦, two 6-pulse thyristor bridges connected in series, and an output filter, see Fig. 8.42.

This topology allows positive and negative output voltages, but imposes a minimum current to control the thyristors. The first harmonic of the output voltage is 600 Hz which helps to reduce the current ripple compared to the previous topology. When the voltage is negative, the energy is given back to the grid. It is a twoquadrant power converter.

Last, a back to back thyristor rectifier is shown as an example of 4-quadrant power converter. In this case, two 6-pulse rectifiers are connected back to back, see Fig. 8.43.

**Fig. 8.43** Back-to-back thyristor rectifier with circulating current

This topology requires placing inductors between the rectifiers to limit the circulating current which is necessary to control the thyristor rectifiers. In this case, the current can be positive and negative in the load as well as the voltage.

Thyristor devices are known to be robust, with low losses, and easy to drive. The main drawbacks of this type of power converters are their high susceptibility to perturbations from the grid, they generate reactive power on the grid, and they have a slow dynamic response. It also requires 50Hz transformers which can be bulky. Nevertheless, this type of power converter is widely used for particle accelerators. It was for example, the main type for the LEP accelerator. Nowadays, the thyristor controlled rectifiers are mainly used for high power converters (above 500 kW) which requires very often a reactive power compensator on the grid.

### **<IP_ADDRESS> Switch-Mode Power Converter**

Switch-mode power converters incorporate power semiconductors which switch quickly between full-on and full-off states. The voltage regulation is provided by varying the ratio of on, off time, which is called duty cycle. Pulse-Width Modulation is the most familiar technique used to control the duty cycle. The main advantages are a better efficiency and a smaller size due to the reduction of the magnetics component size, at the cost of a greater complexity. Many types of switch-mode power converters exist and are too numerous to be listed in this chapter. Two main types will be presented, first, a topology with a 50Hz transformer and second, a topology with a high frequency transformer.

### <IP_ADDRESS>.1 Switch-Mode Power Converter With 50 Hz Transformer

A transformer is always required to isolate the magnet from the grid. If the volume of the power converter is not an issue, 50 Hz transformers can be used as they are produced by industry for other applications at affordable prices. The most classical topology used for particle accelerators can be seen in Fig. 8.44. The 50 Hz transformer adapts the voltage for the rectifier, then an H-bridge comprising of IGBTs, control the voltage applied to the magnet. The switching frequency of the IGBT depends on the DC-link voltage and on the current to control. For power

**Fig. 8.44** Switch-mode power converter with 50 Hz transformer, connected to the grid at the left and connected to the magnet at the right

**Fig. 8.45** Switch-mode power converter with high frequency transformer

converters above 10 kW, the classical switching frequency is in the range of 1 kHz to 20 kHz.

The H-bridge topology allows 4-quadrant operation. When the magnet gives back its energy, the return energy can be dissipated in a brake chopper or stored in the capacitor bank of the DC-link. Another possibility is to replace the diode rectifier by an active front end provided by IGBTs. In this case, the energy is returned to the grid. The main advantage of this topology is the use of the IGBT semiconductors which are widely used and produced at reasonable cost. They can be easily controlled with PWM (pulse-width modulation) technique at a switching frequency above few kHz; this helps to reduce the current ripple and improve the feedback loop performance. The IGBT rating ranges from 600 V to 6.5 kV and from 50 A to 3 kA, allowing a large scale of the requirements to be met.

<IP_ADDRESS>.2 Switch-Mode Power Converter with High Frequency Transformer

One of the main interests of using a high frequency transformer is to reduce the volume of the power converters. Ferrite cores are widely produced which allow the use of high frequency transformers at a competitive price. A classical topology is shown in Fig. 8.45.

The diode bridge is directly connected to the grid. An inverter drives a high frequency transformer. A diode bridge is connected at the output of the secondaries of the transformer to obtain a DC voltage to apply to the magnet. This type of power converter operates only in one-quadrant mode. 4-quadrant operation can be obtained by adding another stage but the return energy has to be dissipated at this level (Fig. 8.46) [73].

Energy recovery to the grid can be achieved, but with a much more sophisticated topology which will not be described here [71]. The switching frequency of the

inverter is usually from 10 kHz to several 100 kHz. Due to the high frequency spectrum of the semiconductor's commutation, an important design constraint for the power converters is the EMC (Electro Magnetic compatibility) immunity and emission. Soft commutation of the inverter semiconductors is an elegant solution to reduce the switching losses and to improve the EMC. In the case of the CERN LHC, where power converters have to be installed underground with limited space, the switch-mode power converter was chosen for power converter up to 200 kW. In this case, many sub-converters have to be placed in parallel to reach this power level. The superconducting magnets require a high current (many kA) but few volts (less than 20 V); for this application, the solution was to drive many highfrequency transformers in series with one inverter. All the transformer secondaries are connected in parallel after the output filter, see Fig. 8.47.

To improve reliability by increasing redundancy, N+1 sub-converters are placed in parallel, where a sub-converter comprises one inverter with 8 transformers. In case of failure of one sub-converter, the other sub-converters compensate without any disturbance to the load. A modulator construction of the power converter can be done due to the high number of converters in parallel which eases the operation and maintenance of it.

For power converter below 1 kW, the preferred semiconductor is the MOSFET which has lower losses than the IGBT thereby allowing a higher switching frequency. Nevertheless, its voltage range is limited from 5 V to 500 V.

### **<IP_ADDRESS> Fast Pulsed Power Converter**

When the presence of the magnetic field in the magnet is required for a very short duration, discharged power converters are a very interesting technique to reduce power consumption. This is the case for example for beam transfer lines where

the beam can be present for few μs every second or minute. It is also the case for the Klystron Modulators in a Linac. An example of a discharged power converter topology is shown in Fig. 8.48.

In this case, a capacitor bank is charged to a nominal value (less than 15 kV) which can be low compared to the need of the load (from 60 kV to 140 kV). A main switch discharges the capacitor bank via a pulse transformer.

The voltage is applied to the load while the switch stays ON but generally for a short time (2.4 ms for LINAC4 at CERN), as the capacitor bank voltage decreases (few %), the droop voltage has to be compensated by a bouncer which is a passive resonant circuit. The main challenges are the design of the pulse transformer and of the main switch. In case of an arc in the Klystron, the energy deposit has to be limited to few joules (~20 J). This needs a fast turn OFF of the main switch. A redundancy policy has to be implemented to be sure to be able to open the circuit. For LINAC4, 4 IGCT (Integrated Gate-Commutated thyristor) are placed in series where only 3 are required.

### **<IP_ADDRESS> High Power System with Local Energy Storage**

For high power system (above 1 MW), Thyristor rectifiers are the preferred technology. The principal drawbacks are:

One example is the new POPS system [74] designed for the CERN PS accelerator, see Fig. 8.49.

The principle is to store energy in capacitor banks and to exchange this energy with the magnets during the cycles. As the rating power is very high (60 MW peak), many switch-mode power converters are associated in series and in parallel. Only the losses of the system (magnets and converters) are taken from the electrical network (5 MW peak). 20 MJ are stored in the capacitor banks where 14 MJ can be

**Fig. 8.49** Power system with capacitive energy storage

exchanged during each cycle with the magnets. A redundancy is also implemented; the system can operate without one capacitor bank or one DC/DC converter or one transformer. In this case, no reactive power is generated on the grid and the active power taken from the grid is reduced to the minimum. This new type of power system helps reduce the energy consumption of particle accelerators.

# *8.4.4 High Accuracy in Power Converters for Particle Accelerators*

Magnets in particle accelerators are powered by electrical power converters. These can be seen as controlled current sources in which a feedback loop ensures that the output current follows the reference to the best possible accuracy. The accuracy that can be achieved is greatly determined by the current measurement transducer and, in the case of digitally controlled power converters, the control algorithm and the ADC employed in the feedback loop.

As energies reached by particle accelerators become greater, accuracy requirements for the magnet current increase proportionally. Accuracy requirements depend also on the powering strategy chosen for the accelerator. In a synchrotron, the main dipole and quadrupole circuits are normally powered in series to ensure synchronism and homogeneity in the magnetic field around the circumference. However this is not always true: in the case of the LHC the main circuits are divided into eight sectors due to the very high stored magnetic energy and constraints in the protection of the superconducting magnets. As a consequence, individual sector currents must be controlled with very high absolute accuracy in amplitude and time [75] to ensure tracking between all sectors. Requirements for accuracy in current control are also determined by the type of magnet and its function: the need for accuracy in the current control for corrector magnets is much less stringent than for the main quadrupole and dipole magnets.

### **<IP_ADDRESS> Power Converter Control**

In the past, power converter control in accelerators was usually based on analogue feedback loops using PID (Proportional/Integral/Derivative) control. In such systems, the reference value at the input of the loop is often given by a DAC (Digital to Analogue Converter) and the output current of the power converter measured by a precision current transducer which provides the feedback signal for the control loop [76]. The accuracy achieved with such techniques is limited by errors due to drift, linearity and temperature dependency. Moreover, adjustment of control parameters can be cumbersome, as it might require trimming of potentiometers or replacement of components.

Developments in digital electronics and in particular DSPs, PLDs and Microcontrollers, as well as the need for increased performance in power converter applications fuelled significant progress in digital control during the last decades. The first applications using digital control in power converters for accelerators were implemented in the late 1980s [77]. Amongst the advantages of using digital control are increased stability and reproducibility, less susceptibility to noise and thermal effects, easy implementation of different control methods (state-space, robust, fuzzy) as well as easy loop parameterization. On the other hand, the use of digital control increases system complexity and introduces new sources of error such as the ones resulting from ADC measurement uncertainty and limited resolution on arithmetic calculations, which might lead to arithmetic errors.

When high accuracy is required, one effective power converter control strategy is to have an external current loop controlling a power supply that works as a voltage source. In a digitally controlled system, the output current of the converter is measured by a current transducer connected to an ADC and then compared with a digital reference. The error is fed into a digital regulator and the result sent to a DAC that provides an analogue signal to control the voltage source [77].

This solution is implemented in the control of the LHC power converters at CERN. In this case, the control challenge is even more demanding due to the 8 sector powering strategy used for the main dipole and quadrupole circuits. This powering strategy requires not only an accurate control of the current of each power converter but also an accurate generation and synchronization of the current references sent to the converters along the 27 km circumference of the LHC. For this purpose each power converter in the LHC has a dedicated controls electronics which is actually an embedded microcontroller-based computer capable of performing full local state control, reference function generation and measurement acquisition as well as running a digital current regulation loop. Reference functions are synchronized using a timing network. Each digital controller is connected to a field bus (WorldFIP) and the timing network is used to synchronise the cycles of all segments of the field bus. The digital controller disciplines a phase-locked loop to align its clock to the start of each WorldFIP cycle guaranteeing synchronism of the references along the machine.

The digital control strategy implemented in the LHC power converters is based on an R-S-T algorithm. The canonical structure of an RST controller is presented in Fig. 8.50 [78].

This structure has two degrees of freedom, i.e. the digital filters *R* and *S* are designed in order to achieve the desired regulation performance and the digital filter *T* is designed to achive the desired tracking performance. The structure can be described by the following discrete equation [79]:

$$\mathcal{S}\left(z^{-1}\right)u(t) + \mathcal{R}\left(z^{-1}\right)y(t) = T\left(z^{-1}\right)r(t),\tag{8.44}$$

where *u*(*t*) and *y*(*t*) are the input and output of the plant, *r*(*t*) the desired tracking trajectory, *R*, *S* and *T* are *z*−1 polynomials and *t* is the normalized discrete time.

The corresponding time domain expression is given by:

$$u(t) = -\sum\_{l=1}^{n\_S} S\_l u\left(t - i\right) - \sum\_{l=0}^{n\_R} R\_l \mathbf{y}\left(t - i\right) + \sum\_{l=0}^{n\_T} T\_l r\left(t - i\right) \text{[84]}\,. \tag{8.45}$$

The RST controller makes it possible to obtain the desired tracking behaviour (following the reference) independent of the desired regulation behaviour (rejection of a disturbance) [80].

The application of this control strategy to the LHC power converter control resulted in excellent performance. Recent results proved that the tracking error on

**Fig. 8.50** Canonical structure of a digital RST controller

the LHC main power converters is in the order of one ppm and that tracking between different sectors is within a couple of ppm [78].

### **<IP_ADDRESS> Current Measurement in Particle Accelerators**

Traditionally, accurate current measurement devices for particle accelerators are associated with beam current measurement. Magnetic transducers and in particular current transformers have been for a long time the preferred transducers to measure beam currents. The requirements for beam current measurement have driven progress in transducer technology, culminating with the introduction of the DCCT (Direct-Current Current Transformer) for beam current measurement at CERN in late 1960s. The idea was to build a magnetic beam current transformer with frequency response extended down to DC to measure beam current in the ISR accelerator. The new transducer combined the zero flux detection principle used in flux-gate magnetometers since the 1930s, with the active transformer circuit as originally proposed by H.G. Hereward (and already used to measure the circulating beam in the CERN PS accelerator) [81]. Although the new transducer was not initially intended for power supply regulation applications, its advantages compared with previous DC instrument transformers (e.g. Kramer and Hingorani [82]) soon became obvious. The concept got picked up by industry and the new transducer was soon being used at accelerators such as DESY in Hamburg. In late 1970s, DCCTs were used for the first time in large quantities in the SPS project at CERN [83].

The use of DCCTs spread to other applications but it continued to be widely used in particle accelerators. In particular, the beginning of the twenty-first century saw important progress in DCCT technology with the development and deployment of the DCCTs for the main dipole and quadrupole power supplies of the LHC, at CERN [84]. Short term stability in the order of two part-per-million (ppm), yearly drifts better than fifteen ppm and linearity better than two ppm have been achieved.

### <IP_ADDRESS>.1 Current Measurement Technologies

The most common current measurement technologies used in electrical power converters include resistive shunts and current sense resistors, Hall-Effect current transducers (based on the polarization of charges in an electrical conductor in the presence of an external magnetic field), Current Transformers, Rogowsky Coils (high current, high bandwidth applications), Active CTs and DCCTs (both based on the zero flux detection principle).

The choice of a current measuring device for a specific application depends on factors such as current range, bandwidth, required accuracy, required output signal, need for isolation, reliability, installation constraints, availability and cost. DCCTs provide isolated measurements for different current ranges and can reach very high accuracy, albeit with a higher cost.

### <IP_ADDRESS>.2 DCCTs (Direct-Current Current Transformers)

A DCCT is a magnetic current transducer of the zero-flux type where a second harmonic or a peak detector is used in a feedback loop to generate a compensation current which is a fractional image of the current being measured, keeping zero flux in the magnetic cores. The working principle of a DCCT is illustrated in more detail in Fig. 8.51: two DC flux sensing cores are modulated by an oscillator. The resulting current peaks are unequal if there is a DC flux in the cores (originated by the DC current being measured). A balanced peak detector circuit will detect any unbalance and give a non zero output when a DC flux is present. The output of the peak detector is combined with the AC component measured by a third core which works as a normal transformer. A control loop is set up to generate the secondary current that will bring the total DC flux back to zero [84].

The secondary current is therefore a fractional image of the primary current, and it can be fed into a precision burden resistor to get a measurable voltage signal. This signal is amplified by an output amplifier to produce a 0 *...* 10 V output.

DCCTs have the potential of reaching short term stability and repeatability in the order of a few part-per-million. This requires not only a careful design of the magnetic part (magnetic "head") as well as the use of high quality burden resistors and very stable precision amplifiers, usually in a temperature controlled environment.

A DCCT "head" used in the LHC is shown in Fig. 8.52.

The head design and in particular the magnetic shielding are important to increase the sensitivity to the primary magnetic field while minimising the sensitivity to external magnetic fields, head centring and return bus-bar fields. Soft magnetic materials and in particular amorphous and nanocrystalline alloys are the

**Fig. 8.51** The DCCT working principle

**Fig. 8.52** A 13 kA DCCT "head", used in the LHC

most commonly used in the DCCT core and inner shielding design because of their magnetic properties such as high initial permeability and low coercivity. As for the outer layer of the shielding, a doughnut-shaped shell containing the cores and the inner shielding, ferromagnetic materials of lower permeability and high saturation are normally used. During the last couple of decades, improvements in the manufacturing process of amorphous alloys contributed to their widespread use and to the development of new materials hence making for a greater availability of candidate materials for magnetic sensors. More recent developments include progress in reducing coercivity and increasing saturation induction of amorphous and nanocrystalline materials [85]. These new breakthroughs have still to find their application in DCCT head design.

The current output of the DCCT is usually connected to a burden resistor, a 2 terminal or 4-terminal resistor depending on the required accuracy. The performance of this component is one of the dominant factors in the overall accuracy of the transducer. Well known effects that can cause resistance change and therefore can affect the performance of DCCTs are temperature coefficient, self heating and thermal settling as well as ageing. Less well know effects include power coefficient, humidity absorption and hysteresis under power cycling. The highest accuracy available in DCCT burden resistors known at the moment is offered by a proprietary Zeranin wire design from PM special measuring systems, which is used in the LHC main dipole and quadrupole DCCTs, but its price limits its use only to the most critical DCCTs. Otherwise there is only one resistor type on the market offering the performance needed: Bulk Metal Foil or "foil". This technique, pioneered by Vishay, but now widely spread, tightly bonds a rolled metal foil to a substrate and seeks to compensate the resulting consistent stress effects as part of the overall resistor performance [86].

The voltage across the burden resistor normally needs to be amplified to produce a voltage output adequate for subsequent ADC conversion. This task is done by a precision amplifier, usually a difference amplifier circuit making use of high precision network ratio resistors to establish the gain. Presently, the consumer electronics market offers a range of choice in precision amplifiers, including low offset, low drift amplifiers that can be used as the output amplifiers in the DCCT. However, this does not exempt the designer from careful design and implementation of the output circuit. Parameters such as offset and gain stability, noise, common mode rejection and output impedance depend strongly on circuit design and implementation.

### <IP_ADDRESS>.3 ADCs (Analogue to Digital Converters)

With the advent of digital control, Analogue to Digital Converters have become essential components for ensuring the accuracy of the current measuring chain in the control loop of power converters. If in the past, most of the control was implemented using analogue electronics, in the last couple of decades digital control has almost completely taken over. The advantages of having a digital representation of the signal are numerous and not limited to power converter control: calibration, traditionally done by adjusting gain and offset potentiometers, is now performed using calibration constants which can be memorised and used to correct the output of the measuring device. If these constants are also kept in a database and updated whenever a calibration takes place, the task of following the behaviour of high precision devices becomes much simpler and less error prone. Another advantage is the possibility of using correction algorithms. A typical example is the use of a temperature sensor and a correction algorithm to correct for the temperature dependency of a measurement device.

ADC technology has significantly evolved in the last couple of decades fuelled mainly by the telecommunications industry. As a consequence, a wide range of solutions in AD conversion are available on the market with tradeoffs in resolution, speed and accuracy. In power converter control for accelerators, ADC speeds above the MHz are seldom required. As for resolution, requirements often range from 16 bits to 24 bits with accuracy following along. In this context Successive Approximation Register ADCs (SAR) have recently become of the most interesting technologies to follow as they are now competing with Delta Sigma ADCs and multi slope integrating ADCs in the high resolution, high accuracy segment. However, to reach effective resolution figures beyond 20 bits, they must operate in oversampling mode. Some ICs have built-in provisions for it, while for others it has to be implemented in external logic [87]. Therefore, Delta Sigma ADCs still remain the most commonly used solution in the segment. They do not require external components, their oversampled nature simplifies circuit design by relaxing the requirements of the analogue anti-aliasing filter and they are often simpler to drive than SARs. However, higher accuracy also requires more complex digital decimation filters which, for linear phase FIR filters, corresponds to increased latency. Filter latency limits the maximum loop bandwidth which means that high accuracy is normally associated with lower speed. The use of minimum phase FIR filters can substantially decrease latency.

**Fig. 8.53** The architecture of the Delta-Sigma Analogue to Digital converter used in the LHC main power converters

ADC accuracy depends greatly on the voltage reference employed. Precision external voltage references are preferred in applications demanding high accuracy as they have lower temperature coefficient, thermal hysteresis and long term drift than an on-chip voltage reference. High end Zener based high precision references usually use buried Zener technology. They can include internal temperature control or temperature compensation. However, for higher accuracy, they might need to be stabilised inside a temperature controlled oven. Reference annealing can also be used to accelerate the ageing process and reduce initial drift.

The main dipole and quadrupole power converters on the LHC use a Delta Sigma converter with a resolution of about 22 bits. The voltage reference is a buried zener type, previously submitted to a burn-in process for minimum drift. Sub-ppm accuracy is achieved albeit at very low sampling speeds (1 kHz) and in a temperature controlled environment.

Figure 8.53 shows the architecture of the Delta-Sigma Analogue to Digital converter used in the LHC [88].

### <IP_ADDRESS>.4 Calibration

There can be different motivations for calibration of measurement devices in accelerator applications. The first is the requirement to keep long term drift within specified limits. Another motivation is to minimise the impact of replacements. When an operational equipment is replaced by a spare, the impact on the accuracy of the power converter depends on the difference between the measurement errors of the two devices. This difference can be kept within specified limits by means of periodic calibration. Finally, calibration might be necessary to guarantee good tracking between different transducers. Such is the case in the LHC at CERN, where the main dipole and quadrupole circuits are divided into eight sectors. In this case, calibration of the current measurement chain using the same reference ensures that all sectors track each other, allowing the beam to circulate around the machine without "seeing" any difference in the magnetic field between sectors.

The periodicity of calibrations must be set according to the accuracy requirements of the power converter. Some devices include automatic calibration mechanisms: a common practice is to use a multiplexer that connects the ADC input to a voltage reference for calibration. However, the references themselves might need periodic calibration, so human intervention might be unavoidable.

Calibration procedures usually involve the use of dedicated equipment which must be previously characterised in a laboratory using well known reference devices. The complexity of the necessary calibration infrastructure depends on the accuracy one is trying to achieve. Some of the methods employed to calibrate DCCTs and ADCs and required calibration equipment are described below.

DCCTs can be calibrated through different methods:

The latter method requires a precision current source to generate the calibration current. At CERN, a programmable current reference has been developed for the calibration of DCCTs equipped with calibration windings [89]. It can produce DC currents ranging from −5 A to 5 A with sub-ppm accuracy. In the LHC, in-situ calibration systems equipped with these devices are installed close to the main power converters. They are housed in temperature controlled racks and can be remotely controlled via an ethernet connection in order to calibrate one or several DCCTs in the main dipole and quadrupole power converters.

The remotely controlled calibration system used in the LHC is depicted in Fig. 8.54.

In applications where a reference current source is not available, DCCTs are usually calibrated using the reference DCCT method. However, since in-situ deployment of a reference device is not always easy, the calibration procedure often requires bringing the DCCT to a laboratory. As removal and transport of the magnetic heads is a difficult process, the calibration in the laboratory is normally

**Fig. 8.54** The remotely controlled calibration system for the main power converters in the LHC

performed using a different magnetic head. This can introduce errors that must be accounted for.

ADCs can be calibrated using different methods depending on the requirements of the application. The most common is a three point calibration i.e. calibration at ± FS (Full Scale) and at zero. Calibration at FS can be performed using a voltage standard connected to the input of the ADC. The use of voltage standards requires constant monitoring and maintenance of these devices, including periodic calibration in an independent standards laboratory. In the LHC case, a set of voltage and resistor standards as well as forty unique 10 mA portable current standards [90] are kept in a controlled environment to be used as the basis for CERN's calibration infrastructure. Some units are used for field calibration whilst a set of standards is kept constantly in the laboratory, under permanent monitoring.

# **8.5 Ultra-High Vacuum**

V. Baglin · J. M. Jimenez

# *8.5.1 Introduction*

In particle accelerators, beams are travelling under vacuum primarily to reduce the beam-gas interactions i.e. the scattering of beam particles by the molecules of the residual gas. These interactions are responsible for machine performance limitations such as reduction of beam lifetime (nuclear scattering) and of luminosity (multiple coulomb scattering), intensity limitation by pressure instabilities (ionization) and, for positive beams only, electron (ionization) induced instabilities, e.g. beam blow up.

Beam-gas scattering can also increase the background to the detectors in the experimental areas (non-captured particles or nuclear cascade generated by the lost particles upstream the detectors) and the radiation dose rates in the accelerator tunnels. Thus leading to material activation, dose rates to intervention crews, premature degradation of tunnel infrastructures like cables and electronics and finally higher probability of electronic single events induced by neutrons which can destroy the electronics in the tunnel but also in the service galleries.

In addition, the design of an accelerator vacuum system must observe severe additional constraints which have to be considered at the design stage since retrofitting mitigation solutions is often impossible or very expensive. Among them, the vacuum system has to be designed to minimise beam impedance and radiofrequency higher-order-modes (HOM) generation as well as to optimise the beam aperture in particular in the magnets. It also must provide enough ports for the pumps and for the vacuum diagnostics and allow for bake-outs in order to achieve Ultra-High Vacuum (UHV) pressures (<10−8 Pa). The impact of other constraints like integration, safety (material and personnel), operational issues (conditioning of RF and HV devices) and costs often lead to a compromise in performances of all systems of an accelerator. This explains why these issues must be addressed at the design stage [91].

For accelerators operating at cryogenic temperatures [92], the heat load induced by scattered beam particles and synchrotron radiations can also be an issue for the cryo-magnets since local heat loads can lead to a magnet quench i.e. a transition from the superconducting to the normal state. The heavy gases are the most dangerous because of their higher ionisation cross-sections. Thus, the beam-pipes shall be designed to intercept heat loads induced by synchrotron radiation, energy loss by nuclear scattering, image currents, energy dissipated during the development of electron clouds. In the LHC, these constraints required, for the first time in a particle accelerator, the use of a beam screen [93]. Increasing further the luminosity of a storage ring operating at cryogenic temperature, such as in the High-Luminosity LHC (HL-LHC), the very large production of collision debris must be intercepted at the level of the beam screen by heavy material, e.g. tungsten. This shielding is designed to offer a protection of the superconducting coil against radiation induced ageing and extract the beam induced heat load at an elevated temperature, e.g. 60 K, to optimise the Carnot efficiency [a].

# *8.5.2 Vacuum Fundamentals*

Vacuum is defined as the absence of matter or a space empty of matter. These are idealistic definitions since a perfect vacuum is a theoretical limit. Realistically, whenever a pressure in an enclosed space is less than the pressure of the surrounding atmosphere, the enclosed space is defined to be under vacuum. Hence, vacuum is obtained by removing molecules of gas from an enclosed space to the necessary level required for a specific process or experiment. A gas in an enclosed space can be physically described by its volume, its temperature and the amount of molecules or the pressure.

### **<IP_ADDRESS> Total, Partial and Vapor Pressures**

The residual gas is usually composed of several types of molecules (ex: air, gas in vacuum systems). The total pressure, *P*tot, is the sum of all the partial pressure, *Pi*, as shown by the Dalton law:

$$P\_{\text{tot}} = \sum P\_l = kT \sum n\_l. \tag{8.46}$$

The saturated vapor pressure of gasses (Fig. 8.55) is of major importance for the accelerators operated at cryogenic temperatures. Above ambient temperature, only water condensation is a limitation justifying the use of bake-out to improve the outgassing. At 1.9 K, the operating temperature of the LHC cold mass, helium is of concern in case of leaks. In the 5–20 K range, the hydrogen is pumped onto the cold bore due to the beam screen's perforation which has a conductance designed to maintain the partial pressures below the 100 h life time limit. If operated between 20 and 40 K, then the scheme is less favorable and strong pressure oscillations can be expected in presence of temperature variations. This is one reason why this range of

**Fig. 8.55** Saturated vapour pressure [94]

temperature is avoided others are the cryogenic implications and magneto-resistance of the beam-pipe materials.

### **<IP_ADDRESS> Gas Laws and Gas Densities**

The vacuum system of an accelerator will behave as the gas it contains. The major Laws of interest to predict the behaviour of gasses are Boyle's Law, Charles's Law, Gay-Lussac Law and the General Gas Law which resulted from the combination of Boyle's and Charles' Laws.

The Avogadro's Law is very useful to convert pressures, *P*, into gas densities, *n*, for a given volume, *V*. Under the same conditions of pressure and temperature, equal volumes of all gases have the same number of molecules: called a mole.

$$PV = nk\_B T,\tag{8.47}$$

with:

$$k\_B = 1.38 \times 10^{-23} \left[ \frac{\text{Nm}}{\text{K}} = \frac{\text{Pa} \cdot \text{m}^3}{\text{K}} \right] = 1.38 \times 10^{-22} \left[ \frac{\text{mbar} \cdot \text{l}}{\text{K}} \right]. \tag{8.48}$$

For *T* = *T*RT = 296 K (23 ◦C):

$$\frac{1}{k\_B T\_{\rm RT}} = 2.45 \times 10^{20} \left[ \text{Pa} \cdot \text{m}^3 \right]^{-1} = 2.5 \times 10^{19} \left[ \text{mbar} \cdot \text{l} \right]^{-1},$$

in other words, a volume of 1 l at room temperature and 1 mbar contains 2.5 × 1019 molecules.

### **<IP_ADDRESS> Gas Flow, Mean Free Path, Throughput and Ultimate Pressure**

After having pumped out the gas molecules from the volume (Fig. 8.56), the residual pressure in the beam-pipe is dominated by the surface desorption then, at much lower pressures, by the diffusion from the beam-pipe walls and the permeation through them. Modern pumping systems allow roughing the accelerator beampipes quickly enough to have only to consider the molecular regime, laminar and intermediate regimes being ruled out in few minutes. The molecular flow regime occurs when molecules are so far apart that they no longer have any influence on each other. Their motion is strictly random and their mean free path, i.e. the path length that a molecules traverse between two successive impacts with other molecules becomes larger than the beam-pipe dimensions. The mean free path for

air at room temperature is given by:

$$
\lambda\_{\text{air}}\,\text{[m]} = \frac{6.67 \times 10^{-3}}{P\,\text{[Pa]}}; \ \lambda = 67 \,\text{m at } 10^{-4} \text{Pa} \,\left(10^{-6} \text{mbar}\right), \tag{8.49}
$$

In steady-state or equilibrium conditions, the throughput (quantity of gas per unit of time), *Q*, is conservative: the same at one end of a vacuum system as it is at the other.

$$\mathcal{Q} = \frac{PV}{t} = P\frac{V}{t} = P \cdot S,\tag{8.50}$$

*S* being defined as the pumping speed [m3/h], often in l/s.

In reality, Eq. (8.49) becomes Eq. (8.50) where, *P*0, is defined as the ultimate pressure. In general, *S* varies in the range of three orders of magnitude (~1 → 1000 l s−1) while *Q* can extend over more than 10 orders of magnitudes: ~10−5 mbar·l·s−1·cm−2 for plastics → 10−15 mbar·l·s−1·cm−2 for metals [95]. The right choice of materials and treatments is compulsory in the design of vacuum systems especially those for accelerators. In this respect the measurement of outgassing rates is a basic activity for an ultra-high vacuum expert.

Equation (8.50) shows that the ultimate pressure which is intrinsic to the system dominates at low pressure regimes. At a given stage, increasing the pumping speed will not lead to the expected pressure decrease.

$$P = \frac{\mathcal{Q}}{S} + P\_0,\tag{8.51}$$

### **<IP_ADDRESS> Outgassing of Materials**

The outgassing is the spontaneous evolution of gas from solids or liquids. To be compared with the degassing which is the deliberate removal of gas from a solid or a liquid and with the desorption which is the stimulated release of adsorbed chemical species from the surface of a solid or liquid.

The intrinsic outgassing rate is the quantity of gas leaving per unit time and per unit of exposed geometric surface, or per unit of mass, at a specified time after the start of the evacuation. The geometric surface is the visible surface without correction for roughness or open porosity. The measured outgassing rate is the net difference between the intrinsic outgassing rate and the rate of re-adsorption in the test chamber. The re-adsorption rate depends on test chamber and on method of measurement.

For unbaked metals, water is the main gas desorbed. The outgassing rate of water decreases following a 1/*t* law. The outgassing of unbaked metals is not an intrinsic value. However, measurements have shown that the water outgassing does not depend significantly on the nature of metals, on surface treatments and on operating temperature for temperatures lower than 110 ◦C. At present no methods, except heating (bake-out), exist to quickly remove water from unbaked metals. The fact that desorption rates depend exponentially on temperature allows a faster reduction of outgassing through heating (bake-out procedure). If a heat of adsorption of 15 kcal/mol and a bake-out temperature of 150 ◦C are assumed, the rate of gas removal will be increased by a factor of roughly 5000 relative to the value at room temperature.

The outgassing of baked systems is dominated by H2 diffusing out of the metallic walls. The remaining outgassing species CH4 and CO are believed to be related to the presence of H2 and its recombination with the surface contaminants. These species will decrease if the H2 level is reduced. Contrary to water outgassing, the value of the outgassing rate of hydrogen is stable at room temperature. When the thermal history is known, the outgassing of hydrogen is an intrinsic property of metals. The diffusion model predicts values for the hydrogen outgassing that are in agreement with experimental observations. For the vacuum-fired chambers (950 ◦C × 2 h, 10−3 Pa H2), the outgassing rate is limited by the background signal induced by the gauges. The upper limit at room temperature is 10−14 mbar·l s−1·cm−2. In UHV systems, the outgassing of the beampipes can often be compared to the outgassing of the vacuum instrumentation. Therefore, the outgassing of the instrumentation has to be considered in the design of an accelerator, in particular close to the detectors in the experimental areas or in regions where non-evaporable getter (NEG) coatings are used.

### **<IP_ADDRESS> Kinetic Theory of Gasses**

The gas density velocity distribution (mass of gas *m*) at a temperature, *T*, in a stationary large volume and at equilibrium follows a Maxwell-Boltzmann distribution law:

$$\frac{dn}{d\nu} = 2n\sqrt{\frac{m^3}{2\pi k^3 T^3}} e^{-\frac{mv^2}{2kT}} \nu^2. \tag{8.52}$$

The average velocity of molecules is given by Eq. (8.52) in m/s with *T* in K and *M* the molar mass. The number of molecular hits on a wall per second is given by (8.53).

$$
\overline{\upsilon} = \sqrt{\frac{8kT}{\pi m}} = 146\sqrt{\frac{T}{M}},\tag{8.53}
$$

$$
\mu = \frac{n}{4} \sqrt{\frac{8kT}{\pi m}} = \frac{1}{4} n \overline{\nu}.\tag{8.54}
$$

### **<IP_ADDRESS> Conductance and Effective Pumping Speed**

The conductance of an orifice of surface *A*, and of a tube of diameter *D* and length *L*, can be derived from the previous expression and are given for air at room temperature by Eqs. (8.54) and (8.55), respectively.

$$\mathcal{C}\_{\text{air},\ 20^{\circ}C} \text{ [l/s]} = 11.6 \, A \, \left[ \text{cm}^2 \right],\tag{8.55}$$

$$C\_{\rm air,20^{\circ}C} \text{ [l/s]} = 12.1 \, \frac{D \text{[cm]}^3}{L \text{ [cm]}},\tag{8.56}$$

to be noted that both equations show that the conductance varies with √*T /M*. The conductances add when in parallel (*C* = *Ci*) and they add in the inverse when in series (1/*C* = (1/*Ci*)). The flux through a conductance is given by: *Q* = *C*(*P*2 − *P*1) [96, 97].

As any type of discrete pump is connected to the beampipe through a connecting piece with a conductance, *C*, the efficient pumping speed is given by:

$$S\_{\rm eff} = \frac{\mathcal{Q}}{P} = \frac{\mathcal{C} \cdot \mathcal{S}}{C + \mathcal{S}},\tag{8.57}$$

in practice, *S*eff ~ S if *C* >> *S*, *S*eff ~ *C* if *C* << *S*, and *S*eff ~ *S*/2 if *C* ~ *S*. It is therefore of great importance to optimise the conductance of the connecting pieces to benefit as much as possible of the pumping system.

# *8.5.3 Vacuum Dynamics*

### **<IP_ADDRESS> Synchrotron Radiation**

When a particle beam circulates in a bending magnet or circulates off-axis in a quadrupole magnet, it might radiates photons and lose energy by synchrotron radiation (SR). The interaction of the synchrotron radiation with the vacuum chamber wall stimulates molecular gas desorption and dissipates heat load. Therefore, the vacuum chamber design must take into account these effects [98, 99].

The synchrotron radiation is due to the acceleration (centripetal or longitudinal) of the charged particles. Therefore, these charged particles loose energy which must be compensated by the RF system in order to keep the particles on the closed orbit. The dissipated power due to the centripetal acceleration is much larger than the longitudinal acceleration. The proportional factor is equal to the relativistic factor γ to the square. Due to the relativistic effects, the radiation is strongly emitted in the forward direction. The opening angle is roughly 1/γ. The energy of the emitted photons varies from meV to MeV.

The synchrotron radiation spectrum is characterised by the critical energy *ε*c. This energy separates the power spectrum in two equal amounts. However, 90% of the emitted photons have energy below the critical energy. The critical energy is given by Eq. (8.57) where *h* is the Planck constant, *c* the speed of light and *ρ* the curvature radius.

$$
\varepsilon\_c = \frac{3}{2} \frac{hc}{2\pi} \frac{\nu^3}{\rho},
\tag{8.58}
$$

A practical equation for engineers is given by Eq. (8.58) for electrons and protons.

$$\varepsilon\_c \text{ [eV]} = 2.218 \times 10^3 \frac{\text{[GeV]}^3}{\rho \text{[m]}} \text{ for electrons, and} \\ \varepsilon\_c \text{ [eV]} = 3.5837 \times 10^{-7} \frac{\text{[GeV]}^3}{\rho \text{[m]}} \text{ for protons.}$$

At CERN, the critical energy of the Large Electron Positron Collider (LEP) was varying from 6 keV at injection till 660 keV at 104 GeV. For the Large Hadron Collider (LHC), the critical energy varies from 10 meV at injection till 44 eV at 7 TeV.

Practical equations for engineers of the dissipated power, *P*0, and photon flux, *Γ* , as a function of beam energy, *E*, and beam current, *I*, are given by Eqs. (8.59) and (8.60).

*P*0 [W*/*m] = *α* E [GeV]4 2*πρ*[m]2 I [mA] *,* with *α* = 88*.*7 or 7*.*79 × 10−12 for electrons or protons*,* (8.60)

$$\dot{I}^{\prime} \left[ \text{ph}/\text{m}/\text{s} \right] = \beta \frac{\text{E} \left[ GeV \right]}{\rho \left[ \text{m} \right]} \text{I [mA]}, \text{ with} \\ \beta = 1.288 \times 10^{17} \text{ or } 7.017 \times 10^{13} \quad \text{for electrons or protons.} \tag{8.61}$$

In accelerators with synchrotron radiation (SR), e.g. LEP, DIAMOND, SOLEIL, *...* , the heat load of some 10 kW/m requires the use of coolant and dedicated engineering design in order to evacuate the heat deposited on the beam-pipe wall. In the LHC, the heat load of 0.2 W/m is evacuated by the beam screen's cooling circuit maintained between 5 and 20 K while the cold bore is operating at 1.9 K.

The photo-desorption of neutral gas from the oxide layer is a 2 steps process where photo-electrons and secondary electrons desorb molecules from the near surface and excite strongly bounded molecules which subsequently desorb thermally. The desorb species are H2, CH4, H2O, CO, O2 and CO2. The phenomenon is characterised by the photo-desorption yield *η*, which is the ratio of the desorb molecules to the number of incident photons. The photodesorption yield increases when decreasing the angle of incidence. Below 1 keV, the photo-desorption yield scales roughly like the critical energy and is almost constant above 1 keV. The desorption yield, which decreases under photon irradiation, can be expressed as a function of the initial desorption yield, *η*0, initial and accumulated photon dose, *D*0 and *D*, by Eq. (8.61) with *D*0 ~ 1021 *...* 1022 ph/m and *a* ~ 0.9 *...* 1.3.

$$
\eta = \eta\_0 \left(\frac{D}{D\_0}\right)^{-a}.\tag{8.62}
$$

At 3.75 keV, after a period of beam cleaning of 1024 *...* 1025 ph/m accumulated, the photo-desorption yield is reduced from 10−2 *...* 10−3 to 10−5 *...* 10−6 molecules/ph for unbaked and baked Cu or baked stainless steel surfaces. The desorption yield of aluminium is a factor 10 higher, most probably owing to the fabrication process. The amount of gas desorbed during the process varies from 0.5 in the baked case to ~10 monolayers in the unbaked case. At large doses, the irradiated surfaces have a pumping speed of ~100 l/s/m for CO and CO2. The pumping capacity is however very small (10−4 monolayer). Figure 8.57 shows typical curves measured during photon stimulated desorption studies.

Beside its pumping characteristics, Non Evaporable Getter (NEG) coating such as TiZrV is also used to reduce the desorption yield. The diffusion barrier created during the activation after the surface oxide layer has diffused into the bulk could be the origin the low intrinsic yields. At 4.5 keV critical energy, the intrinsic photodesorption yield is as low as 10−5 H2/ph and even lower for other gas species. When the film is saturated with CO, the photo desorption yields remain constant. Photon induced pumping by the getter is also observed for CO at a rate of 10−5

CO/ph [101]. A cleaning rate *a* = 0.4 (Eq. 8.61) was observed with 20 keV critical energy.

At cryogenic temperature, the photo-desorption yields are reduced by one order of magnitude as compared to room temperature. The primary desorption equals 10−4 molecules/ph for unbaked Cu held at 5 K when irradiated by SR of 200 eV critical energy. The cleaning rate *a* equals ~0.6. During irradiation, the previously strongly bounds molecules are weakly bounded (physisorbed/condensed)to the cold surface. In a closed geometry, these molecules can in turn be recycled into the gas phase by the subsequent irradiation. A recycling yield as large as 1 H2/ph is reached at one monolayer. In this case, the pressure level inside the vessel can increase up to the saturated vapour pressure. However, the operating pressure, *P*op, inside a cold bore can be controlled by inserting a perforated liner with a conductance *c*. In this case *P*op is given by Eq. (8.62) [102].

$$\mathbf{P}\_{\rm op} = \frac{\eta \Gamma}{c}.\tag{8.63}$$

### **<IP_ADDRESS> Electron Cloud**

Operation with trains of bunches of high intensity can lead to the formation of a cloud of electrons. This was and is the case of machines such as ISR, PSR, KEK-B, PEP-II, SPS, RHIC and LHC. This electron cloud affects the beam properties but also contribute to the vacuum dynamics. When an electron is in the vicinity of the beam potential, it can be attracted or repelled in the case of a positive or negative beam. In both cases, there can be beam conditions which produce photoelectrons, ionise the residual gas and/or allow the multiplication of secondary electrons with time. Once the energy given to electrons is above the binding energy of physisorbed and/or chemisorbed molecules (0.1 *...* 1 eV) the bombardment stimulate gas desorption from the vacuum chamber wall. Clearly, the highest gas load is observed in the multipacting regime.  At the wall, these electrons stimulate gas desorption but also produce secondary electrons. The secondary electrons are further accelerated to ~100 eV by the following bunch, 25 ns apart, leading to a multiplication of electrons in the vacuum system.

Similarly to photon stimulated molecular desorption, electron simulated molecular desorption is characterised by the electron desorption yield. The electron desorption yield is also decreased under electron bombardment according to Eq. (8.61). The electron desorption yield increases almost linearly with the electron energy. Table 8.17 shows the initial yield and cleaning rate for unbaked and baked copper when perpendicularly irradiated by 300 eV electrons. At an integrated dose of 5 × 1016 e/cm2, the desorption yield of the baked Cu is about one order of magnitude lower than unbaked Cu. After an accumulated dose of 1018 e/cm2, i.e. 1.6 mC/mm2, 1 *...* 10 monolayers of gases have been desorbed, mainly H2. The hydrogen electron desorption yield can be explained by a diffusion model (*a* ~ 0.5). The H atoms are produced by the dissociation of the hydroxides and diffuse under the electron bombardment.

Electron desorption yields of metallic surfaces are about the same. As a comparison to the baked case, after activation, the initial yields for NEG coatings are further reduced by 1 and 2 orders of magnitude for H2 and CH4, CO, respectively. Like the SR case, electron induced pumping is observed for CO at a rate of 10−3 CO/e [105]. At 4.2 K, the electron desorption yield of physisorbed/condensed molecules is linear up to a monolayer and then levels-off. Values up to 500 H2/e were reported with 300 eV electrons [106].

The secondary electron yield (SEY) is another key parameter which defines the vacuum level in a beam tube. It is defined as the ratio of the number of produced electrons to the number of incident electrons. The SEY value determines the amount of stray electrons between each bunch and therefore the electron flux to the wall. Therefore, there are strong interests to reduce the SEY for the vacuum scientist. The maximum of the SEY curve *δ*max, lies in the range 200 *...* 300 eV. Typical *δ*max values for as received metallic surface are ~2. Baked Cu has 1.8

**Table 8.17** Desorption yield parameters *δ* for unbaked and baked copper perpendicularly irradiated by 300 eV electrons [103, 104]

and atomically cleaned Cu has 1.5. Water condensation on atomically cleaned Cu resets *δ*max to 2 which correspond to the as received state. Coating such as baked TiN, activated TiZrV or amorphous carbons are used to reduce *δ*max close to 1. Due to graphitization of the carbon oxides, an accumulated electron dose of a few mC/mm2 is also effective by beam scrubbing to reduce *δ*max of a metallic surface (except Al) close to 1 [107]. These methods are used in recent machines to control the multipacting process. Thanks to their morphology, laser engineered structured surfaces can reduce *δ*max below 1. However, their exploitation in future accelerator is still under study.

### **<IP_ADDRESS> Vacuum Stability**

In storage rings, the circulating particle beam ionise the residual gas. The produced ions are then repelled toward the vacuum chamber wall desorbing neutral gasses. As a consequence, the amount of beam-ionisation is increased leading to a higher gas load. Ultimately, this mechanism, which was first observed in the Intersecting Storage Rings (ISR), can conduct to a particle loss and a pressure run-away [108]. Modern accelerators operated with high beam intensities are designed to maintain vacuum stability (SNS, LHC).

The flux of molecules *Q*(*I*), inside the vacuum chamber is a function of the ion desorption yield, *η*, the gas pressure, *P*, the ionisation cross section, *σ*, and the thermal outgassing, *Q*0. It is given by Eq. (8.63) where *I* is the beam intensity and *e* the electron charge.

$$
\mathcal{Q}(I) = \eta P \sigma I / e + \mathcal{Q}\_0. \tag{8.64}
$$

With a linear pumping speed, *S*, the dynamic pressure is given by Eq. (8.64).

$$P(I) = \frac{\mathcal{Q}(I)}{S} = \frac{\mathcal{Q}\_0}{S - \eta \sigma I/e}.\tag{8.65}$$

The stability limit is then given by Eq. (8.65) when the denominator of Eq. (8.64) equals zero. During operation, when the beam current approaches the critical current, the pressure increases drastically leading to strong particle losses and ultimately to beam dump.

$$(\eta I)\_{\text{crit}} = \frac{eS}{\sigma}.\tag{8.66}$$

In practice, a treatment to reduce the ion desorption yield and the optimisation of the pumping speed at each position of the vacuum system is required to achieve vacuum stability. Ex-situ Argon glow discharge with in-situ bake-out was successfully applied in the ISR.

In the LHC, the ion impact energy is ~500 eV. For baked materials, ion desorption yields are a few 0.1 molecules/ion while minor beam conditioning is expected during operation. When using NEG coatings, the vacuum stability is ensured by lumped pumping to constraint CH4. This allows to achieve a critical current larger than 4 A in the LHC experiments and in the long straight sections [109]. At 4.2 K and 5 keV, the ion desorption at a monolayer for a condensed gas is as large as 2000 and 2 for H2 and CO2 respectively. Due to the closed geometry of the beam tube and the possibility to physisorbed/condensed gas, the critical current of Eq. (8.65) is modified into Eq. (8.66). It is a function of the sticking probability *α* and the ion desorption yield at cryogenic temperature, *η'*.

$$I\_{crit} = \frac{\alpha S}{\left(\eta + \eta'\right)\sigma/e}.\tag{8.67}$$

For such a closed geometry when operating at cryogenic temperature, the critical current is less than 1 A for vacuum chambers of 1 m length. However, the perforation of the LHC beam screen inserted inside the cold bore guarantee a minimum pumping speed. Thus, the equilibrium coverage of the condensed gas is below a monolayer and the product (*ηI*)crit is ~ 100 [98, 99].

### **<IP_ADDRESS> Particle Losses**

In heavy ions storage rings or accelerators, beam losses linked to charge transfer induce large pressure rises (RHIC, LEAR, GSI, LHC *...*) which could trigger the beam dump. These pressure rises are due to heavy ions bombarding the vacuum chamber wall at grazing incidence. At high energy, the heavy ions lose energy in the solid by electronic losses (stopping power) which determines the desorption yield. The reported desorption yields are very large but decrease when increasing impact energy above the Bragg maximum (1 MeV/u for lead ions on Cu). At grazing incidence, the yields range from 102 to 105 molecules/ion as a function of surface treatment and impact energy. Possible mitigation techniques implemented in operating machines are the use of dedicated collimators, beam conditioning (2 orders of magnitude is gained after 100 h i.e. 1013 ions/cm2), NEG coatings, etc. [110]. For machines operating at cryogenic temperatures, the dominant factor is the quench level of the cryomagnets. For these typical loss rates, pressure rises are often negligible.

# *8.5.4 Vacuum Engineering*

The engineering of the vacuum system of a particle accelerator has to be started right from the beginning of the project. Indeed, if considered later on, the resulting integration and performance issues will lead to a significant increase of the cost of the vacuum system (complex shapes, more pumps, retrofitted modifications, etc.) and even into performance limitations. Experience has shown that the vacuum engineering shall proceed in parallel on the following topics: expertise provided to beamrelated components (magnets, beam instrumentation, radio-frequency systems, etc.), engineering of vacuum related components (beampipes, bellows, pumping ports, etc.) and machine integration including cabling and services.

### **<IP_ADDRESS> Vacuum Pumping**

The pumping scheme is often decided at the early stages of the design since it affects the overall engineering of the accelerator. Indeed, the pumping scheme will define the reserved space for the pumping and in case of integration problems will lead to alternative solutions to preserve the expected performances or to compromise. The number and types of pumps will allow reaching the design operating pressure which is linked to the beam lifetime, a parameter in relation with the beam-gas scattering.

As the pumping speeds vary between a few litre-per-seconds to thousands of litre-per-seconds while the outgassing rates of materials in the vacuum system vary by up to 8 orders of magnitude, an appropriate selection of material and design is required to achieve the specified vacuum performances. Said differently, increasing the installed pumping speed in an accelerator by a factor 2 is already challenging and costly, whereas losing several orders of magnitude in outgassing rates could easily result from an inappropriate use of materials or bad vacuum engineering or cleaning of the materials.

### <IP_ADDRESS>.1 Discrete Pumping

In particle accelerators, discrete pumping is the most commonly used solution and is often obtained by ion pumps combined with sublimation or non-evaporable getter (NEG) cartridge pumps, cryogenic and turbomolecular pumps.

Ion pumps [111] are widely used since they are very reliable and provide a large pumping speed, up to 800 l/s. In addition, the discharge current of an ion pump is directly proportional to the pressure, and thereby provides an indication of pressure for a limited cost. This signal is often used to trigger vacuum interlocks for machine protection. Ion pumps have also the advantage of pumping all gas species and once baked-out at 250–300 ◦C, the ultimate pressure is in the low 10−10 Pa. Special attention has to be taken while pumping noble gasses and water. Above a given quantity of gas pumped, part of the pumped noble gasses will be released as hydrogen (via dissociation of the water molecules) when pumping water.

Sublimation pumps [112] are often used to speed up the pump down to the UHV pressure range or as a complement to ion pumps at very low pressures (<10−10 Pa). If used at high pressures, the pump's bodies must be water cooled to prevent the heating induced by the frequent activations (several per minute). Similarly to NEG pumps, the major limitation of the sublimation pumps is that the pumping speed of noble gasses and methane is very small.

NEG pumps are commercially available as different types: cartridges [113], strips and coatings. Only the first type is used as discrete pumping, strips and coatings are, by nature, used as distributed pumping. NEG cartridges offer a huge pumping speed for hydrogen, carbon mono- and dioxide. Once the NEG material is saturated, the pumping capacity can be recovered by heating via Joule effect, most of the commercial products include this option in the body of the NEG cartridge.

Turbo-molecular pumps are widely used by the industries and this has resulted in a significant decrease of prices and increase in reliability. Most vacuum suppliers provide a large variety of turbo-molecular pumps off-the-shelf. The improvement in performance and lifetime over the last decades has stimulated their use in particle accelerators. The major limitation comes from the radiation inherent in particle accelerators. Indeed, this requires decoupling the power supply and associated electronics from the body of the pump, a technical solution contrary to the needs of industry. Thus explaining why most of the suppliers are reluctant to develop and maintain such products in their catalogues.

Cryogenic pumps are also widely used by industry and similarly to turbomolecular pumps, the prices have decreased. Cryogenic pumps are used in accelerators to cope with huge local outgassing, mainly on unbaked systems. Special operating precautions have to be taken to limit the back streaming of condensed gasses in case of power cuts or compressor failure.

### <IP_ADDRESS>.2 Distributed Pumping

Distributed pumping has been used for decades in particle accelerators and is of special interest for conductance limited beam pipes. The most commonly used distributed pump was the ion pumps cells inserted in the dipole beampipes [114]; the dipole magnet field serving also for the ion pump cells. Later on and in particular in the large electron-positron collider (LEP), NEG strips were used. The NEG strips [115] were activated by the Joule effect.

More recently, the large hadron collider (LHC) could profit from the development of the NEG coatings [116], a technology developed and industrialized at CERN. These coatings provide many advantages such as a huge pumping speed, large pumping capacity for hydrogen and low yields for secondary electrons and stimulated desorption by electrons, photons and ions. The activation temperature has decreased; 180 ◦C is enough to obtain nominal pumping speed and capacity.

### **<IP_ADDRESS> Vacuum Instrumentation**

### <IP_ADDRESS>.1 Pressure Sensors

Similar to the pumps, the evolution of the pressure sensors is stimulated by the needs of the industry and the tendency is to use pressure sensors with electronics on their heads. All types of pressure sensors are now available in catalogues covering the range of pressure from several atmospheres (106 Pa) down to UHV pressures (10−10 Pa). These products are cheap, reliable and easy to maintain.

However, their use in particle accelerators is also compromised by the inherent radiation. An alternative are the so-called passive gauges with the electronics decoupled from the pressure sensor. The existing sensors can be placed far away, up to 2 km, from their controllers. It should be noted that the installation of appropriate cables is an important issue to allow use of the sensors up to their design specifications. Special attention has to be taken while laying the cables, to avoid electromagnetic incompatibility and interference (EMI) perturbations; it is recommended to lay these cables in special cable trays or with instrumentation cables and to pay special attention to cable shielding and grounding loops.

The ion pumps are also often used as pressure indicators since their discharge current is proportional to the pressure. Modern controls electronics allow a fast conversion of the currents into pressures. The stability of the discharge current explains why these signals are used as pressure interlocks.

### <IP_ADDRESS>.2 Residual Gas Analyzers (RGA)

The residual gas analysers are of primary importance to understand the beam-gas scattering since, as mentioned earlier, the ionisation cross-section varies with the gas species. Therefore, while operating an accelerator with beams, knowing the residual gas composition can allow calculating the beam lifetime and predicting potential limitations.

As the modern accelerators require more and more UHV conditions to operate, the RGAs must provide partial pressure resolutions in the low 10−11 Pa range to provide useful information. This type of residual gas analyser is available off-theshelf, but in many cases, the electronics is attached to the head or placed at a few meters. This limitation still exists and the demand being very small, most of the suppliers do not plan to modify the position of the electronics thereby limiting the use of RGA to radiation free environment.

### **<IP_ADDRESS> Vacuum Sectorisation**

The sectorisation of the beam vacuum system results from the combination of various constraints, the major being: venting and bake-out requirements, conditioning requirements (RF and HV devices), protection of fragile and complex systems (experimental areas and ceramic chambers), decoupling of baked vacuum parts, which are at room temperature, from non-baked parts at cryogenic temperature, radiation issues, etc.

For UHV beam vacuum systems, all-metal gate valves are preferred in order to allow for bake-out at temperature above 250 ◦C. VITON-sealed valves are less expensive but limited in bake-out temperature. A special treatment of the VITON seals is recommended prior to their use nearby NEG coatings or pumps since minor outgassing of Fluor will degrade the pump characteristics.

Interlocking the sector valves is not an obvious task. Indeed, increasing the number of sensors will provide more pressure indications but might results in a degradation of the overall reliability. Protection at closure (pressure rise, leaks) is treated differently from the protection while recovering from a technical stop. In the latter case, parts of the accelerator beampipe vented or being pumped down must not be put in communication with upstream or downstream sectors which remained under vacuum.

### **<IP_ADDRESS> Corrosion Issues**

In vacuum systems, feed-throughs and bellows are particularly exposed to corrosion. Feed-throughs, particularly those of the ion pumps where high voltage is permanently present, are critical parts. Despite the design optimization made by many suppliers, a direct heating of the protective cover to reduce the relative humidity around the feed-through is the most efficient and commonly used technique to limit the corrosion.

The bellows are also vulnerable due to their thinness, often between 0.1 *...* 0.15 mm. Aluminum bellows are exposed to corrosion by nitric acid (HNO3) which is generated by the combination of O3 and NOx. In presence of PVC material, radiation can lead to the creation of hydrochloric acid (HCl) which corrodes stainless steel materials. This corrosion is strongly penetrating, and once seen at the surface, it is often too late to mitigate the effects.

Relative humidity is the critical parameter and must be kept below 50%. However, accidental spillage can compromise locally the conditions and therefore, corrosion-resistant design are strongly recommended.

Corroded components like feed-throughs and bellows normally start to leak after a mechanical action or a venting to atmosphere. If several components are affected, this could result in a long sequence of pumping, leak searching, venting, repumping, etc., leading to a long downtime and often subsequent radiation dose rates to personnel doing the interventions.

### **<IP_ADDRESS> Experimental Areas**

Their design must include the following additional constraints: integration, reliability, availability, engineering and performances.

The installation of the vacuum system follows the closure of the detector. Therefore, the design has to be validated beforehand in order to prevent integration issues which could prevent the closure of the detector and lead to significant delay and increase of costs. Temporary supports and protection are required at each stage of the installation. Indeed, as compared to the size of the detectors, the beam pipes are small, fragile and need to be permanently supported and protected while moving the detector components.

The leak tightness and bake-out testing are compulsory at each step of the installation since all vacuum systems are later on encapsulated in the detector, thereby preventing any access, even for repair. Their reliability is critical.

The installation of the detectors dictates the speed and sequence of installation of the beam-pipes. To avoid delays, the vacuum components must be available (tested and ready for installation) in advance in order to adapt to the installation sequence.

The experimental beam-pipe must be thin and manufactured from light material in order to allow the particles created inside the beam-pipe to escape from it through the vacuum envelope. Since the detectors are extremely demanding in terms of operating pressure (normally expressed in gas densities) light materials are mandatory. Beryllium and aluminium materials are the most commonly used. Titanium is sometimes an alternative. These materials can be NEG coated by plasma discharge and baked-out in-situ. Beryllium being is extremely expensive and dangerous in case the beampipe breaks; beam-pipe design attempts have been made to replace the beryllium by composite chambers. Carbon-carbon materials have been used with metallic layers but the ultimate pressure is not yet in the range of the specification of the modern detectors. The engineering solutions for the bakeouts have also to be studied in details since the bake-out solutions (heaters, probes and cables) must fit within the limited space available between beam-pipes and the detector parts.

The excellent performances of the vacuum system in the experimental areas are a determinant factor for the performances of the detectors themselves. The most important issues to follow are the beam-pipe transparency, gas density and residual gas composition, impedance and high order mode trapping and precise alignment. The last point is difficult to achieve once the beam-pipes are installed in large detectors.

# **8.6 Beam Instrumentation and Diagnostics**

### R. Jones · T. Lefevre · H. Schmickler

Beam instrumentation and diagnostics [117, 118] combines the disciplines of accelerator physics with mechanical, electronic and software engineering, making it an extremely interesting field in which to work. The task of a beam instrumentation physicist or engineer is to design, build, maintain and improve the diagnostic equipment for the observation of particle beams with the precision required to tune, operate and improve the accelerators and their associated transfer lines. This chapter will give an overview of the instrumentation in use in modern accelerators, although the choice available today is so vast that inevitably it will not be possible to cover them all.

# *8.6.1 Beam Position Measurement*

A beam position monitoring system can be found in every accelerator. Its role is to provide information on the position of the beam in the vacuum chamber. In linacs and transfer lines Beam Position Monitors (BPMs) are used to measure and correct beam trajectories, while in synchrotrons such monitors are distributed around the ring, providing the global orbit. Their location is usually chosen to be close to the main quadrupole magnets where the *β*-functions are largest and so any orbit distortion a maximum.

### **<IP_ADDRESS> Pick-Ups**

The measurement of beam position relies on processing information from pick-up electrodes located in the beam pipe.

Four pick-up families are commonly employed (see e.g. [118]):

• **Electrostatic**

These consist of two electrodes insulated from and located on opposite sides of the vacuum chamber (either left & right for the measurement of horizontal position and/or up & down for the measurement of vertical position). As the beam passes inside the pick-up it charges up the electrodes, which act as capacitors. The amount of charge collected by each electrode will depend on the position of the beam. Hence, by comparing the charge on opposite electrodes, a beam position can be calculated. A so called "shoe-box" design (Fig. 8.58) is often used for linearity, while a button design (Fig. 8.59a, b) is favored for short bunches and its low cost, but needs correction for its non-linear response [119].

• **Electromagnetic**

**Fig. 8.58** Example of a horizontal shoe box pick-up from the CERN SPS showing right electrode, left electrode and the full assembly in its vacuum chamber

**Fig. 8.59** (**a**) Example of a button electrode from the CERN LHC. (**b**) Schematic of the full LHC button pick-up assembly for dual plane measurement using four electrodes. (**c**) Example of a stripline pick-up from the CERN-SPS

**Fig. 8.60** Principle and example of a cavity pick-up (ATF2, KEK, Japan)