11institutetext: Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali
del Sud, Catania, Italy

# Microwave Discharge Ion Sources

L. Celona

###### Abstract

This chapter describes the basic principles, design features and
characteristics of microwave discharge ion sources. A suitable source for the
production of intense beams for high-power accelerators must satisfy the
requirements of high brightness, stability and reliability. The 2.45 GHz off-
resonance microwave discharge sources are ideal devices to generate the
required beams, as they produce multimilliampere beams of protons, deuterons
and singly charged ions. A description of different technical designs will be
given, analysing their performance, with particular attention being paid to
the quality of the beam, especially in terms of its emittance.

##  1 Introduction

The production of high-current beams is a key requirement for various
applications, and this is expected to increase in coming years, either for
industrial applications or for research projects. High-current and high-
brightness H+ beams can be provided by microwave discharge ion sources
(MDISs), which present many advantages in terms of compactness, high
reliability, ability to operate in continuous-wave (CW) or pulsed mode,
reproducibility and low maintenance. Some applications based on intense proton
beams [1] are as follows:

  * •

accelerator-driven systems (ADSs) for nuclear waste transmutation and energy
production,

  * •

radioactive ion beams,

  * •

intense neutron spallation sources,

  * •

radiation processing, and

  * •

neutrino factory.

The main parameters of the related proton drivers are listed in Table 1, while
Table 2 shows a list of projects (operating and under construction) using
high-current proton beams or intense H- sources with low transverse emittance.

Table 1: Proton driver requirements. Proton driver | Energy (GeV) | Beam power (MW)
---|---|---
ADS: XADS | $\sim{0.6}$ | $\sim{5}$
ADS: Ind. burner | $\sim{1}$ | $\sim{50}$
Spall. neutron source (ESS) | 1.33 | 5
Irradiation facility | $~{}1$ | $>10$
Neutrino factory (CERN) | $2.2$ | $4$
RIB: ‘one stage’ | $\sim{0.2}$ | $\sim{0.1}$
RIB: ‘two stage’ | $\sim{1}$ | $\sim{5}\mbox{--}10$
Table 2: High-power accelerator requirements. | p/H- | mA | ms | Hz | Duty factor (%) |  mm mrad
---|---|---|---|---|---|---
LEDA | p | 100 | CW | CW | 100 | 0.25
IPHI | p | 100 | CW | CW | 100 | 0.25
TRASCO | p | 30 | CW | CW | 100 | 0.2
ESS | p | 60/90 | 2.84 | 14 | 4 | 0.3
SPL | H- | 50 | 1.5 | 50 | 7.5 | 0.2
SNS | H- | 50 | 1 | 60 | 6 | 0.25
JKJ | H- | 30 | 0.5 | 50 | 2.5 | 0.25

The optimization of beam formation and transport through the low-energy beam
transport (LEBT) plays a fundamental role in the provision of a high-quality
beam to the accelerator. This is a common requirement of the projects reported
in Table 2, where emittances at the entrance to the radio frequency quadrupole
(RFQ) of the order of 0.20–0.30 mm mrad are needed, making it essential to
design and test the ion source and LEBT as a whole. The major challenge of the
accelerator front-end is therefore the preparation of a high-quality beam,
with a pulse that is well defined in time and has a small transverse
emittance. In the following, a review of the major experiences in the
production of intense proton beams are reported (Table 2) together with future
perspectives.

##  2 Microwave ion source for high-intensity proton production

###  2.1 Historical notes

The history of 2.45 GHz high-current source (HCSs) started about 35 years ago
with different source designs proposed by Sakudo [2] and by Ishikawa _et al._
[3], especially for industrial applications. The sources produced remarkable
results not only for protons, but also for deuterons and singly charged light
ions. A simple concept of the microwave discharge source was based on a non-
confining magnetic field higher than the resonance field (i.e. 87.5 mT).
Sakudo and his collaborators at the Central Research Laboratory of Hitachi
Limited pioneered the development of high-current microwave ion sources for
ion implantation [4]. The first Hitachi ion source (see Fig. 1) is composed of
a plasma generator, that is, essentially, a section of coaxial waveguide with
an axial magnetic field supplied by three solenoids. The 2.45 GHz microwaves
are introduced via a water-cooled antenna connected to the inner conductor of
a coaxial-to-rectangular waveguide transition. The magnetic induction is
varied along the length of the antenna to match the impedance of the plasma-
filled chamber to the impedance of the microwave line [5]. The extraction
system is a multiaperture triode with 124 apertures 3 mm in diameter
distributed over a 50 mm diameter circle. The sources built by Sakudo’s group
were able to supply 2 mA of As+ and 15 mA of B+, and they were successfully
adapted to industrial application setups.

Figure 1: Hitachi microwave ion source with multiaperture extraction system

The second microwave ion source developed by Sakudo _et al._ was especially
designed to generate a slit-shaped ion beam. The plasma chamber illustrated in
Fig. 2 is a tapered ridged waveguide with all but the volume between the
ridges filled with boron nitride. The 2.45 GHz microwaves are introduced
through a dielectric window from a rectangular waveguide. The electric field
between the ridges is relatively uniform, ensuring a reasonably constant
plasma density over the entire length.

Figure 2: Hitachi microwave ion source with slit extraction system

A step forward was made by Ishikawa [6], whose design was very compact
(chamber diameter was 50 mm) and the source was able to produce milliampere
beams of any species, finding applications not only in ion implantation
devices but also for ion beam deposition. The absence of antennas made this
equipment more reliable for long-time operations.

###  2.2 The CRNL ion source

In 1991 a simple and robust design was proposed by Taylor and Mouris at Chalk
River National Laboratory (CRNL; see Fig. 3). This source can be considered as
the basis of all the different designs proposed in the past 25 years. The main
innovation consisted in the use of a matching unit to adapt the waveguide to
plasma impedance, which enhanced the plasma density and finally the current
density of the extracted beam. Moreover, two separately fed solenoids,
approximately placed at the two extremes of the plasma chamber, allowed the
magnetic field profile to be adapted. The extraction system was not
sophisticated but adequate for high-current beam formation, using the three
electrodes in the accelerate–decelerate operation mode.

Figure 3: The CRNL microwave source

The configuration of the Chalk River electron cyclotron resonance (ECR) proton
source is illustrated in Fig. 4. The plasma generator is simply a hydrogen-
filled chamber, with a ceramic rectangular waveguide window, encircled by two
solenoids. The extraction system is a 50 kV multiaperture triode.

Figure 4: The CRNL microwave source

The microwave line is isolated from the plasma chamber by a d.c. waveguide
break consisting of a Teflon sheet sandwiched between a choke flange and a
standard flange. Since the solenoids are also electrically isolated from the
plasma chamber, only the plasma chamber itself remains at high voltage. All of
the power supplies, d.c. as well as microwave, are at ground potential. The
ion source generates beam current densities of up to 350 mA cm-2 at a
microwave power of 1000 W. The three-stub tuner is adjusted to optimize the
impedance match. Figure 5 illustrates the evolution of the beam current with
the mass flow, microwave power and magnetic induction on the plasma chamber
axis.

Figure 5: Beam current as a function of mass flow, microwave power and
magnetic induction

###  2.3 The LEDA injector

This design was further improved by J. Sherman and co-workers at Los Alamos
National Laboratory (LANL), who improved the extraction system and the LEBT in
order to optimize the beam coupling to the RFQ of the LEDA project. Then the
CRNL plasma generator was integrated with a 75 kV acceleration structure at
Los Alamos (Fig. 6) [7]. Plasma is generated by the interaction of 2.45 GHz
microwaves with H2 gas in the presence of an approximate 875 G axial magnetic
field.

Figure 6: Line drawing of the 75 keV microwave proton source

Beam measurements were made on a prototype injector shown in Fig. 7. The
proton source is mounted on a beam diagnostics and pump box, which is followed
by two solenoids. The beam current is characterized by two d.c. current
monitors (DC1 and DC2), an a.c. beam current transformer for beam noise
measurements, an $x$ and $y$ video profile system for beam position and width
measurements, and an emittance measuring unit (EMU), which also serves as the
beam dump. The typical operating parameters of the injector are listed in
Table 3.

Figure 7: Injector used for the beam measurements Table 3: LEDA injector parameters. Injector parameter | Value
---|---
H2 gas flow | 4.1 sccm*
Ion source pressure | 2 mTorr
Ion source gas efficiency | 24%
Discharge power, at 2.45 GHz | 1.2 kW
Beam energy | 75 keV
High-voltage power supply current | 165 mA
DC1 current | 154 mA
DC2 current | 120 mA
Proton fraction | 90%
Injector emittance, 1 r.m.s. norm. | 0.18 mm mrad
*sccm = standard cubic centimetres per minute.
Figure 8: Injector used for the beam measurements

From Fig. 8 we can see that beam current is measured at DC1, DC2 and in the
RFQ entrance collimator for 6.7 MeV RFQ; beam focusing accomplished with LEBT
is achieved thanks to solenoid magnets S1 and S2; and beam centroid is
controlled with steering magnets SM1 and SM2.

###  2.4 The SILHI source

Following the same track, at CEA-Saclay (Commissariat à l’Énergie Atomique,
Saclay), the SILHI source obtained large brightness and high reliability in
the second half of the 1990s. All the parts of the source, which is shown in
Figs. 9 and 10, are robustly engineered, including the beam line elements and
diagnostics, adapted to beams exceeding 10 kW, typically 95 kV, 140 mA. A
proton/deuteron fraction above 80% and an emittance below 0.2 mm mrad have
been obtained, while the reliability has increased over the years, even
reaching 99.9% in a one-week test. The SILHI source (see Fig. 10) has been
developed at CEA-Saclay, in the framework of the IPHI project, devoted to the
production and acceleration of intense proton beams (currents up to 100 mA).
The source design and results are described in detail elsewhere [8, 9, 10],
and in Table 4 we report the main features.

Figure 9: Render view of the SILHI source operating at CEA Figure 10: Layout of the SILHI ion source and the beam line Table 4: SILHI source typical operating parameters. Parameter | Value
---|---
Total beam current | 140 mA
Proton fraction | $\sim{85}\%$
Beam density | 220 mA cm-2
Beam energy | 95 keV
Discharge RF power, at 2.45 GHz | 1.2 kW
Beam emittance, at 75 mA | 0.1  mm mrad
Hydrogen mass flow |  $\sim{2}$ sccm

A collaboration arranged between CEA and the Istituto Nazionale di Fisica
Nucleare (INFN) has allowed in recent years a significant increase of beam
quality produced by SILHI, reaching the outstanding value of 0.1 mm mrad for
0.75 mA as described in detail in the next section.

###  2.5 TRASCO Intense Proton Source (TRIPS) at INFN-LNS

The TRIPS ion source [11] has been designed, realized and commissioned at
INFN-LNS, within the framework of the TRASCO Project (an R&D programme, the
goal of which was the design of an accelerator driving system (ADS) for
nuclear waste transmutation). With reference to the three experiments outlined
above, a series of innovations were implemented on the TRASCO project. The
goal of TRIPS was less demanding in terms of currents than it was for the
other projects in Table 2, but there was a very strong requirement for source
reliability, with an r.m.s. normalized emittance below 0.2 mm mrad for an
operating voltage of 80 kV (Table 5).

Table 5: TRIPS typical operating parameters. Parameter | Value
---|---
Total beam current | 60 mA
Proton fraction | 90%
Beam energy | 80 keV
Microwave power, at 2.45 GHz | 0.3–1 kW
Beam emittance, at 35 mA | 0.07 mm mrad
Gas flow | 0.4–0.6 sccm
Duty factor, at 35 mA | 99.8%
Reliability, at 35 mA | 99.8%

The major innovation consisted in the use of two movable coils permitting the
magnetic field profile to be varied. The plasma chamber dimension and the
four-step matching transformer were defined to get a uniformly dense plasma at
the extraction hole (6 or 8 mm diameter). The microwave coupling with the
matching transformer and the automatic tuning unit allowed operation with low
values of reflected power (below 5%) and a high electric field on the axis,
thus increasing proton fraction and current density, up to 200 mA cm-2. The
extraction system was designed in collaboration with Saclay, exploiting the
experience already gained at INFN-LNS for the design of extraction geometries
from plasma sources. Measurements with the 8 mm hole plasma electrode have
given results largely exceeding the TRASCO design current: up to 61 mA were
extracted at 80 kV and about 90% of the beam has been transported to the beam
stop.

Figure 11 shows the TRIPS source and Fig. 12 shows the experimental set-up.
The first section of the low-energy beam transfer line (LEBT) devoted to beam
analysis consists of a current transformer (DCCT1), a focusing solenoid, a
four-sector ring to measure beam misalignments and inhomogeneities, a second
current transformer (DCCT2) and an insulated 10 kW beam stop (BS), which
measures the beam current.

Figure 11: The TRIPS ion source on the 100 kV platform Figure 12: The
experimental set-up: (1) demineralizer; (2) 120 kV insulating transformer; (3)
19 inch rack for the power supplies and for the remote control system; (4)
magnetron and circulator; (5) directional coupler; (6) automatic tuning unit;
(7) gas box; (8) DCCT1; (9) solenoid; (10) turbomolecular pump; (11) DCCT2;
(12) quartz tube; (13) 10 kW beam stop.

Systematic measurements with movable coils have been carried out for different
positions and currents, by leaving the other parameters unchanged. From these
measurements it can be determined that the source is more sensitive to
variations in the extraction coil than in the injection one. The best
performance is clearly obtained when the two ECR zones are located exactly on
the boron nitride discs at the two ends of the plasma chamber. Figure 13 shows
the best obtained profile (the straight line represents the value of the
magnetic field corresponding to the resonance at 2.45 GHz).

Figure 13: Magnetic field optimization through changes in the coil current and
position (above) and ideal profile (below).

Systematic emittance measurements have been made with an emittance measurement
unit provided by the CEA-Saclay SILHI group, showing the effect of each
parameter on the beam emittance; more details are reported in the next
section.

###  2.6 Versatile Ion Source (VIS)

The TRIPS source exceeded all the requirements of the TRASCO project, but in
order to simplify it, the VIS source was built in 2006 [12]. In particular, in
the VIS source, the movable coils have been replaced with permanent magnets,
and the extraction geometry and extraction column have been simplified. With
these modifications it has been possible to avoid the high-voltage platform
and the insulating transformer, by insulating the gas pipe and the waveguide
line. All these changes decreased the high-voltage sparks and increased the
source reliability. All the devices for the remote control were placed at
ground potential, thus leaving only the plasma chamber and the permanent
magnets at high voltage. The compact dimensions have also resulted in better
and easier maintenance. The magnetic system consists of a set of three Vacodym
745 HR permanent magnets; they are packed together with two soft iron spacers
and they are supported by a stainless-steel tube. The layout of the VIS source
is reported in Fig. 14 [13].

Figure 14: A render view of the VIS source together with the focusing solenoid
Figure 15: VIS microwave line

The microwave line, in Fig. 15, is the result of an optimization study carried
out with tools for high-frequency structure simulation in order to reduce
microwave losses, simultaneously with an adequate matching of the waves to the
plasma chamber. A plasma is generated by means of the microwaves provided by a
2.45 GHz magnetron through a WR 340 (86.4 mm $\times$ 43.2 mm) waveguide
excited in the TE10 dominant mode. An automatic tuning unit adjusts the
modulus and phase of the incoming wave in order to match the plasma chamber
impedance with and without the plasma, and a dual-arm directional coupler is
used to measure the forward and the reflected power.

In TRIPS both the microwave line and the microwave generator are placed on the
high-voltage platform, while in VIS the microwave generator is placed at
ground potential. Then, in order to separate the high-voltage region from the
grounded one, a waveguide d.c. break has been designed and realized with the
support of the HFSS electromagnetic simulator. It is made of 31 aluminium
discs of a WR 340 waveguide insulated from one another by means of fibreglass.
The conductive parts will be fixed to voltages gradually decreasing from 80 kV
to ground voltage, still keeping the insertion loss low. The high-pressure
quartz window is placed before the WR 284 water-cooled copper bend in order to
avoid any damage due to back-streaming plasma electrons. Finally, a maximally
flat matching transformer has been inserted before the plasma chamber, shown
in Fig. 16, which is an optimized version of a similar device used in MIDAS
and TRIPS ion source. This realizes an impedance matching with the plasma
chamber and concentrates the electromagnetic field near the axis. The
enhancement of the electromagnetic field in the plasma chamber cavity
increases the plasma density locally and finally the ionization process.

Figure 16: Electric field amplitude at 2.45 GHz Figure 17: Magnet Figure 18:
VIS beam line

The ionic component of the plasma produced in the plasma chamber is then
extracted by means of a four-electrode extraction system. The low-energy beam
transport line (LEBT) allows beam analysis, and it consists of a focusing
solenoid, a four-sector diaphragm to measure the beam misalignments, a d.c.
current transformer, a 30∘ bending magnet (Fig. 17) and an insulated beam stop
to measure the beam current, shown in Fig. 18. The extraction system consists
of a plasma electrode made of molybdenum at 65 kV voltage, two water-cooled
grounded electrodes and a 3.5 kV negatively biased screening electrode
inserted between them, in order to avoid secondary electrons due to residual
gas ionization, back-streaming to the extraction area. The VIS extraction has
been optimized to work around 40 mA, fulfilling the requirement of high
brightness. The beam emittance measurements are described in the next section.
The beam availability has been further increased and damage to the electronics
because of high-voltage sparks is negligible.

##  3 Beam emittance measurements

The production of a high-quality beam has been, since the first measurements
made at CRNL by Taylor and Wills, one of the major challenges for such
sources, together with beam reliability. Over the years, many developments
have been carried out to improve these aspects, and the most important results
have been obtained through a deep optimization of the extraction geometry
together with an appropriate design of the low-energy beam transfer line.

###  3.1 SILHI beam emittance improvements

A significant step forward in this field, namely the production of a high-
quality beam, was made within the framework of the collaboration between INFN
and CEA, in which an innovative method based on the controlled injection of a
gas into the line was developed [14]. The idea is based on the fact that the
ions obtained from residual gas ionization are expelled from the centre of the
beam line, where the potential is positive, towards the wall. Electrons from
the wall are attracted towards the beam, so that the beam is compensated,
provided that the pressure is high enough to have an adequate number of
electrons (a compromise between beam losses and space-charge compensation is
to be found experimentally). According to that approach, the most effective
gases are the heaviest, which easily release a large number of electrons. If
$N$ hydrogen atoms per unit volume are required for optimum compensation (i.e.
if $N$ electrons neutralize the beam space charge), for a species that gives
$Z_{\rm eff}$ electrons when the atoms interact with the 95 keV proton beam,
the optimum number of atoms per unit volume is $N/Z_{\rm eff}$ (this clue
neglects the dissociation process, which does not require a large amount of
energy).

Experiments have been carried out by injecting different gases (H2, N2, 84Kr
and Ar) into the SILHI beam line through a leak valve placed after the LEBT
solenoid and comparing the emittance measurements at different pressures with
an extracted beam in range of 75–80 A. Two gauges (measuring $p_{1}$ and
$p_{2}$) are placed, respectively, at the extraction column exit and between
the sampler and the profiler in the diagnostic box (Fig. 10). In all the cases
considered here, a decrease of beam emittance has been observed with the beam
line pressure increase. These results have been explained by a higher degree
of space-charge compensation as confirmed by a series of measurements carried
out in collaboration with the Los Alamos National Laboratory (LANL).

Figure 19: Emittance plot after injecting Ar into the beam line:
$p_{1}=4.5\times 10^{-5}$ Torr, $p_{2}=4.4\times 10^{-5}$ Torr, $\epsilon_{\rm
rms}=0.124$ mm mrad.  Figure 20: Emittance plot after injecting N2 into the
beam line: $p_{1}=4.5\times 10^{-5}$ Torr, $p_{2}=4.5\times 10^{-5}$ Torr,
$\epsilon_{\rm rms}=0.13$ mm mrad.  Figure 21: Emittance plot after injecting
H2 into the beam line: $p_{1}=5\times 10^{-5}$ Torr, $p_{2}=4.9\times 10^{-5}$
Torr, $\epsilon_{\rm rms}=0.198$ mm mrad.

As observed, the behaviour depends upon the atomic mass of the species
injected. In particular, an r.m.s. normalized emittance of 0.1 mm mrad has
been obtained with 84Kr injected into the beam line ($p_{1}=3\times 10^{-5}$
Torr). The emittance is reduced by a factor of 3 with respect to the value
0.33 mm mrad measured without gas ($p_{1}=1.8\times 10^{-5}$ Torr). Emittance
values below 0.15 mm mrad have been easily obtained also using Ar with
pressure values of the first gauge around $2.5\times 10^{-5}$ Torr. For this
gas, the minimum value of r.m.s. normalized emittance of 0.125 mm mrad has
been measured (see Fig. 19). A lower efficacy is obtained with N2 and H2
injection: in particular, with N2 injection we have measured 0.13 mm mrad at
relatively high pressure ($p_{1}=4.5\times 10^{-5}$ Torr; see Fig. 20), while
for H2 the minimum value of emittance obtained is 0.198 mm mrad, as shown in
Fig. 21.

Figure 22: Emittance picture without injecting 84Kr into the beam line:
$\epsilon_{\rm{rms}}=0.33$ mm mrad, $p_{1}=8\times 10^{-5}$ Torr,
$p_{2}=1.2\times 10^{-5}$ Torr.  Figure 23: Emittance picture after injecting
84Kr into the beam line: $\epsilon_{\rm{rms}}=0.11$ mm mrad, $p_{1}=3.5\times
10^{-5}$ Torr, $p_{2}=2.7\times 10^{-5}$ Torr.

Figures 22 and 23 show the emittance measurement obtained with 84Kr. It must
be pointed out that the emittance pictures become straight with the gas
injection and present a lower beam size and lower aberrations. This is also
evident during the measurement because each beamlet selected by the sampler
has a lower width and a higher intensity.

Figure 24: Space-charge compensation with H2, N2, Ar and Kr Figure 25: Losses
of the beam current

Figure 24 summarizes the results obtained and in all cases a decrease of beam
emittance has been observed with the increase of beam line pressure. Figure 25
summarizes also the losses at the end of the beam line at the different
pressures, losses that are less than 5% for masses heavier than Ar.

###  3.2 TRIPS beam emittance improvements

The requirement in terms of proton current for the TRIPS source (Table 2) was
significantly lower than that for the SILHI source, and therefore (at the
nominal beam current) gas injection has been not necessary to achieve the
required goal. However, also in this case this method has been important to
decrease the emittance at higher currents.

In this case the measured values were coherent with the calculated ones and
close to those predicted by the equation

$\epsilon_{\rm{normal,rms}}=\frac{1}{4}\times
0.0653r\left(\frac{kT}{A}\right)^{1/2}\qquad\quad(\rmpi{\>}\mathrm{mm}{\>}\mathrm{mrad}),$
(1)

where $r$ is the radius of the extraction aperture in millimetres, $A$ is the
rest mass of the ion in atomic units and $kT$ is the ion temperature in
electronvolts. Assuming an ion temperature of 1 eV and with an extraction hole
of 3 mm radius, the expected r.m.s. normalized emittance is circa 0.05 mm
mrad. The emittance values measured are close to the theoretical one for a
beam current close to the nominal value, while at higher currents the space-
charge effects play an important role in the beam blowup, and a gas must be
added into the beam line to decrease the beam emittance.

Measurements [15] have been carried out at different current levels (between
30 and 50 mA); for a fixed current value, we have explored the effect of some
parameters such as puller voltage and solenoid current on the beam emittance.
A first observation was that the emittance slightly changes with the puller
voltage for a fixed current. Measurements performed on a 42 mA beam, with the
solenoid fixed at 290 A, a hydrogen flux of 0.49 sccm and a discharge power of
650 W, show a decrease of emittance from 0.208 to 0.172 mm mrad just by
increasing the voltage drop between the extraction and puller electrode from
38 to 43 kV. The optimal operating value ranges between 40 and 42 kV;
unfortunately, for higher voltage HV discharges occur and it was not possible
to operate the source safely. Another important observation was obtained by
looking at the evolution of the beam emittance by changing the solenoid
strength for fixed source conditions.

Figure 26: The r.m.s. normalized emittance versus beam current

Measurements were carried out on a 32 mA beam with the puller fixed at 40 kV,
the discharge power at 550 W and the hydrogen flux at 0.45 sccm; the emittance
changes between 0.069 and0.137 mm mrad by decreasing the solenoid current.
This in turn means that the position of the crossover along the beam line is
extremely important for the optimum coupling with the RFQ, as at the crossover
the space-charge forces are more important, as confirmed by the measurements
with a four-grid analyser. An optimal value of solenoid current for the
operation with the EMU around 280 A has been found to avoid an excessive power
density over the EMU sampler. Finally Fig. 26 shows the evolution of the
emittance with the beam current increase; this confirms the influence of beam
line pressure on the space-charge compensation (and thus on the emittance) by
means of the injection of a controlled amount of argon into the beam line, as
already done for the SILHI source for different gases.

Figure 27: Proton beam emittance measured without gas ($P_{\rm
source}=1.5\times 10^{-5}$ mbar, $P_{\rm line}=8.8\times 10^{-6}$ mbar,
$I_{\rm extr}=32{\>}$ mA, $\epsilon_{\rm norm}=0.069$ mm mrad).

The measures have been carried out for fixed solenoid current (280 A) and
puller voltage (40 kV) and by changing the discharge power from 450 to 650 W
and the hydrogen flux from 0.45 to 0.59 sccm. It has been observed that the
space-charge forces play a role for currents greater than 40 mA; the
background pressure in that condition was around $1.5\times 10^{-5}$ mbar in
the extraction column and around $8.5\times 10^{-6}$ mbar in the beam line. By
adding an argon leak, the pressure increased to $2.1\times 10^{-5}$ mbar in
the whole line, and a 30% beam emittance decrease was obtained without
significant beam losses.

Figure 27 shows the emittance measured for the nominal current, while Figs. 28
and 29 show the emittance patterns for higher currents with and without gas
injection.

Figure 28: Proton beam emittance measured without Ar ($P_{\rm
source}=1.9\times 10^{-5}$ mbar, $P_{\rm line}=1.1\times 10^{-6}$ mbar,
$I_{\rm extr}=51$ mA, $\epsilon_{\rm norm}=0.283$ mm mrad).  Figure 29: Proton
beam emittance measured with Ar ($P_{\rm source}=2.45\times 10^{-5}$ mbar,
$P_{\rm line}=2.2\times 10^{-5}$ mbar, $I_{\rm extr}=47$ mA,
$\epsilon_{norm}=0.178$ mm mrad).

In these cases the emittance growth is justified because of the lower space-
charge compensation; then the benefits of argon injection are visible. In fact
such gas injection improves the compensation and leads to lower value of
emittance.

##  4 Future perspectives

In the off-resonance microwave ion sources, the ECR is not a predominant
condition for plasma generation; in fact, in this case higher electron
densities can be obtained by means of a microwave discharge at higher magnetic
field value and higher pressures. The plasma–cavity system is a distributed
parameter resonant circuit, since the length of the plasma is of the same
order of magnitude as the free-space electromagnetic wavelength. Then,
differently from the ECR ion sources, the cavity diameter and excitation
frequency are chosen to allow only one cavity mode to be excited for a given
cavity length. In this case the power coupling into a given mode is usually
accomplished by means of tuning stubs in order to achieve the necessary
impedance match. The steady-state microwave discharge is characterized by the
equality between the power absorbed by the plasma and the lost power, mainly
due to inelastic ionization, excitation collisions and energy transmission out
of the active discharge region. The power absorbed by the plasma is given by
one-half of the real part of the complex Poynting vector, and therefore it
depends on the electric field strength in the plasma. In order to optimize the
coupling for a given mode, the maximization of that electric field is
therefore important. A waveguide transformer (usually maximally flat design)
is widely used for such purposes for most microwave sources in operation
nowadays. Such a device realizes a progressive matching between the waveguide,
normally operating in the dominant mode, and the equivalent impedance of the
plasma-filled chamber, also concentrating the electric field at its centre.
Figure 30 shows a comparison of the electric field on the plasma chamber axis
in the case that no transformer is used or by employing the TRASCO Intense
Proton Source (TRIPS) or Versatile Ion Source (VIS) [16]. The excitation
frequency is 2.45 GHz in all cases and it can be observed that an increase by
a factor of 2 can be obtained, in the frequency range of circa 400 MHz, by
appropriately shaping the waveguide ridges as discussed in detail elsewhere
[17].

Figure 30: Comparison of the electric field on the plasma chamber axis in
different cases

Therefore, both matching transformers concentrate the electric field around
its axis in a smaller region than the original WR 284 cross-section. This
feature has been observed in the traces on the boron nitride disc at the
injection side of the TRIPS and VIS plasma chambers, and it is particularly
remarkable for the production of ion beams because the extraction system is
centred on the axis of the plasma chamber and any enhancement of the plasma
density at the centre of the cavity leads to a similar increase in the ion
beam current. Even higher enhancements are made possible with such a device
with different designs or by extending the ridge also within the span of the
plasma chamber. Nowadays most of the high-intensity ion sources use automatic
tuning units to optimize the power coupling into the operational mode and
waveguide transformers similar to those previously described to enhance the
plasma density inside the source. The increase in the latter parameter is
mandatory for further increase in the produced currents.

Usually in microwave discharge ion sources used for intense beam production,
the microwaves are provided by means of a waveguide located longitudinally
with respect to the chamber axis. In these devices, the axis of symmetry of
the magnetic field coincides with the chamber axis; this means that the
injected wave is mainly an O or R wave when it propagates inside the plasma.
However, because of the complex structure of the magnetic field lines, and
because of possible reflections at the chamber walls, these modes may convert
each other, and also X modes can be generated somewhere inside the cavity,
through an O–X conversion. At that time, the X waves can be directly converted
into a Bernstein electrostatic wave (BW) at the upper hybrid resonance (UHR)
layer. BWs are a great advantage, as they travel into the plasma without any
cutoff and provide heating even in the case of overdense plasmas. However, if
the injection angle of the O mode is not optimal, the BW creation process has
a low efficiency. The variations of the power and the background pressure
change the plasma properties, and in turn affect the conversion efficiency. As
BWs are known to be absorbed at cyclotron harmonics, the electrostatic wave
generation in an MDIS is possible and can be used as an alternative plasma
heating method. In order to increase the BW creation efficiency, the proper
injection angle is needed: this can be achieved by using single cut antennas
(waveguides) launching O waves in the right direction with respect to the
magnetic field lines. In this way O–X–B conversion is possible, as observed in
Ref. [18]. More details are discussed in Ref. [19]. A detailed investigation
of this new approach to plasma heating in an MDIS may make it possible to take
a large step towards higher extracted beam currents: in fact the key parameter
in MDISs is the electron density, more so than the temperature (low charged
ions are usually required), and by means of electrostatic wave heating we
should be able to overcome the cutoff density at 2.45 GHz of a factor of 5 or
6.

## References

  * [1] B. Wolf, _Handbook of Ion Sources_ (CRC Press, Boca Raton, 1995).
  * [2] N. Sakudo, _Rev. Sci. Instrum._ 49 (1978) 940.
  * [3] J. Ishikawa, Y. Takeiri and T. Takagi, _Rev. Sci. Instrum._ 55 (1984) 449.
  * [4] I.G. Brown, _The Physics and Technology of Ion Sources_ (Wiley-VCH, Weinheim, 2004).
  * [5] T. Taylor, _Rev. Sci. Instrum._ 63 (4), April (1992), 2507
  * [6] J. Ishikawa, Y. Takeiri and T. Takagi, _Rev. Sci. Instrum._ 55 (1994) 449.
  * [7] J. Sherman, A. Arvin, L. Hansborough, D. Hodgkins, E. Meyer, J.D. Schneider, H.V. Smith Jr., M. Stettler, R.R. Stevens Jr., M. Thuot, T. Zaugg and R. Ferdinand, Status report on a dc 130 mA, 75 keV proton injector (invited). _Rev. Sci. Instrum._ 69 (2) (1998) 1003.
  * [8] P.-Y. Beauvais et al., _Rev. Sci. Instrum._ 71(3) (2000) 1413–1416.
  * [9] J.-M. Lagniel et al. _Rev. Sci. Instrum._ 71(2) (2000) 830–835.
  * [10] R. Gobin et al. _Rev. Sci. Instrum._ 73, (2002), 922
  * [11] L. Celona, G. Ciavola, S. Gammino, R. Gobin and R. Ferdinand, TRIPS: the high intensity proton source for the TRASCO project. _Rev. Sci. Instrum._ 71 (2000) 771–773.
  * [12] G. Ciavola, L. Celona, S. Gammino, M. Presti, L. Ando, S. Passarello, X.Zh. Zhang, F. Consoli, F. Chines, C. Percolla, V. Calzona and M. Winkler, A version of the Trasco Intense Proton Source optimized for accelerator driven system purposes. _Rev. Sci. Instrum._ 75 (2004) 1453–1456,.
  * [13] F. Maimone, G. Ciavola, L. Celona, S. Gammino, D. Mascali, N. Gambino, R. Miracoli, F. Chines, S. Passarello, G. Gallo and E. Zappala, Status of the Versatile Ion Source VIS, Proc. 11th European Particle Accelerator Conf. (EPAC08), Genoa, Italy, 2008, MOPC151, 430.
  * [14] R. Gobin, P.-Y. Beauvais, R. Ferdinand, P.-A. Leroy, L. Celona, G. Ciavola and S. Gammino, Improvement of beam emittance of the CEA high intensity proton source SILHI. _Rev. Sci. Instrum._ 70 (6) (1999) 2652.
  * [15] L. Celona, G. Ciavola, S. Gammino, R. Gobin and R. Ferdinand, Status of the TRASCO proton source and emittance measurements. _Rev. Sci. Instrum._ 75 (2003) 5.
  * [16] L. Celona, G. Ciavola, S. Gammino, F. Chines, M. Presti, L. Ando, X.H. Guo, R. Gobin and R. Ferdinand, _Rev. Sci. Instrum._ 75 (2004) 1423.
  * [17] L. Celona et al., _Rev. Sci. Instrum._ 81 (2010) 02A333.
  * [18] H.P. Laqua, W7-AS Team and ECRH Group, _Plasma Phys. Controlled Fusion_ 41 (1999) A273.
  * [19] H. Laqua, M. Otte, Y. Podoba, D. Mascali, S. Gammino, L. Celona, G. Ciavola, N. Gambino, R. Miracoli and F. Maimone, Study of the Bernstein wave heating in the WEGA stellarator plasma and possible application to ECRIS, INFN, Report No. INFN/AE-09/1 (2009).


††thanks: Deceased††thanks: Deceased††thanks: Deceased

# Magnetic-induced force noise in LISA Pathfinder free-falling test masses

M Armano  European Space Technology Centre, European Space Agency, Keplerlaan
1, 2200 AG Noordwijk, The Netherlands  H Audley  Albert-Einstein-Institut,
Max-Planck-Institut für Gravitationsphysik und Leibniz Universität Hannover,
Callinstraße 38, 30167 Hannover, Germany  J Baird  APC, Univ Paris Diderot,
CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris Cité, France  P Binetruy
APC, Univ Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris
Cité, France  M Born  Albert-Einstein-Institut, Max-Planck-Institut für
Gravitationsphysik und Leibniz Universität Hannover, Callinstraße 38, 30167
Hannover, Germany  D Bortoluzzi  Department of Industrial Engineering,
University of Trento, via Sommarive 9, 38123 Trento, and Trento Institute for
Fundamental Physics and Application / INFN  E Castelli  Dipartimento di
Fisica, Università di Trento and Trento Institute for Fundamental Physics and
Application / INFN, 38123 Povo, Trento, Italy  A Cavalleri  Istituto di
Fotonica e Nanotecnologie, CNR-Fondazione Bruno Kessler, I-38123 Povo, Trento,
Italy  A Cesarini  DISPEA, Università di Urbino “Carlo Bo”, Via S. Chiara, 27
61029 Urbino/INFN, Italy  A M Cruise  The School of Physics and Astronomy,
University of Birmingham, Birmingham, UK  K Danzmann  Albert-Einstein-
Institut, Max-Planck-Institut für Gravitationsphysik und Leibniz Universität
Hannover, Callinstraße 38, 30167 Hannover, Germany  M de Deus Silva  European
Space Astronomy Centre, European Space Agency, Villanueva de la Cañada, 28692
Madrid, Spain  I Diepholz  Albert-Einstein-Institut, Max-Planck-Institut für
Gravitationsphysik und Leibniz Universität Hannover, Callinstraße 38, 30167
Hannover, Germany  G Dixon  The School of Physics and Astronomy, University of
Birmingham, Birmingham, UK  R Dolesi  Dipartimento di Fisica, Università di
Trento and Trento Institute for Fundamental Physics and Application / INFN,
38123 Povo, Trento, Italy  L Ferraioli  Institut für Geophysik, ETH Zürich,
Sonneggstrasse 5, CH-8092, Zürich, Switzerland  V Ferroni  Dipartimento di
Fisica, Università di Trento and Trento Institute for Fundamental Physics and
Application / INFN, 38123 Povo, Trento, Italy  E D Fitzsimons  The UK
Astronomy Technology Centre, Royal Observatory, Edinburgh, Blackford Hill,
Edinburgh, EH9 3HJ, UK  M Freschi  European Space Astronomy Centre, European
Space Agency, Villanueva de la Cañada, 28692 Madrid, Spain  L Gesa  Institut
de Ciències de l’Espai (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n,
08193 Cerdanyola del Vallès, Spain  Institut d’Estudis Espacials de Catalunya
(IEEC), C/ Gran Capità 2-4, 08034 Barcelona, Spain  D Giardini  Institut für
Geophysik, ETH Zürich, Sonneggstrasse 5, CH-8092, Zürich, Switzerland  F
Gibert  Dipartimento di Fisica, Università di Trento and Trento Institute for
Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy
isardSAT SL, Marie Curie 8-14, 08042 Barcelona, Catalonia, Spain  R Giusteri
Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik und
Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany  C
Grimani  DISPEA, Università di Urbino “Carlo Bo”, Via S. Chiara, 27 61029
Urbino/INFN, Italy  J Grzymisch  European Space Technology Centre, European
Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands  I Harrison
European Space Operations Centre, European Space Agency, 64293 Darmstadt,
Germany  M-S Hartig  Albert-Einstein-Institut, Max-Planck-Institut für
Gravitationsphysik und Leibniz Universität Hannover, Callinstraße 38, 30167
Hannover, Germany  G Heinzel  Albert-Einstein-Institut, Max-Planck-Institut
für Gravitationsphysik und Leibniz Universität Hannover, Callinstraße 38,
30167 Hannover, Germany  M Hewitson  Albert-Einstein-Institut, Max-Planck-
Institut für Gravitationsphysik und Leibniz Universität Hannover, Callinstraße
38, 30167 Hannover, Germany  D Hollington  High Energy Physics Group, Physics
Department, Imperial College London, Blackett Laboratory, Prince Consort Road,
London, SW7 2BW, UK  D Hoyland  The School of Physics and Astronomy,
University of Birmingham, Birmingham, UK  M Hueller  Dipartimento di Fisica,
Università di Trento and Trento Institute for Fundamental Physics and
Application / INFN, 38123 Povo, Trento, Italy  H Inchauspé  APC, Univ Paris
Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris Cité, France
Department of Mechanical and Aerospace Engineering, MAE-A, P.O. Box 116250,
University of Florida, Gainesville, Florida 32611, USA  O Jennrich  European
Space Technology Centre, European Space Agency, Keplerlaan 1, 2200 AG
Noordwijk, The Netherlands  P Jetzer  Physik Institut, Universität Zürich,
Winterthurerstrasse 190, CH-8057 Zürich, Switzerland  N Karnesis  APC, Univ
Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris Cité, France
B Kaune  Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik
und Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany  N
Korsakova  Observatoire de la Côte d’Azur, Boulevard de l’Observatoire CS
34229 - F 06304 NICE, France  C J Killow  SUPA, Institute for Gravitational
Research, School of Physics and Astronomy, University of Glasgow, Glasgow, G12
8QQ, UK  L Liu  Dipartimento di Fisica, Università di Trento and Trento
Institute for Fundamental Physics and Application / INFN, 38123 Povo, Trento,
Italy  J A Lobo  Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB,
Carrer de Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain  Institut
d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034 Barcelona,
Spain  J P López-Zaragoza<EMAIL_ADDRESS>Institut de Ciències de l’Espai
(ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Cerdanyola del
Vallès, Spain  Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran
Capità 2-4, 08034 Barcelona, Spain  R Maarschalkerweerd  European Space
Operations Centre, European Space Agency, 64293 Darmstadt, Germany  D Mance
Institut für Geophysik, ETH Zürich, Sonneggstrasse 5, CH-8092, Zürich,
Switzerland  V Martín  Institut de Ciències de l’Espai (ICE, CSIC), Campus
UAB, Carrer de Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain  Institut
d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034 Barcelona,
Spain  J Martino  APC, Univ Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris,
Sorbonne Paris Cité, France  L Martin-Polo  European Space Astronomy Centre,
European Space Agency, Villanueva de la Cañada, 28692 Madrid, Spain  F Martin-
Porqueras  European Space Astronomy Centre, European Space Agency, Villanueva
de la Cañada, 28692 Madrid, Spain  P W McNamara  European Space Technology
Centre, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The
Netherlands  J Mendes  European Space Operations Centre, European Space
Agency, 64293 Darmstadt, Germany  L Mendes  European Space Astronomy Centre,
European Space Agency, Villanueva de la Cañada, 28692 Madrid, Spain  N
Meshksar  Institut für Geophysik, ETH Zürich, Sonneggstrasse 5, CH-8092,
Zürich, Switzerland  M Nofrarias<EMAIL_ADDRESS>Institut de Ciències
de l’Espai (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193
Cerdanyola del Vallès, Spain  Institut d’Estudis Espacials de Catalunya
(IEEC), C/ Gran Capità 2-4, 08034 Barcelona, Spain  S Paczkowski  Albert-
Einstein-Institut, Max-Planck-Institut für Gravitationsphysik und Leibniz
Universität Hannover, Callinstraße 38, 30167 Hannover, Germany  M Perreur-
Lloyd  SUPA, Institute for Gravitational Research, School of Physics and
Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK  A Petiteau  APC, Univ
Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne Paris Cité, France
P Pivato  Dipartimento di Fisica, Università di Trento and Trento Institute
for Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy  E
Plagnol  APC, Univ Paris Diderot, CNRS/IN2P3, CEA/lrfu, Obs de Paris, Sorbonne
Paris Cité, France  J Ramos-Castro  Department d’Enginyeria Electrònica,
Universitat Politècnica de Catalunya, 08034 Barcelona, Spain  Institut
d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034 Barcelona,
Spain  J Reiche  Albert-Einstein-Institut, Max-Planck-Institut für
Gravitationsphysik und Leibniz Universität Hannover, Callinstraße 38, 30167
Hannover, Germany  F Rivas  Institut de Ciències de l’Espai (ICE, CSIC),
Campus UAB, Carrer de Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain
Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034
Barcelona, Spain  D I Robertson  SUPA, Institute for Gravitational Research,
School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK
G Russano  Dipartimento di Fisica, Università di Trento and Trento Institute
for Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy  D
Serrano<EMAIL_ADDRESS>Institut de Ciències de l’Espai (ICE, CSIC),
Campus UAB, Carrer de Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain
Institut d’Estudis Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034
Barcelona, Spain  J Slutsky  Gravitational Astrophysics Lab, NASA Goddard
Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 USA  C F
Sopuerta  Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, Carrer de
Can Magrans s/n, 08193 Cerdanyola del Vallès, Spain  Institut d’Estudis
Espacials de Catalunya (IEEC), C/ Gran Capità 2-4, 08034 Barcelona, Spain  T
Sumner  High Energy Physics Group, Physics Department, Imperial College
London, Blackett Laboratory, Prince Consort Road, London, SW7 2BW, UK  D
Texier  European Space Astronomy Centre, European Space Agency, Villanueva de
la Cañada, 28692 Madrid, Spain  J I Thorpe  Gravitational Astrophysics Lab,
NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 USA
D Vetrugno  Dipartimento di Fisica, Università di Trento and Trento Institute
for Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy  S
Vitale  Dipartimento di Fisica, Università di Trento and Trento Institute for
Fundamental Physics and Application / INFN, 38123 Povo, Trento, Italy  G
Wanner  Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik
und Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany  H
Ward  SUPA, Institute for Gravitational Research, School of Physics and
Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK  P J Wass  High Energy
Physics Group, Physics Department, Imperial College London, Blackett
Laboratory, Prince Consort Road, London, SW7 2BW, UK  Department of Mechanical
and Aerospace Engineering, MAE-A, P.O. Box 116250, University of Florida,
Gainesville, Florida 32611, USA  W J Weber  Dipartimento di Fisica, Università
di Trento and Trento Institute for Fundamental Physics and Application / INFN,
38123 Povo, Trento, Italy  L Wissel  Albert-Einstein-Institut, Max-Planck-
Institut für Gravitationsphysik und Leibniz Universität Hannover, Callinstraße
38, 30167 Hannover, Germany  A Wittchen  Albert-Einstein-Institut, Max-Planck-
Institut für Gravitationsphysik und Leibniz Universität Hannover, Callinstraße
38, 30167 Hannover, Germany  P Zweifel  Institut für Geophysik, ETH Zürich,
Sonneggstrasse 5, CH-8092, Zürich, Switzerland

###### Abstract

LISA Pathfinder was a mission designed to test key technologies required for
gravitational wave detection in space. Magnetically driven forces play a key
role in the instrument sensitivity in the low-frequency regime, which
corresponds to the measurement band of interest for future space-borne
gravitational wave observatories. Magnetic-induced forces couple to the test
mass motion, introducing a contribution to the relative acceleration noise
between the free falling test masses. In this Letter we present the first
complete estimate of this term of the instrument performance model. Our
results set the magnetic-induced acceleration noise during the February 2017
noise run of $\rm 0.25_{-0.08}^{+0.15}\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz and
$\rm 1.01_{-0.24}^{+0.73}\,fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz. We also discuss
how the non-stationarities of the interplanetary magnetic field can affect
these values during extreme space weather conditions.

## Introduction

LISA Pathfinder [1, 2] was an ESA mission with NASA contributions designed to
test key technologies for the future gravitational-wave observatory in space,
the Laser Interferometry Space Antenna (LISA) [3]. LISA Pathfinder was
launched on December 3rd 2015 and, after a one-month cruise phase, reached the
L1 Lissajous orbit where it operated until July 2017. The main scientific
result of the mission was to demonstrate the level of relative acceleration
between free falling test masses required to detect gravitational wave from
space [4, 5]. The main experiment on-board the LISA Pathfinder mission
consisted of two gold-platinum test masses sitting within a 6 degree-of-
freedom capacitive position sensor and actuator, the Gravitational Reference
Sensor (GRS) [6, 7]. The position and orientation of the test masses was
continuously monitored by a high precision interferometric readout system, the
Optical Metrology System (OMS) [8, 9]. These measurements were fed to the on-
board control system in charge of isolating the test mass from the
perturbations coming from outer space [10]. This architecture, the so called
_drag free_ control loop, ensured the required free fall purity of one of the
test masses by means of a continuous actuation on the spacecraft attitude
through the micro-Newton propulsion system [11]. The drag free control loop
was not intended to isolate the test mass free fall from forces arising
internally to the spacecraft. Instead, mission and payload were designed to
enforce that these effects did not affect the instrument performance. This had
implications, for instance, in the selected orbit —the L1 orbit allowed a very
thermally stable environment as well as reduced gravitational field gradients—
or several design drivers in the payload to isolate the test masses from
potential disturbing forces, typically of thermal or magnetic origin.

The LISA Pathfinder Data and Diagnostics Subsystem (DDS) included a set of
high precision sensors on-board precisely to monitor environmental
disturbances with potential impact in the main scientific result of the
mission, the relative acceleration between the free falling test masses. The
DDS was composed by a temperature measurement subsystem [12, 13], a magnetic
diagnostic subsystem [14, 15] and a radiation monitor [16, 17, 18, 19]. A
crucial role of the DDS was to split up the experiment performance into
different contributions to help on the design for future space-borne
gravitational wave detectors. For that reason, it also carried out a set of
heaters and coils that were activated during flight operations to characterise
the response of the instrument to intended environment disturbances. In this
Letter we report on the results obtained in the estimate of the magnetic-
induced contribution to the differential force noise of the test masses.

## Magnetically induced force noise contribution

Magnetic fluctuations couple into the dynamics of the free falling test masses
on board the satellite acting as a dipole embedded in a magnetic field

$\displaystyle\mathbf{F}$
$\displaystyle=\left\langle\left(\mathbf{M}\cdot\mathbf{\nabla}\right)\mathbf{B}+\frac{\chi\rm{V}}{\mu_{0}}\,\left[\left(\mathbf{B}\cdot\mathbf{\nabla}\right)\mathbf{B}\right]\right\rangle,$
(1)

where in our notation bold letters stands for vectors, being $\mathbf{M}$ the
3-dimensional intrinsic remanent moment of the magnetic dipole, $\chi$ its
magnetic susceptibility and $\mathbf{B}$ the surrounding magnetic field. The
right angle brackets denote TM volume, V, average of the enclosed quantity:
$\left\langle\ldots\
\right\rangle\equiv\dfrac{1}{\rm{V}}\int_{\rm{V}}\,(\ldots)\,d^{3}x$. This
expression can be further expanded [20], however in this Letter we will be
interested in the noise contributions mainly focusing on the x-component which
is the most sensitive axis, providing the main scientific output of the
instrument. Under reasonable assumptions –homogeneity and stationarity of the
test mass properties– we can express the main contributions to the
acceleration noise budget as

$\displaystyle S_{F,x}(\omega)$ $\displaystyle=$
$\displaystyle\left(\frac{\chi V}{\mu_{o}}\left<\mathbf{\nabla
B_{x}}\right>\right)^{2}S_{\mathbf{B}}(\omega)+$ (2) $\displaystyle+$
$\displaystyle\left(\mathbf{\left<M\right>}+\frac{\chi
V}{\mu_{0}}\left<\mathbf{B_{x}}\right>\right)^{2}S_{\mathbf{\nabla
B_{x}}}(\omega)$

Figure 1: Magnetic elements of the LPF DDS: 2 coils and 4 tri-axial fluxgate
magnetometers. The axis represents the spacecraft reference system frame.

where $\rm S(\omega)$ stands for the Power Spectral Density (PSD). The first
term in Eq. (2) is the dominant one in the low frequency regime, since it
couples fluctuations of the magnetic field —with a $f^{-1}$ behaviour due to
the interplanetary contribution— through an effective coupling
$\sim\chi\left|\mathbf{\nabla B_{x}}\right|$. Precisely this coupling factor
explains the stringent requirements set on the magnetic field gradient value
generated by units on the spacecraft in the test mass location. Notice that
while the magnetic susceptibility is a test mass property and, therefore,
difficult to modify after the design phase for it to be as low as possible,
reducing a potential gradient in the test mass location has an equal direct
effect in the reduction of this leading term in the magnetic noise
contribution. The second term in Eq. (2) have a lesser impact in the low
frequency band since the fluctuations associated with the gradient of the
magnetic field show a flat spectrum, i.e. $\rm S_{\mathbf{\nabla
B_{x}}}(\omega)\sim ct.$, we find this contribution to be orders of magnitude
below.

## Determination of magnetic parameters

The magnetic diagnostic subsystem on-board LISA Pathfinder consisted of four
tri-axial magnetometers and two induction coils. The two induction coils had a
radius of 56.5 mm and were built with 2400 windings of a copper alloy mounted
on a titanium support, 85.5 mm away from the test mass. Both coils were
aligned with the axis joining both test masses so that the generated magnetic
field had axial symmetry and driven by a dedicated high stability current
driver to ensure that high precision magnetic forces were produced [14]. An
extensive campaign of experiments were conducted to study magnetically-induced
forces on the test masses during flight operations by applying controlled
magnetic-induced forces in the test mass [21]. The result of these suite of
experiments can be summarised in two type of parameters as we show in Table 1.
A first set correspond to _intrinsic_ properties of the test mass, the
magnetic susceptibility ($\chi$) and the remanent magnetic moment
($\mathbf{M}$) which obviously determine the reaction of the test mass to any
applied magnetic field. A second set of parameters correspond to _extrinsic_
parameters to the test mass, the background magnetic field $\rm B_{\rm
back.,x}$ and magnetic field gradient $\rm\nabla_{x}B_{\rm back.,x}$, which
also contribute to the test mass force when an external magnetic field is
applied.

Parameter | Value
---|---
$\chi(\times 10^{-5})$ | $-3.3723\pm 0.0069$
$\rm M_{\rm x}\,[nAm^{2}]$ | $0.140\pm 0.138$
$\rm M_{\rm y}\,[nAm^{2}]$ | $0.178\pm 0.025$
$\rm M_{\rm z}\,[nAm^{2}]$ | $0.095\pm 0.010$
$\rm B_{\rm back.,x}[nT]$ | $414\pm 74$
$\rm\nabla_{x}B_{\rm back.,x}[nTm^{-1}]$ | $-7400\pm 2100$
Table 1: TM1 magnetic parameters, measured in [21], that will be used for the
calculation of the $\Delta g$ disturbances by magnetic forces.

The magnetic susceptibility was estimated at different frequencies during in-
flight experiments. We notice that the relevant impact in the noise
contribution will be entering our estimates in the LISA Pathfinder band, i.e.
in a low enough frequency regime where we can safely treat this parameter as a
constant value since, for the LISA Pathfinder test masses, the susceptibility
cut-off frequency is expected around the 630 Hz [22, 23]. Hence, for our
calculations we will consider our best estimate, obtained at f = 5 mHz. The
value for the three components of the remanent magnetic moment are shown in
Table 1. All results were only measured for test mass #1 due to the
malfunctioning of the coil near the other test mass. We note here that,
despite the high relative error carried by the measurement these are the most
precise values obtained for the remanent moment of the test masses. The
dedicated measurements on-ground could only find an upper limit of 4 $\rm
nAm^{2}$, i.e. one order of magnitude above the ones presented here.

Figure 2: Noise projection of the magnetic induced forces in the free-falling
test masses relative acceleration. In blue the $S^{1/2}_{\Delta g}$ from Feb.
17th to Mar. 2nd 2017. In red the $\rm S^{1/2}_{\mathbf{B}}$ acceleration
projection from the measurements of the magnetometers on-board during the same
noise run. Black and purple dots represent an averaging of the spectra and the
latter includes the uncertainty propagation after applying Eq. (2).

When exerting a magnetic induced force with the coil we are able to recover
the background magnetic field gradient, since it will add up to the magnetic
field induced by the coil. The experiments on-board can only estimate the
x-component for this contribution. The value obtained for TM1 during in-flight
experiments, $\rm\nabla_{x}B_{\rm back.,x}=(-7400\pm 2100)\,nT/m$, points
towards this contribution being originated in the thermistors attached to the
external wall of the GRS Electrode Housing. These NTC (Negative Temperature
Coefficient) sensors are manufactured using materials that can show
ferromagnetic behaviour. Despite undergoing a degaussing process prior to
their assembly in the satellite, their close proximity to the test mass
—roughly 13 mm— makes them prone to create a local gradient [24]. It is worth
noting here that the estimates of $\rm B_{\rm back.,x}$ and
$\rm\nabla_{x}B_{\rm back.,x}$ obtained during the experiments with coils on-
board are the most precise that can be obtained in the test mass location,
since magnetometers must be located sufficiently far from the test mass so
that the magnetic field they generate do not perturb the test mass dynamics.

Given that the X-component of the local gradient is the only one measurable,
we are forced to extrapolate these results to the Y and Z component and to the
other test mass as well. To do so, a Monte Carlo (MC) simulation was performed
with test mass #1 and all eight NTCs surrounding it. For each NTC the
remanence was randomly selected within the values [5$\times 10^{-7}$, 5$\times
10^{-5}$] Am2, in accordance with the range of magnetic moments measured for
these sensors during on-ground characterisation, and its orientation chosen at
random in spherical coordinates. The magnetic field gradients across the
volume of the test masses were found to be Gaussian distributed around zero
with 5$\mu$T/m of standard deviation (for all components). To account that the
LPF interferometric measurements involved the relative differences in
positions of both test masses, the MC uncertainties were multiplied by a
factor of $\sqrt{2}$. Thus, the estimated total magnitude of the background
magnetic field gradient was given mainly by $\nabla_{x}B_{\rm back.,x}$, as
the other two components ($\nabla_{y}B_{\rm back.,x}$ and $\nabla_{z}B_{\rm
back.,x}$) obtained from the simulation were negligible, but its standard
deviation took into account all MC results leading to $\rm\left|\mathbf{\nabla
B_{x}}\right|=7.4_{-2.1}^{+5.5}\,\mu$T/m.

Figure 3: Statistical distribution of the estimated magnetic contribution to
acceleration noise (in red) evaluated at 20$\mu$Hz (top), 0.1 mHz (middle),
and 1 mHz (bottom). The associated Gaussian distribution with its 1$\sigma$,
2$\sigma$ and 3$\sigma$ ranges is also shown. For comparison, we display as
well the median values of measured $S^{1/2}_{\Delta g}$ (in blue) for each of
the 12 noise runs during the mission duration.

## Results and Discussion

The main scientific result from LISA Pathfinder is expressed in terms of the
differential force per unit mass acting on the two test masses. In order to
obtain this parameter, a series of signals were injected during the in-flight
operations which allowed a complete description of the dynamic model of the
motion of the test mass inside the spacecraft [25]. The model derived in this
way was then used to translate the high precision interferometric measurement
of the distance between the test masses into relative acceleration between
them. The evaluation of this relative acceleration was performed in the so
called noise runs, i.e. periods where the instrument was kept in its most
precise configuration for several days in order to obtain a good estimate of
the $\Delta g$ spectrum down to the millihertz regime.

In Fig. 2 we show the spectrum of fluctuations of the relative acceleration
between both test masses in the noise run spanning from Feb. 14th at 01:59:50
to Feb. 27th at 09:53:29, 2017. The blue line represents the Amplitude
Spectral Density (ASD) —the square root of the PSD— of the $\Delta g$ time
series, $S^{1/2}_{\Delta g}$, which, in this segment, is well below the $\rm
30\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz required for LISA Pathfinder and even
attaining the $\rm 3\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz required for LISA. The
red line corresponds to first term in Eq. (2). As previously explained, this
is the leading contribution in the low frequency regime due to its coupling
with the interplanetary magnetic fluctuations, $\rm S^{1/2}_{\mathbf{B}}$, and
their $\propto f^{-1}$ dependence with frequency. Black dots represent an
averaging of the spectra $S^{1/2}_{\Delta g}$. In purple, the same averaging
is applied to the magnetic projection. In the latter case, however, the error
bars include not only the statistical error from the Welch periodogram
estimate but also the uncertainties from $\rm\left|\mathbf{\nabla
B_{x}}\right|$, which includes the propagation of the MC analysis previously
explained to Eq. (2). According to our estimate, the magnetic contribution to
$\Delta g$ during the February noise run accounts for a $\rm
1.46_{-0.77}^{+3.73}$% in noise power at 0.1 mHz.

We use the same data segment to evaluate the second term in Eq. (2). These
contributions couple to the $\Delta g$ through the fluctuations of the
_gradient_ of the magnetic field. Being a gradient, fluctuations show a flat
spectrum, reducing thus its relevance at low frequencies. Our estimates show
the value to be $\rm\simeq 14\,am\,s^{-2}/\sqrt{Hz}$. These terms would start
playing a significant role above 10 mHz, where the overall contribution
flattens due to the gradient components starting to have a larger impact and
the decay of the $f^{-1}$ term. However, we note that above these frequencies
the read-out noise of the magnetometers starts dominating the spectrum over
the interplanetary magnetic field fluctuations.

In Fig. 2 we have conveyed our complete understanding of the magnetic
contribution to acceleration noise during the February 2017 noise run.
However, the low frequency fluctuations of the interplanetary magnetic show a
non-stationary behaviour which follows closely the dynamics of the solar
weather parameters, notably to the solar wind speed [15]. In order to study
this variability we extend our analysis to the complete magnetometers time
series and, therefore, extrapolate the impact of this non-stationary behaviour
in the estimation of the magnetic contribution to the relative acceleration
between test masses for the whole mission duration. In order to do so, we
compute the ASD of the interplanetary magnetic field at different frequencies
logarithmically spaced within the very low frequency regime [20$\mu$Hz, 2
mHz], in segments of 8 days to have enough statistics at 20$\rm\mu$Hz, and
then we project it into force noise by considering the first term in Eq. (2).
In Fig. 3 we show this magnetic projection ASD during the entire LPF mission
by using the median value of $\rm\left|\mathbf{\nabla B_{x}}\right|$ and only
considering the first term in Eq. (2). We show this analysis for the frequency
bins at 20$\mu$Hz, 0.1 mHz and 1 mHz, which correspond to the three panels in
the figure. For comparison, we also display (in blue) the 12 noise runs
performed during the whole mission.

Given that we have a sufficient statistic for the magnetic contribution to the
$\Delta g$, we can compute the associated confidence intervals at 1$\sigma$,
2$\sigma$ and 3$\sigma$ by considering the 16th and 84th percentiles, the
2.5th and 97.5th percentiles and the 0.15th and 99.85th percentiles,
respectively. The distribution of the magnetic noise contribution implies that
the $\rm 1.01_{-0.24}^{+0.73}\,fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz that we have
obtained for the February run conditions could raise up to $\rm
2.70_{-0.77}^{+2.00}\,fm\,s^{-2}/\sqrt{Hz}$ for extreme solar wind conditions,
where we have considered the uncertainty in $\rm\left|\mathbf{\nabla
B_{x}}\right|$ in the error estimate.

Finally, we want to emphasize that the the statistical distribution of the
magnetic noise contribution due to the interplanetary magnetic field non-
stationarity can not be directly associated with the variability of the
measured acceleration noise in the test mass since the magnetic contribution
is only one of the contributions –and not to dominant one– to the overall
$\Delta g$ model. Fig. 3 compares this distribution to the few measured
$S^{1/2}_{\Delta g}$ for the sake of completeness, although one should not
derive a causal connection between both.

## Conclusions

We have presented the first complete estimate of the magnetic-induced force
noise contribution to the acceleration noise between free-falling test masses
in the context of a space-borne gravitational wave detector. The results are
based on a precise in-flight characterisation of those parameters affecting
the magnetic behaviour of the test mass. Our results set a value for the
magnetic contribution to the LISA Pathfinder acceleration noise during the
noise run of February of $\rm 0.25_{-0.08}^{+0.15}\,fm\,s^{-2}/\sqrt{Hz}$ at 1
mHz considering the magnetic gradient uncertainties, which is close to the
initial assessments [4] and well below the requirements established before
launch for this contribution of $\rm 12\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz. Our
estimate at 0.1 mHz is $\rm 1.01_{-0.24}^{+0.73}\,fm\,s^{-2}/\sqrt{Hz}$, a
$\rm 1.46_{-0.77}^{+3.73}$% PSD contribution to $\Delta g$, which is in the
order of other contributions such as the charging noise, with an estimated
contribution of $\rm 1\,fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz [26] or the actuation
noise, which is expected to be the dominant contribution with an expected
value of $\rm 4.5\,fm\,s^{-2}/\sqrt{Hz}$ [7] at 0.1 mHz. We find that, as
expected, the leading term of the magnetic-induced force noise to the test
mass motion in these low frequencies is originated by the coupling with the
fluctuations of the interplanetary magnetic field to the local magnetic field
gradient through an effective coupling constant given by
$\sim\chi\left|\mathbf{\nabla B_{x}}\right|$.

Magnetic field fluctuations have a non-stationary behaviour related to space
weather conditions, predominantly the solar wind speed, which will induce
excess test mass acceleration noise in the low frequency band for some extreme
conditions of the solar wind. Those non-stationarities could rise the noise
power contribution to $\Delta g$ of magnetic fluctuations up to a factor
$\simeq 4.6$ at 0.1 mHz in the worst case scenario, that is during the most
extreme solar wind condition, measured during LPF, and the largest predicted
value of the gradient magnetic field $\rm\left|\mathbf{\nabla
B_{x}}\right|=7.4_{-2.1}^{+5.5}\,\mu$T/m. These low frequency magnetic field
non-stationary behaviour is implicit to the interplanetary field and, hence, a
potential disturbance future space-borne gravitational wave observatories will
need to account for, although not being the dominant one in the case of LISA.
The local magnetic field gradient in the test mass location is the design
parameter that these future gravitational wave observatories in space can use
to suppress this potential noise contribution. Our analysis shows that, in
LISA Pathfinder, the temperature sensors (NTCs) located close to the test mass
can be considered a potential source of the magnetic local gradient. Despite
that the estimate is not expected to limit the instrument performance in most
of its operations, this potential excess noise contribution could be further
suppressed by using Platinum temperature sensors with no magnetic
contribution. The results reported here are applicable to future space-borne
detectors and other missions sharing the technology that was put to test by
the LISA pathfinder mission.

## Acknowledgements

This work has been made possible by the LISA Pathfinder mission, which is part
of the space-science program of the European Space Agency. The French
contribution has been supported by CNES (Accord Specific de projet CNES
1316634/CNRS 103747), the CNRS, the Observatoire de Paris and the University
Paris-Diderot. E. P. and H. I. would also like to acknowledge the financial
support of the UnivEarthS Labex program at Sorbonne Paris Citeé
(ANR-10-LABX-0023 and ANR-11- IDEX-0005-02). The Albert-Einstein-Institut
acknowledges the support of the German Space Agency, DLR. The work is
supported by the Federal Ministry for Economic Affairs and Energy based on a
resolution of the German Bundestag (FKZ 50OQ0501 and FKZ 50OQ1601). The
Italian contribution has been supported by Agenzia Spaziale Italiana and
Instituto Nazionale di Fisica Nucleare. The Spanish contribution has been
supported by Contracts No. AYA2010-15709 (MICINN), No. ESP2013-47637-P, and
No. ESP2015-67234-P (MINECO). M. N. acknowledges support from Fundación
General CSIC (Programa ComFuturo). F. R. acknowledges support from a Formación
de Personal Investigador (MINECO) contract. The Swiss contribution
acknowledges the support of the Swiss Space Office (SSO) via the PRODEX
Programme of ESA. L. F. acknowledges the support of the Swiss National Science
Foundation. The UK groups wish to acknowledge support from the United Kingdom
Space Agency (UKSA), the University of Glasgow, the University of Birmingham,
Imperial College, and the Scottish Universities Physics Alliance (SUPA).
J.I.T. and J.S. acknowledge the support of the U.S. National Aeronautics and
Space Administration (NASA).

## References

  * Anza  _et al._ [2005] S. Anza _et al._ , Class. Quant. Grav. 22, S125 (2005).
  * Antonucci  _et al._ [2012] F. Antonucci _et al._ , Classical and Quantum Gravity 29, 124014 (2012).
  * Amaro-Seoane  _et al._ [2017] P. Amaro-Seoane _et al._ , ArXiv e-prints (2017).
  * Armano  _et al._ [2016] M. Armano _et al._ , Phys. Rev. Lett. 116, 231101 (2016).
  * Armano  _et al._ [2018a] M. Armano _et al._ , Phys. Rev. Lett. 120, 061101 (2018a).
  * Dolesi  _et al._ [2003] R. Dolesi, D. Bortoluzzi, P. Bosetti, L. Carbone, A. Cavalleri, I. Cristofolini, M. DaLio, G. Fontana, V. Fontanari, B. Foulon, C. D. Hoyle, M. Hueller, F. Nappo, P. Sarra, D. N. A. Shaul, T. Sumner, W. J. Weber, and S. Vitale, Classical and Quantum Gravity 20, S99 (2003).
  * Armano  _et al._ [2017a] M. Armano _et al._ (LISA Pathfinder Collaboration), Phys. Rev. D 96, 062004 (2017a).
  * Armano  _et al._ [2021] M. Armano _et al._ , Phys. Rev. Lett. 126, 131103 (2021).
  * Armano  _et al._ [2022] M. Armano _et al._ , Phys. Rev. D 106, 082001 (2022).
  * Armano  _et al._ [2019a] M. Armano _et al._ (LISA Pathfinder Collaboration), Phys. Rev. D 99, 082001 (2019a).
  * Armano  _et al._ [2019b] M. Armano _et al._ (LISA Pathfinder Collaboration), Phys. Rev. D 99, 122003 (2019b).
  * Sanjuán  _et al._ [2007] J. Sanjuán, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, Review of Scientific Instruments 78, 104904 (2007).
  * Armano  _et al._ [2019c] M. Armano _et al._ , Monthly Notices of the Royal Astronomical Society 486, 3368 (2019c), http://oup.prod.sis.lan/mnras/article-pdf/486/3/3368/28536406/stz1017.pdf .
  * Diaz-Aguiló  _et al._ [2013] M. Diaz-Aguiló, I. Mateos, J. Ramos-Castro, A. Lobo, and E. García-Berro, Aerospace Science and Technology 26, 53 (2013).
  * Armano  _et al._ [2020] M. Armano _et al._ , Monthly Notices of the Royal Astronomical Society 494, 3014 (2020), https://academic.oup.com/mnras/article-pdf/494/2/3014/33129159/staa830.pdf .
  * Canizares  _et al._ [2009] P. Canizares _et al._ , Class. Quant. Grav. 26, 094005 (2009), arXiv:0810.1491 [gr-qc] .
  * Canizares  _et al._ [2011] P. Canizares, M. Chmeissani, A. Conchillo, M. Diaz-Aguiló, E. García-Berro, L. Gesa, F. Gibert, C. Grimani, I. Lloro, A. Lobo, I. Mateos, M. Nofrarias, J. Ramos-Castro, J. Sanjuán, C. F. Sopuerta, H. M. Araújo, and P. Wass, Classical and Quantum Gravity 28, 094004 (2011).
  * Armano  _et al._ [2018b] M. Armano _et al._ , The Astrophysical Journal 854, 113 (2018b).
  * Armano  _et al._ [2018c] M. Armano _et al._ , Astroparticle Physics 98, 28 (2018c).
  * Diaz-Aguilo  _et al._ [2012] M. Diaz-Aguilo, E. García-Berro, and A. Lobo, Phys. Rev. D 85, 042004 (2012).
  * [21] M. Armano _et al._ , Phys. Rev. D .
  * Vitale [2007] S. Vitale,  _Effect of Eddy currents on down-conversion of magnetic noise._ , Tech. Rep. Memo LTP package (University of Trento, 2007).
  * Trougnou [2007] L. Trougnou,  _AC magnetic susceptibility of LPF TMs, issue 2_ , Tech. Rep. TEC-EEE/2007149/LT (ESA, 2007).
  * Sanjuán  _et al._ [2008] J. Sanjuán, A. Lobo, M. Nofrarias, N. Mateos, X. Xirgu, P. Cañizares, and J. Ramos-Castro, Review of Scientific Instruments 79, 084503 (2008), https://pubs.aip.org/aip/rsi/article-pdf/doi/10.1063/1.2968113/14844880/084503_1_online.pdf .
  * Armano  _et al._ [2018d] M. Armano _et al._ , Phys. Rev. D 97, 122002 (2018d).
  * Armano  _et al._ [2017b] M. Armano _et al._ (LISA Pathfinder Collaboration), Phys. Rev. Lett. 118, 171101 (2017b).