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

# Microwave Coupling to ECR and Alternative Heating Methods

L. Celona

###### Abstract

The Electron Cyclotron Resonance Ion Source (ECRIS) is nowadays the most
effective device that can feed particle accelerators in a continuous and
reliable way, providing high-current beams of low- and medium-charge-state
ions and relatively intense currents for highly charged ions. The ECRIS is an
important tool for research with ion beams (in surface, atomic, and nuclear
science) while, on the other hand, it implies plasma under extreme conditions
and thus constitutes an object of scientific interest in itself. The
fundamental aspect of the coupling between the electromagnetic wave and the
plasma is hereinafter treated together with some variations to the classical
ECR heating mechanism, with particular attention being paid to the frequency
tuning effect and two-frequency heating. Considerations of electron and ion
dynamics will be presented together with some recent observations connecting
the beam shape with the frequency of the electromagnetic wave feeding the
cavity. The future challenges of higher-charge states, high-charge breeding
efficiency, and high absolute ionization efficiency also call for the
exploration of new heating schemes and synergy between experiments and
modelling. Some results concerning the investigation of innovative mechanisms
of plasma ignition based on upper hybrid resonance will be described.

##  1 Introduction

The Electron Cyclotron Resonance Ion Source (ECRIS) is used to deliver beams
of singly or multiply charged ions for a wide range of applications in many
laboratories. In particular, such devices are well suited for the production
of Highly Charged Ions (HCIs) – a key consideration for the new acceleration
facilities (e.g. FAIR, RIA, HRIBF, etc.), which will require milliampere
levels of HCIs. In order to get such high currents, the recent progress in the
performance of the ECRIS has been mainly linked to improvement of the plasma
magnetic confinement within the source chamber and to an increase of the
frequency for the feeding microwaves which, under proper conditions, develop
to higher plasma densities [1]. The trend followed until now has been to
increase the frequency and the magnetic field, leading to rising costs for the
technology and safety problems for the magnet’s cryostat because of the growth
of hot electrons: the frequency and magnetic field scaling are close to
saturation. Apart from this main route, various techniques are also employed
to enhance the production of HCIs, such as the use of secondary emission
materials, the wall coatings, the installation of a bias disc, or gas mixing,
to mention the most important ones [2].

Moreover, in the past decade, some experiments involving new approaches to
feeding have allowed an increase in the performance of the conventional ECR
ion sources with a minimum-$B$ magnetic field structure by feeding them with
electromagnetic waves that have a large spectral content, or that are obtained
by the superimposition of a discrete set of microwaves at different
frequencies [3, 4, 5, 6].

Even if these experiments have provided interesting results, they have not
given us an explanation or a methodology to convey a better understanding of
the coupling mechanism between a feeding waveguide and a cavity filled with
plasma, and the energy transfer between the electromagnetic field in the
source plasma chamber and the plasma confined therein. An increase of
knowledge in terms of microwave coupling to ECRIS plasma, and therefore
optimization of the ECR power transfer processes, may allow us to design ion
sources with higher performance. Further improvements of ECRIS output currents
and the average charge state require a deep understanding of electron and ion
dynamics in the plasma, and of the impact of the electromagnetic structure on
the electron density distribution: theoretical investigations, in order to
find a reasonable and adequate model for these mechanisms and to predict their
possible improvement, may lead to the design of a future innovative ECR ion
source.

Over recent years, dedicated experiments at INFN-LNS have aimed to investigate
these topics and, at the same time, some theoretical studies have been
undertaken to describe them in detail [7].

The microwave coupling between the electromagnetic wave and the plasma
determines the efficient transfer of the energy from the microwaves to the
plasma electrons inside the ECRIS. The plasma chamber, on the other hand, can
be considered as a resonant cavity for the electromagnetic waves and, when the
magnetized plasma is created, the electrical permittivity of the medium
filling the chamber is no longer homogeneous and no longer electrically
isotropous. A detailed investigation has been carried out to demonstrate that
the performance of ECR ion sources depends on the electromagnetic field
excited inside the plasma chamber and on the coupling mechanism used to
provide the microwaves to the plasma. In the following, the various approaches
used over the years are presented, together with the possible alternative
heating schemes.

##  2 The ECR Standard Model

Up to now, the so-called ‘ECRIS Standard Model’ has, for the greater part of a
decade, been the road map followed by ECRIS designers. The main rules were
confirmed by experiments performed at MSU-NSCL in 1993–4 and 1995, and can be
summarized as follows [8]:

  * •

the radial magnetic field value at the plasma chamber wall must be
$B_{\mathrm{rad}}$ $\geq$ $2B_{\mathrm{ECR}}$;

  * •

the axial magnetic field value at injection must be $B_{\mathrm{inj}}$
$\simeq$ $3B_{\mathrm{ECR}}$ or more;

  * •

the axial magnetic field value at extraction must be about $B_{\mathrm{ext}}$
$\simeq$ $B_{\mathrm{rad}}$;

  * •

the minimum value of the axial magnetic field must be in the range
$0.30<B_{\mathrm{min}}/B_{\mathrm{rad}}<0.45$; and

  * •

the optimum power must increase with the volume of the plasma and with the
square of the frequency.

Up to now, almost every operating ECRIS has complied with the Standard Model:
the extracted current increases as the microwave frequency increases, but only
an increase in the mirror ratio can exploit the optimal performance, making
the increase of the electron density with frequency effective. Also, according
to the Standard Model, the development of the ECRIS is strictly linked to
improvements in superconducting magnets and in the technology of microwave
generation. Various authors have studied the RF coupling to the plasma in
terms of the maximum power rate per unit volume and its relationship with the
beam intensity produced by different ECR ion sources [9], but this description
is not satisfactory. The cavity design, and the microwave injection geometry,
are of primary importance for high-RF-energy transmission to the plasma
chamber. Note that the problem of wave energy transmission into the plasma
must be divided into two parts: the first is related to the microwave
generator–waveguide–plasma chamber coupling, while the second concerns the
wave–plasma interaction. Both of these two aspects play notable roles for the
future improvement of ECRIS performance. Many experiments have been undertaken
outside the framework traced by the Standard Model, to verify the possibility
of improving the plasma heating. Principally, they follow three different road
maps. A first series of experiments has been devoted to the study of the
variation of ECRIS performance with slight variations of the microwave
frequency. The second route regards the possibility of operating with more
than one frequency for plasma heating (usually two) or of using broad
microwave spectra. The third method is actually a mixture of the previous
ones: two or more frequencies are used for plasma heating, but at least one is
provided by a broadband microwave generator (such as a Travelling-Wave Tube,
or TWT), which allows the effects of frequency tuning and of multi-frequency
heating to be combined.

###  2.1 The ECRIS plasma chamber as a resonant cavity

In order to characterize the electromagnetic field that is present inside the
plasma chamber of an ECR ion source and where the particle motion occurs, it
is fundamental to make the following assumption: the plasma chamber is a
resonating cavity for the electromagnetic wave feeding the plasma. The
coupling between the electromagnetic wave and the plasma-filled chamber and
the electromagnetic field patterns that can be excited inside the resonating
cavity are of primary importance for the characterization and for the
properties of the plasma. Furthermore, the characterization of the plasma
chamber in terms of the excitable electromagnetic field allows us to make some
assumptions about the charged particle motion and energy, as described in the
following sections.

###  2.2 Resonant modes inside a cylindrical plasma chamber

A plasma chamber can be represented, in a first-order approximation, by a
cylinder of radius _a_ and length _l_ , filled by a medium with a certain
electric permittivity $\epsilon$ and a certain magnetic permeability $\mu$.
Then, a discrete number of electromagnetic field patterns can exist inside the
plasma chamber: the so-called resonant modes. They can be defined by the
following equations, defined using a system of cylindrical coordinates
($\rho$,$\phi$,$z$):

$\cases{E}_{\rho}=-\displaystyle\frac{x_{n\nu}}{a}\displaystyle\frac{r}{l}\displaystyle\frac{\pi}{h^{2}}C_{n}J^{\prime}_{n}\left(\frac{x_{n\nu}\rho}{a}\right)\cos{n\phi}\sin{\left({\displaystyle\frac{r\pi
z}{l}}\right)},\\\
E_{\phi}=\displaystyle\frac{n}{\rho}\displaystyle\frac{r}{l}\displaystyle\frac{\pi}{h^{2}}C_{n}J_{n}\left(\displaystyle\frac{x_{n\nu}\rho}{a}\right)\sin{n\phi}\sin\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\
E_{z}=C_{n}J_{n}\left(\displaystyle\frac{x_{n\nu}\rho}{a}\right)\cos{n\phi}\cos\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\
H_{\rho}=-i\displaystyle\frac{\epsilon\omega}{h^{2}}\displaystyle\frac{n}{\rho}C_{n}J_{n}\left(\displaystyle\frac{x_{n\nu}\rho}{a}\right)\sin{n\phi}\cos\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\
H_{\phi}=-i\displaystyle\frac{\epsilon\omega}{h^{2}}\displaystyle\frac{x_{n\nu}}{a}C_{n}J^{\prime}_{n}\left(\displaystyle\frac{x_{n\nu}\rho}{a}\right)\cos{n\phi}\cos\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\ H_{z}=0.$ (1)

These are the equations describing the Transverse Magnetic (TM) modes, with
only the magnetic field components on the transverse plane. The Transverse
Electric (TE) modes, with only the electric field components on the transverse
plane, can be calculated using the following equations:

$\cases{E}_{\rho}=\displaystyle\frac{\mu\omega}{h^{2}}\displaystyle\frac{n}{p}C_{n}J_{n}\left(\displaystyle\frac{x^{\prime}_{n\nu}\rho}{a}\right)\sin{n\phi}\sin\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\
E_{\phi}=\displaystyle\frac{\mu\omega}{h^{2}}\displaystyle\frac{x_{n\nu}}{a}C_{n}J^{\prime}_{n}\left(\displaystyle\frac{x^{\prime}_{n\nu}\rho}{a}\right)\cos{n\phi}\sin\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\ E_{z}=0\\\
H_{\rho}=-i\displaystyle\frac{x^{\prime}_{n\nu}}{a}\displaystyle\frac{r}{l}\displaystyle\frac{\pi}{h^{2}}C_{n}J^{\prime}_{n}\left(\displaystyle\frac{x_{n\nu}\rho}{a}\right)\cos{n\phi}\cos\left({\displaystyle\frac{r\pi
z}{l}}\right),\\\
H_{\phi}=i\displaystyle\frac{n}{\rho}\displaystyle\frac{r}{l}\displaystyle\frac{\pi}{h^{2}}C_{n}J_{n}\left(\displaystyle\frac{x^{\prime}_{n\nu}\rho}{a}\right)\sin{n\phi}\cos\left({\displaystyle\frac{r\pi
z}{l}}\right)\\\
H_{z}=-iC_{n}J_{n}\left(\displaystyle\frac{x^{\prime}_{n\nu}\rho}{a}\right)\cos{n\phi}\sin\left({\displaystyle\frac{r\pi
z}{l}}\right).\\\ $ (2)

Here, the time dependence $\mathrm{e}^{i\omega t}$ is omitted; $J_{n}$ and
$J^{\prime}_{n}$ are, respectively, the Bessel functions and the derivatives
of the Bessel functions of order $n$; and $x_{n\nu}$ and $x^{\prime}_{n\nu}$
are their related $\nu$ roots. A discrete set of frequencies $\omega$/2$\pi$
can exist inside the resonance cavity and they are defined as follows:

$\omega_{n\nu r}=c\sqrt{\frac{r^{2}\pi^{2}}{l^{2}}+h^{2}},$ (3)

where the value $h$ is as follows: 4 h=x’nνa (TE modes),
=xnνa (TM modes). Then, the resonant modes TEn,ν,ρ and TMn,ν,ρ that exist
inside the plasma chamber are identified by the mode parameters and their
strength is related to the amplitude associated with the field strength of the
wave. By supposing that the chamber is filled with a homogeneous and
unmagnetized medium, the corresponding electrical permittivity is given by the
relation

$\epsilon_{r}=1-\left(\frac{\omega_{p}}{\omega}\right)^{2},$ (4)

where $\omega$ is the pulsation generating the plasma and $\omega_{p}$ is the
plasma pulsation:

$\omega_{p}=\sqrt{\frac{n_{\mathrm{e}}e^{2}}{m_{\mathrm{e}}\epsilon_{o}}},$
(5)

in which $m_{\mathrm{e}}$ and $e$ are, respectively, the electron mass and the
electron charge, $\epsilon_{o}$ is the electrical permittivity in vacuum, and
$n_{\mathrm{e}}$ is the electron density. Therefore, under these hypotheses,
the plasma build-up can be seen as a change in the electrical permittivity and
therefore as a change in the resonant frequencies, because of the change of
$\epsilon$ in Eq. (3). This model is certainly oversimplified if we consider
the plasma of an ECR ion source, but has been applied successfully, giving
information on the plasma parameters generated in a small reactor at INFN-LNS.

##  3 Two- and multiple-frequency heating

Since 1994, the so-called Two-Frequency Heating (TFH) has been used [4, 5] to
improve the HCI production by feeding the plasma with two electromagnetic
waves at different frequencies instead of one. In some cases, even three or
more close frequencies have been used.

The performance of the LBL AECR source has been improved by simultaneously
heating the plasma with microwaves of 10 and 14 GHz. The plasma stability was
improved and the ion charge-state distribution was shifted to a higher-charge
state. The production of high-charge-state ions was increased by a factor of
between 2 and 5, or higher, for the very heavy ions such as bismuth and
uranium, as compared to the case of single-frequency (14 GHz) heating [4].

In an ECR source, electron cyclotron resonance heating couples microwave power
into the plasma electrons. This occurs when the microwave frequency
$\omega_{rf}$ matches the cyclotron frequency, $\omega_{c}=B/m_{\mathrm{e}}$,
of the electrons. In high-charge-state ECR sources with one frequency, the
geometry of the minimum-$B$ field results in a closed, approximately
ellipsoidal ECR surface. The electrons are heated in a thin resonance zone at
the surface, as they spiral back and forth between the magnetic mirrors. When
two frequencies are used, it is possible to produce two concentric surfaces,
the physical separation of which depends on the frequency difference and the
strength and gradient of the magnetic field, leading to a higher density of
the energetic electrons. With TFH, the ECR plasma is more quiescent than with
single-frequency heating. Both the short-term and the long-term plasma
stability are improved, and more microwave power could be launched into the
plasma. TFH has been demonstrated to be a powerful method: in the case in Ref.
[4] for 238U, it increased the production of higher-charge states (from 35+ to
39+) by a factor ranging from 2 to 4 and shifted the peak charge state from
33+ to 36+. Two-frequency heating using 10 and 14 GHz in the AECR provided
significantly better performance and indicated that still higher performance
with multiple-frequency heating may be possible. While multiple-frequency
heating would increase the complexity and cost of an ECR source, it could
provide significant gains in performance. In [5], the performance of the
Argonne ECR ion source was improved through the use of TFH, with the primary
frequency of 14 GHz from a klystron and the second frequency from a
Travelling-Wave Tube Amplifier (TWTA) with a tunable range of 11.0–13.0 GHz.
Source output as well as stability were improved, with a shift to higher-
charge states observed. The use of a second frequency increased the intensity
of the medium charge states by 50–100$\%$ and the higher-charge states by a
factor of between 2 and 5. In a modern second-generation ECRIS, TFH is usually
implemented by using frequencies between 14 and 18 GHz, while the best-
performing ECRIS use a combination of 24 or 28 GHz with 18 GHz.

###  3.1 Multiple-frequency plasma heating

Microwaves of various frequencies can be simultaneously launched into and
absorbed by a high-charge-state ECR plasma. The minimum-$B$ magnetic field
configuration in an ECRIS can provide many closed and nested ECR heating
surfaces, as graphically shown in Fig. 1. If two or more significantly
different frequencies are used, two or more well-separated and nested ECR
surfaces will exist in the ECR plasma. With the multiple ECR surfaces,
electrons can be heated four times or more for one pass from one mirror end to
the other, whereas they are only heated twice in the case of single-frequency
heating. Multiple-frequency heating can couple more microwave power with
better efficiency into the plasma and it leads to a higher density of hot
electrons, which is essential for the production of highly charged ions. To
demonstrate that the frequency-domain technique can be used to enhance the
performance of a traditional minimum-$B$ ECR ion source, comparative studies
have been undertaken to assess the relative performance of the Oak Ridge
National Laboratory CAPRICE ECR ion source [10], in terms of its multiply
charged ion-beam generation capability, when excited with high-power, single-
frequency, or multiple-discrete-frequency microwave radiation, derived from
standard klystron and/or TWT technologies. These studies demonstrate that the
charge-state populations for Arq+ and Xeq+move towards higher values when
excited with two- and three-discrete-frequency microwave power compared to
those observed when single-frequency microwave power is used. For example, the
most probable charge state for Xe is increased by one charge-state unit, while
the beam intensities for charge states higher than the most probable one are
increased by factors of $\sim 3$ compared to those observed for single-
frequency plasma excitation. In Ref. [11], particle-in-cell codes have been
used to simulate the magnetic field distributions, to demonstrate the
advantages of using multiple, discrete frequencies over single frequencies to
power conventional ECR ion sources.

Figure 1: A schematic view of four nested ECR surfaces in a high-charge-state
ECR ion source for four well-separated frequency waves [12].

One, two and three-frequency heating experiments have been conducted using Xe
feed gas. With the addition of the second and third frequencies, the most
probable Xeq+ charge state moves towards higher values by one unit; this
clearly illustrates that the performance of conventional-geometry ECR ion
sources can be significantly improved by the use of multiple-discrete-
frequency plasma heating.

##  4 Electron heating with broadband microwave radiation and the volume
effect

The ionization process in Electron Cyclotron Resonance (ECR) ion sources is
based on the sequential removal of electrons in collisions between ions or
neutral atoms with electrons that have been heated stochastically to high
energies by the adsorption of microwave power under ECR conditions. The ECR
zones in a conventional minimum-$B$ geometry ECRIS, powered by narrow-
bandwidth microwave radiation, are thin volumes that are substantially smaller
in relation to their total plasma volumes. Consequently, the probability of an
acceleration resulting in a substantial energy gain for the electrons that
arrive in the ECR zone in phase with the electric field vector of the
electromagnetic wave is lower than is possible in extended-volume ECR zones.
Therefore, it is reasonable to believe that the performance of conventional
minimum-$B$ ECR ion sources can be improved by increasing their respective
resonance volumes. The volume effect has been demonstrated by tailoring the
central magnetic field so that it forms a large resonant volume and by
increasing the number of discrete operational frequencies of the ion source.
Broadband sources of RF power provide a simple and potentially more effective
alternative for increasing the physical sizes of the resonance zones in
conventional $B_{\mathrm{minimum}}$ ECR ion sources.

###  4.1 Experimental procedures

Some experiments have been performed with the JYFL 6.4 GHz conventional
minimum-$B$ geometry ECR ion source at the University of Jyväskylä, using Ar
as the feed gas. The performance of the source was compared when operated with
either narrow or with broadband microwave radiation, under the same neutral
gas pressure and input power conditions. For the narrow-bandwidth experiments,
the carrier signal from the local oscillator (LO, bandwidth 1.5 MHz) was fed
directly into the TWTA. For the broadband experiments, the signal from the LO
was fed into a White-Noise Generator (WNG), producing an output signal with a
bandwidth of 200 MHz, FWHM, equally distributed about the central frequency of
the LO (6.4 GHz). The measurements were carried out at the same absorbed
microwave power level (200 W), determined by subtracting the reflected power
from the forward power of the TWTA. The input power was limited due to
impedance mismatch of certain frequencies in the amplified broadband signal,
resulting in 20$\%$ reflected power of the injected power. This problem cannot
be avoided and it constitutes the main drawback of such a technique, since
frequencies are differently coupled into the ion source depending on the
intrinsic electromagnetic structure of the source itself. In the case of
narrow- bandwidth operation, the reflected power was typically 6$\%$. For the
WNG mode of operation at optimum pressure, the ion plasma density, as
evaluated from the measured drain current and the charge-state distribution,
using Bohm’s criterion, was within 15$\%$ of the neutral density. Although the
beam intensities were higher by factors >2 with the WNG at low pressures,
there was no difference between the broadband and narrow-bandwidth modes of
operation in the high neutral pressure regime due to increased rates of charge
exchange [13, 14]. Enlarged ECR zones improve the production of high-charge-
state ions due to enhanced bombardment with higher populations of energetic
electrons and, especially, due to the enhanced ionization rates of neutrals in
the ECR zone, thereby lowering the probability of charge-exchange collisions.
The tremendous potential of the broadband technique for enhancing high-charge-
state beam intensities over conventional means at equivalent input power
levels is illustrated in Fig. 2, where the ratio of WN/LO-generated high-
charge-state beams is seen to increase continually with the charge state.
Clearly, the potential of the broadband method can only be fully evaluated by
comparing the high charge states produced with the two modes of operation at
the same power density, if this is achievable in practice in terms of the
operational limitations imposed by outgassing effects and the required RF
power.

Figure 2: Intensity ratios of argon ion beams generated with signals from the
WNG and LO versus the charge state

The performance of ECR ion sources can also be significantly improved by
tailoring the central region of the magnetic field so that it is resonant with
single-frequency microwave radiation (spatial domain) [15, 16, 17]. The
spatial-domain technique employs a magnetic field configuration with an
extended central flat region, tuned to be in resonance with single-frequency
microwave radiation. Because of the large resonant plasma volume,
significantly more RF power can be coupled into the plasma, resulting in
heating of electrons over a much larger volume than is possible in
conventional ECR ion sources. The ability to ionize a larger fraction of the
particles in the plasma volume effectively reduces the probability of resonant
and non-resonant charge exchange, thereby increasing the residence time of an
ion in a given charge state and for subsequent and further ionization. All
other parameters being equal, the ‘volume’ ECR source should result in higher-
charge-state distributions, higher beam intensities, and improved operational
stability. The axial magnetic field is shown in Fig. 3: its profile is flat
(constant mod-$B$) in the centre, and extends over the length of the central
field region, along the axis of symmetry, and radially outwards to form a
uniformly distributed ECR plasma ‘volume’. This magnetic field design strongly
contrasts with those used in conventional ECR ion sources, where the central
field regions are approximately parabolic and the consequent ECR zones are
‘surfaces’.

Figure 3: Axial magnetic field profiles of the ‘volume’ (solid line) and
conventional minimum-$B$ configurations in ‘surface’ (dotted line) ECR ion
sources [18].

According to computational studies, the new configuration will result in
dramatic increases in the absorption of RF power, thus enabling the heating of
electrons over a much larger volume, thereby increasing the electron
temperature and the ‘hot’ electron population in the plasma.

##  5 Frequency tuning

Many experiments over recent years have shown that significant improvements of
ECRIS performance (both in terms of total extracted current and the production
of highly charged ions) can be obtained by slightly varying the microwave
frequency in the case of Single-Frequency Heating (SFH), this being defined as
a ‘frequency tuning’ effect. It was already known that a large increase in the
frequency increases ($\sim$GHz) the electron density and improves the ECRIS
performance because of the increase of the cut-off density, but since 2001
several experiments have demonstrated that even slight variations of the
pumping wave frequency ($\sim$MHz) may lead to strong variations in the
extracted current. The first evidence was provided by the different
performances observed for the SERSE and CAESAR ion sources when fed by a
klystron-based or a TWT-based generator [19, 20, 21] at either 14 or 18 GHz.
Other interesting results came from experiments performed at GSI and at JYFL.
In frequency tuning, the microwave frequency is varied in order to select the
most efficient heating mode inside the plasma chamber of the ECRIS. In the
experiments, the input frequency for the klystron was swept from 14.05 to
14.13 GHz in 100 s, using a Rohde $\&$ Schwartz signal generator. This
bandwidth was found adequate to maintain a constant output power over the
whole frequency sweep, using the automatic level control feature of the
klystron.

###  5.1 Effect on beam structure and emittance

The beam emittance and the beam structure were studied as a function of the
frequency with the aid of an Allison-type emittance scanner and a KBr beam
viewer. Figure 4 shows three beam viewer pictures: the beam structure varies
strongly with the microwave frequency, as an indication of the change in the
plasma–wave coupling during the scan. However, no unequivocal explanation
concerning the origin of the beam structure variations can be given: they
could originate from the changes in the plasma, in the electron ion dynamics,
due to electromagnetic field variations and/or in the beam line due to changes
in ion-beam intensity and space charge. The explanation of the data presented
above is based on the assumption that the frequency tuning changes the
electromagnetic field distribution inside the resonator in terms of its
distribution over the resonance surface; that is, where the wave–electron
energy transfer takes place. This assumption requires that even in case of
plasma filling the cavity, the resonant modes persist; that is, the formation
of standing waves is still possible.

Figure 4: (Colour online) The structure of the Ar9+ ion beam with different
plasma heating frequencies is shown: (a) 14.050 GHz, (b) 14.090 GHz, and (c)
14.108 GHz.

###  5.2 The microwave frequency dependence of the properties of the ion beam
extracted from a CAPRICE-type ECRIS

Measurements have been performed with the CAPRICE-type ECRIS installed at the
ECR Injector Setup (EIS) of GSI. The experimental set-up uses a microwave
sweep generator that feeds a TWTA, covering a wide frequency range from 8 to
18 GHz. This arrangement provides a precise determination of the frequencies
and of the reflection coefficient along with the beam properties. A sequence
of viewing targets positioned inside the beam line monitors the evolution of
the beam shape. In the present experiment, the frequency tuning effect has
been analysed in the 12.5–16.5 GHz frequency range. The availability of a TWTA
driven by a signal generator made it possible to change the source operating
frequency in steps of a few hundred kilohertz. This experiment allows us to
analyse the beam properties when the ECRIS operative frequency sweeps over a
wide range of 4 GHz, and hence for increasing ECR surfaces. The influence on
lower- and higher-charge states has been analysed for different source
conditions concerning the magnetic field configuration, the gas pressure, and
the power setting.

###  5.3 Description of experimental set-up

The CAPRICE-type [22] ECR ion source used for this experiment is equipped with
a 1.2 T maximum radial magnetic field. The plasma chamber was 179 mm long and
64 mm in diameter. The RF power was provided by a TWTA working in the 8–18 GHz
frequency range and able to provide an output power higher than 650 W in the
frequency range of 12–18 GHz. The input of the amplifier was driven by a
signal generator able to sweep from 1 to 20 GHz. According to the maximum
manageable power reflected to the amplifier, it has been restricted to working
at a power of 100 W and in the frequency range of 12.5–16.5 GHz. The use of a
waveguide microwave isolator covering this frequency range and handling up to
650 W could allow us to work with higher powers.

The frequency steps were set to 200 kHz, with a dwell time of 20 ms for each
step. The duration of one measurement was then around 400 s. Two directional
couplers with high directivity were inserted in the waveguide line in order to
measure the forward power and the reflected power by means of two microwave
power probes. The experiment was carried out with argon and helium as support
gases, at gas pressures of (3.9–5.0)$\times 10^{-6}$ mbar. The ion currents of
the Ar7+, Ar8+, and Ar9+ charge states were measured using a Faraday cup; the
drain current of the high-voltage power supply of the extraction was also
recorded. The extraction voltage was set to 15 kV; a voltage of $-2$ kV was
applied to the screening electrode. Viewing targets could be remotely inserted
at three positions along the beam line in order to monitor the evolution of
the beam shape right after the extraction, the focused beam, and the analysed
beam [23]. KBr was used as the target coating material for this experiment.

###  5.4 Results and discussion

Different measurements were carried out by sweeping the frequency and setting
different ion source parameters; that is, the injection and extraction
magnetic field values, the gas pressure, and the microwave power. The source
parameters were set to operate using a charge-state distribution with a
maximum on the Ar8+ current (by feeding the plasma with 100 W microwave power
at 14.5 GHz). An Ar8+ current of 85 $\mu$A and a drain current of 2.36 mA were
obtained. From these source conditions, the frequency sweep was started by
ramping the signal generator from 12.5 GHz up to 16.5 GHz, while the
reflection coefficient, the Ar7+, Ar8+, and Ar9+ currents, and the drain
current were recorded simultaneously. The evolution of the reflection
coefficient with the frequency is shown in Fig. 5. As expected by comparison
with previous experiments, the matching impedance between the cavity filled by
the plasma and the electromagnetic wave is strongly dependent on the frequency
[6]. It is remarkable that the plasma properties also change considerably with
varying frequency. The strong correlation between the peaks of the reflection
coefficient and the current amplitude are clearly visible around the
frequencies at which the reflection coefficient is higher than $-9.54$ dB
(matching condition). The relationship between the resonance frequencies and
the heating efficiency has been analysed theoretically and particle-in-cell
codes have been used to correlate the electromagnetic field patterns and the
electron cyclotron resonance surface [24]. However, it is not possible with
our analysis to determine the electromagnetic field patterns (modes) related
to these peaks. The comparison of the current evolution in the frequency range
indicated above is presented in Fig. 5.

Figure 5: (Colour online) The reflection coefficient and current evolution
versus microwave frequency (the coloured solid lines refer to the left-hand
scale, while the dashed black line is the reflection coefficient, referring to
the right-hand scale).

It is clear how the current amplitude is affected by the choice of the
operative frequency. Looking at the Ar8+ current, it ranges from a few
microamperes up to 200 $\mu$A. The experimental results were clearly
reproducible in several runs, thus confirming the reliability of the
measurements. The evolution of the Ar7+ and Ar8+ currents is similar, but
their amplitudes differ. In fact, at the frequencies at which both currents
present a peak, the Ar8+ current is quite a bit higher than the Ar7+ current
(e.g. at 14.119 GHz, the difference between the two currents is 80 $\mu$A).
The opposite behaviour is visible for the minima of the current amplitudes,
where the Ar7+ current is higher than the Ar8+ current. In the range
15.64–16.5 GHz, the currents of the higher-charge states – that is, Ar9+ –
tend to lower values even if the reflected power is less than 10$\%$. This
seems to be due to the confining magnetic field, which restricts the source
operation to lower frequencies. It has been also observed that the evolution
of the drain current follows the trend of the three charge states presented in
Fig. 5. In order to have a complete understanding of the sweep effects on the
ionization process, the charge-state distribution has been analysed for
different frequencies. It was decided to restrict the analysis to the
frequency range of 14–15 GHz. Several frequencies have been considered at
which peaks and minimum amplitudes occur. In Fig. 6, the charge-state
distributions are presented for four different frequencies.

Figure 6: The Ar charge-state distributions for four significant operating
frequencies

The 14.5 GHz value is the normal operational frequency of the CAPRICE ion
source; 14.46 GHz and 14.119 GHz are the frequencies at which the minimum and
the maximum Ar8+ currents, respectively, were measured in the 14–15 GHz
frequency range. The charge-state distribution related to 14.0 GHz operation
is also reported in order to emphasize the importance of the electromagnetic
field pattern and the choice of the frequency. In fact, the charge-state
distributions at 14.0 GHz and at 14.46 GHz are quite similar, even though the
amount of power feeding the plasma was more than doubled. In the first case,
the reflection coefficient (indicated in the legend of Fig. 2) was $-2.3$ dB
and more than half of the power was reflected; and in the second case it was
$-25.8$ dB, the impedance matching condition was fulfilled, and hardly any
power was reflected. It is also interesting that for the frequencies at which
the higher-charge states are favoured, the current of the lower charge state
is decreasing and vice versa. The analysed charge-state distributions confirm
that frequency tuning affects the higher-charge states to a greater extent (at
14.119 GHz, the current enhancement with respect to the 14.5 GHz operational
frequency is 244$\%$ for the Ar8+ current and 456$\%$ for the Ar9+ current).
The enhancement of the current is not the only effect of frequency sweeping;
in fact, the quality, the shape, and the emittance of the ion beam also vary.
The use of beam viewing targets has proven to be a favourable technique for
monitoring the beam shape and a promising beam diagnostic tool. The images
recorded beyond the extracted beam-focusing solenoid (position VT2) and in the
diagnostic box after the mass/charge selection dipole (position VT3) are shown
in Fig. 7.

Figure 7: The Ar8+ beam viewed at the targets located after the focusing
solenoid (left-hand column) and after the dipole (right-hand column).

Here, the same frequencies are chosen as in Fig. 6. The Ar8+ beam is shown in
the right column and the focused beam images also refer to the Ar8+ magnetic
field setting. At 14.0 GHz and 14.46 GHz, which are the frequencies at which
the Ar8+ current presents a minimum, the focused beam shape seems to remain
unchanged in the orientation of the arms (at 14.0 GHz it is a little bit
brighter, also according to the higher intensity measured at the Faraday cup).
At 14.119 GHz, the focused beam is a little bit bigger and brighter than the
one at 14.5 GHz, and in both cases the orientation of the arms is turned by
more then 40∘ clockwise with respect to the 14–14.6 GHz beam shapes.

###  5.5 Frequency tuning combined with the two-frequency heating effect

The relationship between the two frequencies and the respective power was not
univocally determined. In fact, any source features a different set of
parameters and the optimization is done empirically, just by looking at the
maximization of the beam current. Several qualitative explanations have been
offered for this phenomenon, all related to the increase of the average
electron temperature, Te, and to the ionization rate, by assuming that the
crossing of two resonance surfaces helps the electrons to gain more energy.
This simple picture does not explain the reason for the relevant changes in
the charge-state distribution for different pairs of frequencies (even for the
case of minor changes – such as a few megahertz over 14 or 18 GHz), which can
be explained nowadays in terms of the frequency tuning effect. It is important
to underline that, even in the case of TFH applied to many existing sources, a
TWT is often used, the other option being a klystron-based generator. The
choice of a TWT allows the experimentalists to vary the second frequency
slightly. It has been observed – for example, for the production of O7+ – that
60 W emitted by the TWT at the optimum frequency gives the same effect as 300
W emitted from the fixed-frequency klystron. The maximum current is obtained
by means of a klystron at 427 W and a TWT at 62 W ($I$ = 66 $\mu$A), operating
simultaneously; in order to obtain the same current, the experimenters needed
$P_{\mathrm{RF}}$ = 800 W from the klystron in SFH. Furthermore, in the case
of TFH, the current increases almost 20$\%$ (from 57 to 66 $\mu$eA) when the
TWT-emitted frequency shifts from 11.06 to 10.85 GHz, the klystron and TWT
emitted power both being held constant. Then, the TFH is an effective method
to increase the extracted current from an ECRIS, but it can only be fully
exploited by means of frequency tuning. Several measurements have been carried
out with the SERSE ion source. The TFH has been used for operation at either
14 or 18 GHz, with a clear advantage with respect to SFH.

In section 5.2, the evolution of the ion current intensities of Ar7+, Ar8+,
and Ar9+ over the 12.5–16.5 GHz frequency range has been described. The argon
charge-state distributions were analysed for different frequencies, and for
some frequencies an enhanced intensity of the higher-charge states was
observed. We decided to perform an experiment to investigate the double-
frequency heating effect using a single fixed frequency (14.5 GHz in one case
and 14.119 GHz in another) and a second frequency swept over the 12.5–16.5 GHz
range. First, the power feeding the plasma was kept at 100 W, in order to
compare the results of double-frequency heating with single-frequency
sweeping. Then the power distribution between the fixed frequency and the
sweeping frequency was unbalanced by doubling the power of the fixed frequency
in one case and the power of the sweeping frequency in the other. The ion
source parameters – including the magnetic field, the gas pressure, the
extraction voltage, and so on – were set to and maintained at the same values
as used for single-frequency sweep analysis, with the charge-state
distribution optimized for the Ar8+ intensity. The Ar7+, Ar8+, and Ar9+
currents were recorded together with the extractor drain current. The forward
power and the reflected power were measured simultaneously. However, in the
case of double-frequency heating, the power probes cannot distinguish the
measured values of the forward and reflected power related to each of the two
waves. The results of these measurements are shown in Fig. 8.

Figure 8: (Colour online) The reflection coefficient as a function of
frequency: a comparison between the frequency tuning effect and double-
frequency heating.

A comparison between the two techniques concerning the behaviour of the ion
source is possible. As expected, in the case of the two frequencies, the
minima of the reflection coefficient are higher because of the higher level of
reflected power due to the superposition of the two waves. It is interesting
to note that these minima occur at almost the same frequencies for both
techniques. Since the positions of the reflection coefficient minima do not
vary, it can be expected that the peaks of the ion current are located at the
same frequencies for the two heating methods. This comparison is shown in Fig.
9 for the drain current of the high-voltage extractor power supply. In this
case, 50 W is provided at one fixed frequency and the effect of sweeping a
second frequency with a power of 50 W produces a different current behaviour
from that with a single sweeping frequency (at the same power). This can be
seen in Fig. 9 and Figs. 10–11. In fact, during the single-frequency sweep,
the drain current

Figure 9: (Colour online) The drain current of the high-voltage extractor
power supply as a function of frequency: a comparison between the frequency
tuning effect and double-frequency heating. Figure 10: (Colour online) The
Ar7+ current as a function of frequency: a comparison between the frequency
tuning effect and double-frequency heating. Figure 11: (Colour online) The
Ar9+ current as a function of frequency: a comparison between the frequency
tuning effect and double-frequency heating.

varies from around 1.4 mA to 2.8 mA, while with double-frequency heating the
range of variation is 0.6 mA. The drain current appears more stable with
frequency when the double frequency is applied instead of single-frequency
tuning. This behaviour is also observed in the Ar7+ current variation shown in
Fig. 10. A possible explanation might be found in the microwave power provided
by the two methods. In the case of single-frequency tuning, 100 W is provided
to the source and during the frequency sweep, when the impedance is not
matched, most of the forward power is not coupled to the source but is
reflected (see Fig. 8). But in the case of double-frequency heating, just 50 W
of the total forward power of 100 W is associated with the sweeping frequency,
and at the frequencies at which the power is not coupled to the plasma, one
half of the total power is provided at a fixed frequency, which is well
coupled to the source (i.e. at 14.5 GHz or at an optimized frequency such as
14.119 GHz). The choice of the fixed frequency allows enhancement of the ion
currents of the higher-charge states. With respect to single-frequency
operation, with two frequencies the current peaks are broadened and reduced in
amplitude, the frequencies at which they occur remain the same, and the
average current level remains high (see Fig. 10 for Ar7+), while the higher-
charge states tend to higher ion currents when the frequency is increased (see
Figs. 11 and 12). The experimental results indicate that there can be strong
differences when the operating frequency is optimized by frequency tuning. In
fact, when operating in double-frequency mode and optimizing one of the two
frequencies (14.119 GHz for the present case, as described above), the current
increases linearly with frequency (with respect to the 14.5 GHz fixed
frequency).

Figure 12: (Colour online) The Ar8+ current as a function of frequency: a
comparison between the frequency tuning effect and double-frequency heating.

In comparing the two techniques while keeping the ion source settings and the
microwave power constant, note that the behaviour of the ion currents and the
reflection coefficient remain almost the same with frequency. This result is
useful to optimize the performance of an ECRIS further when double-frequency
heating is used. In fact, single-frequency tuning can be used to find the
optimum frequencies to be used for operating in the multiple heating mode.
Note also that when operating with two generators set at the same frequency,
the current level measured is different from the single-generator case. This
is because when the two frequencies become equal, the current of each charge
state and the power provided to the ion source are not stable. A possible
explanation for this phenomenon might be overlapping of the two signals and
the phase difference between the two waves. We plan to explore the use of two
phase-locked generators in forthcoming experiments. The behaviour of argon ion
beams has been explored for different power levels of the fixed frequency and
the sweep frequency. In both cases, two fixed frequencies were chosen and in
this case the possibility of setting the fixed frequency to an optimized
value, obtained by fine-tuning the frequency, allowed us to increase the beam
intensity (Fig. 13).

Figure 13: (Colour online) The Ar9+ current as a function of frequency:
differing power distributions between the two waves.

Figure 13 shows the evolution of the Ar9+ current when 150 W of total power is
distributed between the two microwave feeds in different proportions, one of
fixed frequency and the second swept from 12.5 GHz to 16.5 GHz. Again, the
single-frequency sweep carried out at 100 W is included in the figure for
comparison. For the optimum frequency mentioned previously (14.119 GHz), the
current intensity is still comparable between the two methods even though the
total power is 50$\%$ greater.

When the power associated with the fixed frequency is higher, all the analysed
charge states are less sensitive to variation of the second frequency. This
follows from the reduced dynamic range of the current, indicating a more
stable plasma; in particular, when the fixed frequency is chosen to be at the
optimum value (14.119 GHz). Furthermore, when one of the two frequencies is
optimized, the average extracted current remains high with respect to an
unoptimized frequency (such as 14.5 GHz), increasing with the second frequency
(quite evident above 15 GHz). All these observations are more evident for
higher-charge states. With the ion source running at higher microwave power,
it was possible to perform an experiment with an Ar11+ ion beam. The results
are shown in Fig. 14.

Figure 14: (Colour online) The Ar11+ current as a function of frequency,
showing different power distributions between the two waves.

The power distribution between the two waves is also important. Obviously, it
is more effective to increase the power at the fixed frequency. Figure 14
shows once more that the choice of the optimum frequency, as obtained in the
previous experiment on frequency tuning, is very important for double-
frequency heating at higher power. This result is interesting with respect to
the operation of new-generation ECRIS machines working at 28 GHz, using
gyrotron microwave generators in combination with a second microwave generator
of lower frequency, working in double-frequency mode.

##  6 Alternative heating method: Bernstein waves

ECR devices are density limited, because the electromagnetic waves cannot
propagate beyond a certain density, called the cut-off density. An alternative
to the classical ECR interaction is electrostatic wave heating, driven by
Bernstein waves. Bernstein waves (BW) are very interesting for nuclear fusion
devices [25], because the plasma heating occurs in the absence of any density
cut-off. Electromagnetic Ordinary (O) or Extraordinary (X) modes can be
externally launched into the plasma. O-mode waves may be coupled to an X mode
in the O-mode cut-off layer, and then the X mode can be coupled to a BW mode
at the upper hybrid resonance (UHR). This process is called O-X-B mode
conversion and was described in 1973 by Preinhaelter and Kopecky [25].

Figure 15: A possible design for a microwave injection system producing O-X-B
conversion: two parabolic mirrors are used to bring a focused microwave beam
into the optimal region of the O cut-off layer.

It was shown that O-X-B mode conversion may be optimized by changing the
O-mode insertion angle with respect to the external magnetic field direction:
in this case, the O mode is completely converted into a slow X mode, which
under certain conditions is in turn converted to BWs in the Upper Hybrid
Resonance (UHR) layer [26]. The generated Bernstein waves travel inside the
plasma until they are absorbed at the ECR or at the higher-order cyclotron
harmonics. A possible design for a microwave injection system producing the
O-X-B conversion is shown in Fig. 15: first, an O wave is launched from the
outside, with an oblique angle of incidence obtained with a proper orientation
of the parabolic mirrors. For an optimal launch angle, it is possible to
obtain a correlated optimal parallel refractive index and then a coincidence
of the O and X modes at the critical plasma density (cut-off). This means that
both modes have the same phase and group velocities and the power is
transferred without reflections. Once the X waves are generated, they
propagate towards the UHR. Here, the X mode coincides with the electron
Bernstein mode. In the linear description, the X waves are completely
converted into EBWs. This process is called X–B conversion. It should be noted
that the O-X-B process can only take place if the plasma density is above the
O-wave cut-off density.

O-X-B plasma heating and current driving with BW in an overdense plasma were
demonstrated in the Stellarator WEGA, operating at the Max Planck Institute
for Plasma Physics in Greifswald, Germany [27]. The heating of a plasma by
means of EBW at particular frequencies enabled us to reach densities much
larger than the cut-off ones. Evidence of EBW generation and absorption
together with X-ray emissions due to high-energy electrons is shown in ray
tracing simulations and CCD photographs in Ref. [29].

A plasma reactor operating at the Laboratori Nazionali del Sud of INFN,
Catania, has been used as a test-bench for the investigation of innovative
mechanisms of plasma ignition based on electrostatic waves (ES-W), obtained
via the inner plasma EM-to-ES wave conversion. Evidence of Bernstein wave (BW)
generation is shown in Ref. [28].

In particular, during the experiment, a microwave discharge ion source has
been used: a plasma reactor consisting of a stainless-steel cylinder that is
24 cm long and 14 cm in diameter. A NdFeB permanent magnet system generates an
off-resonance magnetic field along the plasma chamber axis (with a maximum of
0.1 T on axis).

Microwaves have been generated by using a TWT, which is able to generate
microwaves from 3.2 to 4.9 GHz. The typical working frequency when using the
TWT was 3.7478 GHz. The temperature and plasma density measurements have been
carried out by using a movable Langmuir Probe (LP). The LP can host a small
wire used as a local electromagnetic antenna, which can be connected to a
spectrum analyser for the plasma spectral emission analysis. An Si-Pin and a
HPGe X-ray detector have been used for the measurement of X-ray spectra in
different plasma conditions. Both detectors are able to detect X rays with
energies greater than about 1 keV. A CCD camera has been used to visualize the
plasma structure within the chamber at different working frequencies, and at
different microwave powers and pressures. A series of LP measurements has been
carried out with the plasma reactor at the frequency of 2.45 GHz, when both
under-resonance and off-resonance regions are present. In Fig. 16, it is
evident that the electron density is drastically enhanced in regions where the
condition $B<B_{\mathrm{ECR}}$ is satisfied.

Figure 16: (Colour online) Electron density and magnetic field profile at
$1.5\times 10^{-4}$ mbar, and frequency 2.45 GHz, at different microwave
powers. Microwave injection occurs at the right-hand side of the figure.

This effect is observed for all of the different power values that we used; in
particular, at 200 W, an electron density of about $1.5\times 10^{12}$ cm−3
has been measured, a value 20 times greater than the cut-off density. Note
that the electron density is everywhere comparable or larger than the cut-off
density ($n_{c}=7.5\times 10^{10}$ cm−3). In the same magnetic configuration,
X-ray measurements have been carried out at 2.45 GHz and 3.7478 GHz. By
increasing the pumping frequency, it is possible totally to remove the ECR, so
that at 3.7478 GHz the entire plasma chamber is at under-resonance and EBW
heating becomes the unique heating mechanism. Spectral temperatures measured
in the two cases are shown in Fig. 17.

Figure 17: (Colour online) Spectral temperatures. At a frequency of 2.45 GHz,
ECR heating and EBW heating coexist; at 3.7478 GHz, EBW heating is dominant.

At the frequency of 3.7478 GHz, the spectral temperature is significantly
larger (up to 4 keV) than at 2.45 GHz. Around 80 W, it is possible to identify
a threshold for which the temperature slope increases suddenly and becomes
steeper for both configurations. The end-point energy is about 10 times the
value of the spectral temperature. The spectral temperature decreases slightly
with the atomic mass of the gas used and when the pressure is increased.
Further results and discussion can be found in Ref. [29]. The results are
interpreted through the Bernstein wave heating theory, and are very promising
for future high-intensity multicharged ion sources that can, therefore, be
based on the results described here, by employing a simplified magnetic
configuration with respect to typical minimum-$B$ ECR ion sources.

##  7 Conclusion

Microwave coupling to ECR ion sources plays a fundamental role in enhancing
their performance in terms of current extracted and average charge state
produced. Over the past decade, new heating methods have been studied to
overcome the technological limitations due to the magnetic field and frequency
scaling, to achieve the production of milliampere levels of HCI, as requested
for the new accelerating facilities all over the world.

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