Main Challenges of Heating Plasma with Waves at the Ion Cyclotron Resonance Frequency (ICRF)

Abstract

Of all the techniques used for heating plasmas in fusion devices, waves in the Ion Cyclotron Resonance Frequency (ICRF ∼ MHz) continue to be exceptionally advantageous and unique insofar as it enables to deposit of power directly on ions in the core, significantly enhancing fast ion population together with fusion reaction products. However, because of the multiple inherent challenges—such as matching robustness, antenna design, wave coupling efficiency, wave propagation, wave absorption, and plasma surface interactions due to radiofrequency (RF) sheath excitation—ICRF is often one of the most complex heating systems to implement successfully. This chapter provides a brief introduction of these challenges and their respective underlying physics, together with examples of both simulations and experimental results from various tokamaks around the world. Finally, ICRF advantages and applications on present and future devices and perspectives of technological solutions are discussed and summarized.

1. Introduction

The ICRF electrostatic wave is first produced by a generator called a tetrode, which is essentially a multistage amplifier of the power composed of a cascade of electron tubes. Each stage of which increases the power by approximately an order of magnitude, from watts to megawatts [1].

High-power waves enter the coaxial line of characteristic impedance Z₀, that matches the output impedance of the generator; typically, 50Ω or 30Ω as in the case of the Full-Tungsten Environment Superconducting Tokamak (WEST) [2] which Figure 1 shows an overview of the ICRF system with all key elements.

1. Electrostatic waves then propagate towards the antenna and cross at some point the so-called matching unit which ensures a smooth transition between the impedance of the coaxial line Z₀ and the one of the antenna straps Z_S to avoid power reflection. If successfully matched, the wave induces a current on the strap at the extremity of the transmission line.

2. This current oscillating at the ion cyclotron frequency (one the order of MHz), results in the excitation of electromagnetic ICRF waves and their coupling to the low-density edge plasma.

3. These waves must then propagate from the edge up to the resonance layer in the core, where they can be absorbed by the ions. Energy is then spread to all charged particles through collisions, resulting in plasma heating.

Figure 1.

ICRF system seen in 3D (a) and from profile (b), with a schematic of the key components of the RF circuit (c) from the generator to the antenna (case of WEST tokamak) adapted from [3].

These three aspects, namely the matching, wave coupling, and absorption, are the key points mandatory for the successful operation of an ICRF system. Section 2 provides the physics background for each of these steps, while section 3 explains what happens in practice due to all of the imperfect conditions and introduces the challenges inherent in ICRF operation; power reflection, arcing, Radiofrequency (RF) sheath excitation, erosion, impurity generation, and plasma contamination. Despite all of these challenges, the fourth and final sections present the key assets that still make ICRF an attractive auxiliary heating system and some perspectives on solutions worthy of further investigation.

2. The key 3 steps of ICRH (Ion Cyclotron Resonance Heating)

2.1 RF circuit matching

Matching the RF circuit consists of building smooth transitions between the purely real impedance of the transmission line (Z₀ =R₀ ≈10➔50Ω) and the complex impedance of the antenna straps (Z_S =R_C +jX_S) which depends on the plasma. When the system is perfectly matched, the electrostatic wave flows from the generator to the straps without seeing any obstacle or being subject to any reflection. This can be achieved in many ways, relying on various components each with a variable impedance such as:

• Single stub also called “trombones” [4] in the Joint European Torus (JET) ITER-Like Antenna [5, 6] (ITER=International Tokamak Experimental Reactor), Alcator C-Mod [7] and the National Spherical Torus Experiment (NSTX) [8]

• Double stubs loaded by shorted tunable capacitors on TEXTOR [9] and analyzed for ASDEX-Upgrade [10]

• Liquid stubs arranged in a triple stub configuration in the Large Helical Device (LHD) [11] and the Experimental Advanced Superconducting Tokamak (EAST) [12]. The reactance of the short-circuited stubs of fixed geometrical length is varied by changing the height of the dielectric fluid (oil) inside the stubs

• Fast Ferrite Tuners: the reactance of a matching stub of fixed geometrical length is here modified by changing the magnetic characteristics of the ferrites which are disposed inside the stubs which were used in Alcator C-Mod [7] and ASDEX Upgrade [13]

• Sliding Impedances [14]

• Single stubs in the Conjugate-T configuration [15]

• Tunable line-stretchers (or phase shifters) in JET [6]

• Tunable vacuum capacitors in JET ITER-like antenna [16] and WEST ICRF antennas [17]. These are complex components (Z_C =X_L-jX_C), which self-inductance (X_L), and capacitance (X_C) can be tuned to match any load at the strap (cf. purple elements in Figure 1)

If the antenna is facing vacuum, the load is stable as it basically only corresponds to ohmic losses in the antenna. In this case, almost perfect matching can be achieved with the resistive part of the load remaining small (Rc ≈ 0.1Ω). In front of a plasma though, the load is larger than vacuum, so that Rc can increase by up to two orders of magnitude, in correlation with the efficiency by which the power is coupled.

In this case, however, the load (plasma) can change rapidly. This means Z_S is seldom if ever perfectly matched to Z₀, and that the power launched by the generator (P_in) is hardly exactly equal to the one coupled by the antenna to the plasma:

$${\mathrm{P}}_{\text{coupled}}={\mathrm{P}}_{\text{in}}\left(1-{\left|\mathrm{\Gamma }\right|}^2\right)$$E1

where Γ if the reflection coefficient defined as Γ = (Z_s−Z₀) / (Z_s + Z₀).

The fraction of uncoupled power is therefore reflected in the transmission line, which can damage the generator if it is too large. This is avoided by introducing a quarter wavelength phase-shift in the matching circuit—for instance by tuning the height of the oil in EAST stub tuner or by using an impedance transformer in WEST—so that in the section between the generator and the matching circuit, only forward waves exist.

In the section between the matching circuit and the antenna though, coexist waves travelling both forward and backward, which superimpose on one another and give rise to a standing wave pattern. The maximum and minimum voltages of such waves are defined as follows:

$${\mathrm{V}}_{\max }=\left(1+\left|\mathrm{\Gamma }\right|\right)\sqrt{2{\mathrm{Z}}_0{\mathrm{P}}_{\text{in}}}=\sqrt{2{\mathrm{Z}}_0{\mathrm{P}}_{\text{coupled}}\text{VSWR}}$$E2

$${\mathrm{V}}_{\min }=\left(1-\left|\mathrm{\Gamma }\right|\right)\sqrt{2{\mathrm{Z}}_0{\mathrm{P}}_{\text{in}}}=\sqrt{2{\mathrm{Z}}_0{\mathrm{P}}_{\text{coupled}}/\text{VSWR}}$$E3

And the ratio of these voltages is the so-called Voltage Standing Wave Ratio:

$$\text{VSWR}=\frac{1+\left|\mathrm{\Gamma }\right|}{1-\mid \mathrm{\Gamma }\mid }$$E4

It follows that VSWR grows from 1 in the ideal perfectly matched “flat-line” case (V_max = V_min), to infinity when almost all the power is reflected. If the VSWR is too large, the difference of electrical potentials in the lines becomes so high that there is a significant risk of arcing. To prevent such deleterious events, operational safety limits are set on the voltage (V_max) and the current (I_max), above which the power shuts down.

$${\mathrm{I}}_{\max }=\left(1+\left|\mathrm{\Gamma }\right|\right)\sqrt{2{\mathrm{Y}}_0{\mathrm{P}}_{\text{in}}}=\sqrt{2{\mathrm{Y}}_0{\mathrm{P}}_{\text{coupled}}\text{VSWR}}$$E5

with Y₀=1/Z₀. We now understand how crucial it is to transport the power along well-matched lines. It naturally follows that minimizing length of the lines with these undesirable effects by placing the matching system as close as possible to the antenna, will be a key aspect of the system’s efficiency (cf. section 2.5 of [18]).

In addition, decouplers are used to prevent the mutual coupling of adjacent lines which influence each other due to the proximity of the straps to one another. This effect can make a source behave as a receiver and endanger its generator. Decouplers are used in DIII-D [19], EAST [20], Alcator C-Mod [7], NSTX [8] and will be used on ITER [21]. This is also important to equalize the voltages at the inputs of the array and guarantee a homogeneous excitation over the whole surface of the antenna’s front face, which can otherwise have deleterious effects on local fields and RF sheath excitation. Strap-decoupling can also be improved by separating them with a septum in the antenna box to reduce mutual influence.

Excellent explanations of the topic can further be found in the fourth chapter of [18] with more detailed calculations and specific applications to the case of WEST. Once well matched, the system and the antenna are then ready to launch waves which coupling to the plasma remains to be optimized.

2.2 Wave coupling

The front of the antenna faces the plasma inside the vessel. As the power emitted from the generator reaches the antenna, it induces an oscillating current I_RF along the strap as highlighted in red in Figures 1b and 2, which excites ICRF waves at the edge of the plasma, as efficiently as the load or the coupling resistance (R_c) is high.

Figure 2.

Poloidal cut of a tokamak vacuum vessel, with ICRF waves excited by the antenna, propagating in the well-confined region of the plasma, partially absorbed and mode converted near the resonance layer.

$${\mathrm{P}}_{\text{coupled}}=\frac{1}{2}{\mathrm{R}}_{\mathrm{c}}{{\mathrm{I}}_{\mathrm{RF}}}^2$$E6

The problem in coupling ICRF waves at the edge, lies in the fact that to avoid exposure to dense and hot plasma—which would induce unacceptably large heat loads—antennas are retracted away and sit in the Scrape-Off Layer (SOL), a low-density plasma (pink regions in Figures 2 and 3) where the Fast Wave (FW) is generally not propagative but evanescent (${\mathrm{k}}_{\perp }^2<0$). A wave is evanescent when the density is smaller than its cutoff density (n_co). Therefore, the larger the distance from the strap to the cutoff layer (D_Strap-co), the lower the coupling efficiency and vice versa. To give a rough idea, 1 cm increase of D_Strap-co generally results in about 20% drop of the coupling efficiency, meaning that about 1/5 of the power vanishes every centimeter until reaching densities above n_co. In addition, the nature of the spectrum excited by the antenna, according to its geometry (straps width, height and spacing), and in particular, the value of the parallel wave vector (k_//) corresponding to the main components of the spectrum, plays a key role in the coupling process:

Figure 3.

Properties of 120MHz ICRF fast (FW—dashed lines) and slow (SW—solid line) wave modes in a realistic fusion plasma with similar proportions of deuterium and tritium confined by a magnetic field of 10 tesla. Waves are propagative when the sign of ${\mathrm{k}}_{\perp }^2$ is positive, and evanescent elsewhere. Cutoff densities of each branch are written explicitly on the graph.

$${\mathrm{R}}_{\mathrm{c}}=\frac{{\mathrm{Z}}_0}{\text{VSWR}}\sim {\mathrm{R}}_{0}exp\left(-2<{\mathrm{k}}_{//}>{\mathrm{D}}_{\text{Strap}-\mathrm{co}}\right)$$E7

One can observe, in Figure 3, how this parameter typically influences the fast-wave cutoff density which drops by over an order of magnitude as k_// decreases from 18 down to 6 m⁻¹.

ICRF waves comport two modes called fast and slow waves in reference to their respective group velocity (details of mathematical calculations can be found in the second chapter of [22]):

• Fast Waves (FW) are evanescent at low densities typical of the plasma edge and propagative for densities characteristic of the plasma core (Figure 3). FW have wavelengths on the order of few meters and an electric field perpendicular to the magnetic field. Therefore, when talking about coupling maximization, it is common to implicitly refer to this mode, because it is the one suited to heating the ions which rotate perpendicularly around the magnetic field lines.

• Slow Waves (SW) are propagative at very low densities characteristic of the outer most “far” SOL (n_e < 5.2 10¹⁷m⁻³ in Figure 3) and evanescent above. SW have millimetric wavelengths and an electric field parallel to the magnetic field. Because the current straps are not perfectly perpendicular to the tilted magnetic field lines, SW are parasitically excited and are often responsible for exciting the RF-sheath, leading to deleterious plasma surface interactions. The role the faraday screen (Figure 1a) with bars in principle parallel to the magnetic field, is intended to locally increase the conductivity in the parallel direction to screen the SW in front of the straps. Unfortunately, we will see in the next section that this is not enough.

At this point, one should remember when hearing people say that they are trying to “optimize the coupling of an ICRF antenna”, that they are basically trying to maximize its coupling resistance (R_c), either by reducing D_Strap-co or k_// (Eq. (7)).

D_Strap-co can be minimized in different ways [23]:

• Put the antenna closer to the plasma, but this will come with stronger heat loads and usually impurity production

• Globally increase the density of the plasma, but this is limited and associated with an increase of the power lost in radiations

• Locally increase the density by fueling the plasma from valves magnetically connected to the antenna and ideally as close as possible to the middle plane [24, 25]

• Increase the frequency of the waves, which must remain compatible with an efficient scenario for heating the plasma (discussed in the next section)

k_// can be minimized at two different stages:

• While designing the antenna, basically by increasing the space between adjacent straps, but this often limited by the available space in the torus

• During the experiments, by reducing the phase difference of the currents on the adjacent straps (ϕ). Most of the time however, this trick is first limited by the currents induced on the surrounding passive structures, which play an important role in plasma surface interactions [26]. These currents basically tend to add up when currents are in phase (monopole ϕ=0 ̊) instead of compensating each other for largest phasing (dipole ϕ=180 ̊) [27]. Secondly, the larger k_// the more efficient the wave absorption [28].

Once efficiently coupled to the plasma, wave absorption remains to be optimized.

2.3 Wave absorption

Waves that propagate towards the center of the plasma finally reach the resonance layer where ions frequency (w₀) corresponds to a multiple of the wave frequency (nw_ci), enlightened by the vertical yellow line in Figure 2. In this region, the frequency of the wave coincides with the fundamental or harmonics of the cyclotron frequency of ion species to be heated. One can tune the wave frequency, the magnetic field profile, and the plasma composition to pick the desired heating scheme among a variety of techniques [29] by matching the Doppler-shifted wave frequency with the ion cyclotron harmonics:

$$\mathrm{\omega }=\mathrm{n}{\mathrm{\omega }}_{\mathrm{ci}}+{\mathrm{k}}_{//}{\mathrm{v}}_{//,\mathrm{I}}$$E8

• Heating a minority at its fundamental resonance (n=0): such as hydrogen in a deuterium plasma (H-D) with a small concentration of hydrogen, typically n_H/n_H+n_D<15%. So far, minority heating is the most routinely used in most devices. However, while it has long been applied on two-ion species plasmas, it has been found that it can also be applied with great efficiency in plasmas with three (or more) ion species.

• The three-ions scheme also consists in heating the fundamental of the minority specie such as a little helium in a deuterium tritium fusion plasma (ex: (He³)-DT), but here the resonance location of the minority must fall in between the resonances of both others majority species [30], where the amplitude of the left-handed polarization (E₊) can reach very high values and lead to strong diffusion (D) of the wave power:

$$\mathrm{D}\propto {\left|{\mathrm{J}}_0\right|}^2{\left|{\mathrm{E}}_{+}\right|}^2$$E9

• Heating a majority at its harmonic resonance (n>0): this can be an alternative to the minority heating typically if it proves challenging to accurately controlling the isotopic ratio. However, this scenario becomes truly effective only when a population of fast ions is created to improve power absorption. This process usually relies on harmonic heating. While generating a population of fast ions large enough to boost up the absorption, it can also be directly injected by a Neutral Beam Injector (NBI), hence the so-called synergy between NBI and ICRH (cf. experimental [31] and simulation [32] results in JET tokamak). Unfortunately, not only NBI is not available in all devices, but if the confinement is not good enough, for instance in case of low plasma current, this method is counteracted by fast-ions losses.

3. Challenges behind each step

3.1 Real-time matching

In practice, before main experiments start, ICRF operators usually “prepare the matching” and pre-set the parameters (ex: Oil level in the stub tuner in EAST, capacitance of the capacitors in WEST …) with the antenna facing vacuum. Later, the matching is adjusted with the antenna facing the plasma, one of the many reasons why campaigns always include a period for commissioning systems at the beginning. The system starts with low power in case of sources of mismatch or poor coupling efficiency to avoid the risk of arcing due to large fractions of power reflected, and gradually raise it up to power levels relevant for the experiments (MW order). One of the key goals during the experiments is to further improve plasma confinement, often leading to operate in H-mode [33]. H-mode plasmas represent a great challenge for all RF circuit matching, first because during the L-H transition, a pedestal forms at the edge where the density typically drops with sharper gradient compared to L-mode plasmas, lowering the coupling efficiency (R_c) sometimes by half. But also, the so-called Edge-Localized Modes (ELMs) induce important load variations through transient bursts, basically as large as their frequency is low (from kHz range for the smallest type-III ELMs down to tens of Hz for the largest type-I ELMs with R_c suddenly increasing by factors up to 5 within less than a millisecond. One can further show for a strap matched by a 2-port matching unit, if the matching is not reconfigured, the VSWR will raise in similar proportions as R_c (cf. calculation details in section 2.7 of [18]), risking provoking arcs either in the transmission lines [34] or in the antenna box [35]. All this motivates real-time control of the impedance matching that can be achieved with:

• Capacitors, like in Tore Supra Classical antennas [36] and JET-ILA [37]. Amplitudes of the incident and reflected voltages and their phase shift are typically measured either on the transmission lines or ideally as close as possible to the antenna, and mixed to provide error signals driving the capacitors

• Conjugate-T and similar principle as with capacitors [13]

• Fast Ferrite Tuners, like in Alcator C-mod antennas [7]

• Impedance matching by real-time controlling the generator’s frequency [4]

• Decouplers and double stub in ITER [21]

Various algorithms can then be used to automatically tune parameters of interest for each component. However so far, no controller allows tackling sub millisecond variations typically induced by ELMs, hence the need for so-called load resilient matching schemes [38].

3.2 Load resilience

Without load resilience, an ICRF system would stop delivering power every time its VSWR would exceed some safety value, which would basically make it incompatible with steady operation during a discharge with ELMs. A very convincing comparison between resilient and non-resilient system can be found in Figure 13 of [13].

Among existing load-resilient schemes, one can quote:

• 3dB hybrid coupler diverting the reflected power to a dummy load, such as the lossy network in ASDEX-Upgrade [39]

• Conjugate-T concept, connecting pairs of straps, with various designs:

  • External conjugate-T relying on line-stretchers in JET [13] and EAST [40]

  • Internal conjugate-T relying on capacitors in JET-ILA [5], Tore Supra [41] and WEST [17]

  • Stub conjugate-T in Alcator C-Mod [15]

  More details can be found on the conjugate-T under section 4 of the fourth chapter of [18] with detailed mathematical calculations and applications to the internal conjugate-T of WEST and experimental results in [42].

• Travelling wave antenna concept [43] which in case of load drop, takes profit from the mutual coupling between straps to let the wave propagate along the array and recirculate, making it inherently load resilient. This concept has been used in DIIID [44, 45] for driving current and envisaged for heating plasmas in WEST [46]. While never tested for heating tokamak plasmas, the concept somehow lost its appeal, essentially due to the integration challenges it raises, that become even more problematic in the perspective of fusion reactors which must maximize the surface of the tritium breading blanket and therefore focus on heating systems with large power densities.

Note that in most of the cases, load resilient solutions are combined with matching units, so that the problem is most often tackled from the generator perspective, with first goal to deliver constant power despite load fluctuations at the antenna.

After having explained the importance of operating with a well-matched system, we will now place ourselves from the inner vessel perspective and further discuss the challenges that concern an ICRF antenna facing a fluctuating plasma. There the main goal will rather be to prevent the coupling resistance from dropping under some value, not only critical for the VSWR and arcing in the transmission lines, but also for the excitation of near fields and RF sheath.

3.3 RF-sheath and potential rectification

The formation of a sheath on any component facing the plasma is a natural phenomenon [47]. The sheath is a thin layer (usually few millimeters wide) which forms on the surface of all materials in contact with the plasma. Across this layer, a separation of the charges (therefore an electric field) makes it possible to preserve the ambipolarity of the fluxes of charged particles from the plasma towards a surface (cf. Figure 4). Since the mass of electrons is much smaller than that of ions, their speed is much greater. Therefore, when exposed to a plasma, the surface of materials becomes negatively charged, repelling electrons, and attracting ions approaching below a Debye length (${\mathrm{\lambda }}_{\mathrm{De}}=\sqrt{{\mathrm{\epsilon }}_0{\mathrm{k}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{e}}/{\mathrm{n}}_{\mathrm{e}}{\mathrm{e}}^2}$) with ε₀ and k_B respectively electric and Boltzmann constants, T_e and n_e respectively the electron temperature and density and the charge of the electron e = 1.6 × 10⁻¹⁹ coulombs.

Figure 4.

Sketch of a sheath layer forming on a material facing the plasma.

The properties of the sheath can undergo substantial changes depending on several parameters that can typically influence its electric field and width δ_sheath:

$${\delta }_{\mathit{\text{sheath}}}={\lambda }_{\mathit{De}}{\left(\frac{e.V_{\mathit{DC}}}{k_B{T}_e}\right)}^m$$E10

with V_DC the DC potential and m a parameter that typically changes between 2/3 and ¾ depending on the incidence angle of magnetic field lines on materials and the collisional properties of the sheath as explored through Particle in Cell simulations in [48]. In general, the electric field accelerates the ions towards the wall, leading to an increase of the sputtering and the production of impurities (Figure 4) in proportions usually comparable to the increase in electron temperature:

$${\mathrm{V}}_{\text{Thermal sheath}}=3{\mathrm{k}}_{\mathrm{B}}{\mathrm{T}}_{\mathrm{e}}/2$$E11

On the other hand, in the presence of ICRF heating, this phenomenon is further aggravated by the so-called rectification of the oscillating potentials associated with the slow wave carrying electric field in the direction parallel to the magnetic field lines (cf. red curve in Figure 3). Let us now express the current instantly conducted to any object exposed to the plasma as:

$$\stackrel{\sim }{I}\left(t\right)=I_{\mathit{sat}}^{+}\left(1-exp\left(\frac{e}{k_B{T}_e}\left({\varphi }_f-\stackrel{\sim }{V}\left(t\right)\right)\right)\right)$$E12

with I_sat⁺ the ion saturated current, ϕ_f the floating potential and $\stackrel{\sim }{V}\left(t\right)=V_{\mathit{DC}}+V_{\mathit{RF}}cos\left({\omega }_0.t\right)$ the sheath potential in presence of an RF wave. Then the RF➔DC rectification, specific to waves at the ion cyclotron frequency, results from the fact that the electrons (light compared to the ions) react instantaneously to the oscillating electric field of the wave (V_RF), while the ions react only to the average value.

$$⟨\stackrel{\sim }{I}\left(t\right)⟩=\overline{I}=I_{\mathit{sat}}^{+}\left[1-exp\left(\frac{e}{k_B{T}_e}\left({\varphi }_f-V_{\mathit{DC}}\right)\right)I_0\left(\frac{{\mathit{eV}}_{\mathit{RF}}}{k_B{T}_e}\right)\right]$$E13

with I₀ a Bessel function. The consequence at the level of the components facing the plasma on the scale of an RF period, is the appearance of a DC current due to the privileged drift of the electrons. Thus, to compensate this current, the DC potential of the sheath must adjust and get biased by an extra potential V_b:

$$V_b=\frac{k_B{T}_e}{e}{I}_0\left(\frac{{\mathit{eV}}_{\mathit{RF}}}{k_B{T}_e}\right)$$E14

The RF➔DC rectification of the sheath therefore has the effect of increasing the potential drop (electric field) through the skin between the plasma and the wall, i.e., the acceleration of the ions towards the materials. This acceleration often boosts ions incident energies up to critical levels for exposed components (i.e., above sputtering yields threshold values). For deeper understanding of the topic, the reader is highly encouraged to refer to excellent tutorial [49] and reviews of key experimental [26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50] and modelling [51] results.

3.4 Physical sputtering yield

The other key process by which ICRF operation often enhances impurity production is the physical sputtering yield Y_Eff. This parameter represents the probability for an ion to sputter an atom from a target, given its charge, its incident energy, and their respective mass:

$$\text{Impurity outflux}={\mathrm{\Gamma }}_{\text{target atoms out}}={\mathrm{\Gamma }}_{\mathrm{ion}\text{in}}{\mathrm{Y}}_{\mathrm{Eff}}$$E15

For example, the graph in Figure 5 shows how the sputtering of a graphite (∼carbon) target evolves for different bombarding species. The first important aspect of the sputtering yield is that it varies non-linearly with the energy of the incident ion. The second one is that only above a threshold energy of about 30eV, do the incident species start to sputter carbon atoms. The red curve also represents the self-sputtering of lithium which is sometimes used for material coating to prevent from important plasma contamination by high-Z impurities. One can see that a lithium coating will typically get eroded at much lower energy, while plasma facing components in graphite will require larger energies. We have here taken the case of carbon components, sometimes coated with lithium, exposed to various species, which is the case in EAST tokamak. Carbon however won’t be used in future devices plasma facing components due to tritium retention. Tungsten has now become the most suitable candidate. In WEST for instance, antenna limiters are coated with tungsten, which sputtering follows similar trends (cf. Figure 3 of [23]).

Figure 5.

Sputtering yield of various ion species on a target in graphite.

3.5 Poor coupling efficiency and near-field effects

RF-sheath excitation is the phenomenon proper to ICRF which is responsible for its peculiar complexity, due to the non-linear trade-off relation between the maximization of the coupling and the minimization of the interactions with the plasma. For any object in principle, moving away from the plasma results in a strict decrease of their interactions. However, for a classic ICRF antenna, moving away first induces a drop in its coupling efficiency, therefore an increase of excited fields (consistent with an increase of the VSWR in the transmission lines), which in turn can in critical cases result in a local but exponential increase of the RF sheath potential (cf. Figure 3 of [52] and section 3.3 of this chapter). In addition, the sputtering yield not only changes non-linearly, but also reaches its largest values for energies typically in the range of potential rectified by RF sheaths (cf. red region between 100eV and 1keV in Figure 4). It follows that in some cases, increasing the distance between an ICRF antenna and the plasma to reduce their interactions based on linear intuition, can unexpectedly cause an increase of impurity production from local sources, reacting to sharp increase of RF sheath potentials. These phenomena can be modeled in different ways as summarized in [53]. This behavior was also experimentally observed in WEST during a scan of the radial position of an ICRF antenna, where the floating potential measured by a reciprocating probe did not directly decrease as the antenna was retracted but first passed by a maximum for intermediate position (cf. Figure 4 in [50] or Figure 6.23 of [22] in open access). A wide variety of RF-sheath induced plasma surface interactions have also been observed in devices such as:

• EAST with the partial melting of metallic plates at the corners of an ICRF antenna, which precisely did not melt at the closest point to the plasma, but at the locations where simulations predict RF sheath excitation to be maximal (cf. Figure 14 in [54] or Figure 6.27 of [22] in open access)

• Tore Supra with large, enhanced potentials measured with retarded field analyzer [55] causing large heat loads on antennas [56]

• A LineAr Plasma Device (LAPD) using diagnostic magnetically connected to ICRF antenna along large number of reproducible discharges to provide great evidence of ICRF interaction process in the edge plasma [57]

• Alcator C-Mod with strong potentials measured with several different probes [58] caused by RF sheath excitation [59], leading to the increase of impurity sources and deleterious influence on plasma performance [60]

• ASDEX Upgrade with similar experiments [61] that have inspired a series of successful technological upgrades [62, 63] discussed hereafter in section 4

• JET is also subject to these effects [26, 64]

Interactions occurring at vicinity or in regions magnetically connected to the active antenna frame (red start with most branches around the antenna in Figure 2) are often classified as near field effects. Hence, interactions respectively taking place elsewhere will be conveniently referred to as far field effects¹.

3.6 Abnormal wave absorption and far-field effects

Following the same logic, we will categorize interactions occurring in regions without magnetic connection to the active antenna as far field effects. These can be observed in unexpected locations when abnormal propagation and absorption of the wave take place. For instance, if the absorption efficiency is low, the power launched in the plasma is not fully absorbed at the first pass, and a non-negligible fraction of unabsorbed power propagates and reflects on farther objects such as the divertor or the inner wall as represented in Figure 2. In these cases, not only heating performance drop, but RF-sheath can also potentially become excited in global fashion. Such effects were well-observed in

• EAST high field side wall (cf. red star with 4 branches in Figure 2) when the antenna operated in monopole phasing, causing a drop in the absorption efficiency and an increase of fields excitation at the inner wall [54]

• WEST divertor if too low hydrogen ratio leads to poor wave absorption [65]

• NSTX divertor where operating at high harmonics led to the excitation of surface waves [66] and substantial fraction of their power to be coupled to the edge filamentary structures parallel to the magnetic field lines [67], resulting in potential rectification at their extremity and deleterious interactions [68].

4. The beauty of ICRH: assets and technological perspectives

4.1 Assets

Despite the many challenges, ICRF has remained a very important tool for heating plasmas, with constant progress over the past fifty years [69]. ICRF is the only heating system that can directly deposit power onto the ions, allowing to generate fast ions and significantly boost fusion performance. While minority heating has long remained the most widely used method, this past two decades have been marked by the emergence of several modelling tools allowing to predict wave absorption efficiency [70] and power thermalization on the various species [71, 72]. These tools have allowed to explore much wider varieties of heating schemes [29]. Most promising ones were then tried experimentally, and their efficiency confirmed. One can typically quote scenarios based on the synergy with NBI [31, 32, 73] and these relying on three-ion scheme [74]. In particular, the three-ion scheme has gained increasing interest not only due to the efficiency in generating fast ions, but also for the operation flexibility it offers. Indeed, instead of relying on specific fraction of a minority specie—which can be difficult to maintain over operation—it proves much easier to keep control of rough proportions of two (or more) majority species and deposit power on a third very minor one which fraction is easier to control. Most promising scenario for fusion reactor D-T plasmas would therefore consist in depositing power most likely on ³He, which has been successfully achieved in JET and Alcator C-Mod [30] and foreseen for future devices like ITER [74] and SPARC [75].

Another application of ICRH is the control of impurity population in the core. It has for instance been observed in JET, that for ICRF power above 4MW, heating H minority can result in high-Z impurity screening out of the core [76]. Furthermore, the three-ion scheme even allows to directly pump out an impurity by depositing part of the power on it. This was observed with beryllium in JET [29], with Argon on TFR [77] and Alcator C-Mod [78]. The same trick could further allow to pump out tungsten impurity by targeting the second harmonic of W⁵⁶⁺ in SPARC’s high temperature plasmas [78], a powerful tool to prevent tungsten accumulation in the core.

4.2 Technological perspectives

A few research and development ideas for improving current design of antennas yet remain to be tested. One can quote:

• Travelling wave antennas [43] could improve the reliability of ICRF systems thanks to its inherent load resilience and much larger coupling capacities, offering the possibility to place the antenna 10cm further away from the plasma than a classic antenna and still be able to couple similar amount of power. This could have tremendous impact not only on the coupling efficiency but also on the interactions with the plasma and its contamination by metallic impurity. The disadvantage of this concept is its low power density due to the large number of straps (>5). This makes any design hardly compatible with fusion reactor worried of maximizing the surface of the tritium breeding blanket. But maybe some tricks have not yet been thought about …

• Active limiters could allow compensating actively the image currents induced on limiters by nearby current straps. Relying on the concept of proximity effect [27], these currents can be cancelled by powering straps with appropriate phasing and power ratio, as was shown in ASDEX-Upgrade 3-strap antennas [63] and Alcator C-Mod 4-strap antennas [79]. However, operating the ICRF system with optimal settings is not only challenging in terms of control, but mostly limiting in terms of power density. Active limiters would then consist in applying a fraction of the power sent on the straps, directly on the limiters. This could allow reducing the local impurity sources, by canceling off the local currents that tend to be responsible for RF sheath excitation. In addition, such solution would offer two key advantages:

  • more flexibility during ICRF operation by opening the possibility to routinely tune the antenna phasing without aggravating interactions with the plasma. In other words, this would allow operating with different antenna spectra to cope with plasma changes regardless of near-field effects

  • maximize power density. While this is already quite important in nowadays experimental tokamaks, it will be a critical aspect on future fusion reactors, which aim at maximizing the surface of the tritium breeding blanket for producing fuel and extracting the energy radiated by the plasma to generate electricity. Simultaneously satisfying requirements on plasma heating, fuel production and energy exhaust, pushes towards more compact designs with larger power density currently hardly compatible with low level of impurity production. Active limiters could therefore be a major technological solution.

5. Conclusion

Despite all challenges, heating fusion plasmas with waves in the ion cyclotron range of frequency is still very attractive. While several technological solutions remain to be explored, a variety of existing ones are already routinely used and allow successful operation in many devices around the globe. A summary of the key components of an ICRF system, and a selection of the main phenomena that can occur in various location is provided in Figure 6. To conclude on the perspective of fusion reactors, while ICRF may not be the optimal solution in terms of power density, note that as the intensity of the magnetic field due to progress made on low temperature superconductors and the size of the devices will increase, ICRF is the only heating system which difficulty to implement will not be affected.

Figure 6.

Summary of the key components of an ICRF system, and a selection of the main phenomena that can occur in various location. Black boxes enlighten phenomena inherent to ICRF powering. Blue boxes show the physical parameters that are most directly influenced. Red boxes show the potentially deleterious consequences of parameters changes. Green boxes with green and orange borders show the main solutions respectively existing and to be explored.

For further reading of on this topic, the reader is highly encourage to refer to a review of the “Recent Progress in ICRF in Magnetic Confinement Fusion” [80] and references therein.

Acknowledgments

Laurent Colas, Julien Hillairet, Karl Vulliez, Annika Ekedahl, and more globally WEST and EAST ICRF Teams are warmly acknowledged for their efforts in making experiments possible and the numerous fruitful discusssssions. I also want to thank a lot Wouter Tierens, Mari Usoltceva, Vladimir Bobkov, and the rest of ASDEX ICRF team, Ernesto Lerche from ERM and colleagues from the 107 team of Institut Jean Lamour for all the things we collaborated over the past few years.