ICRF antenna and transmission line design

RADIOFREQUENCY WAVES, HEATING AND CURRENT DRIVE IN MAGNETICALLY CONFINED PLASMAS

6.2. THEORY OF RF WAVE PROPAGATION IN A MAGNETIZED PLASMA The theory of wave propagation in magnetized plasmas has been

6.3.2. ICRF antenna and transmission line design

In this section we discuss the conversion of prime RF power to electro- magnetic waves in the ICRF, including transmitters, transmission lines and the launchers (antennas) that excite plasma waves of the desired polarization and spectral characteristics in the edge of the plasma.

6.3.2.1. ICRF transmission line architecture

A schematic layout of the simplest possible system with a single element antenna is shown in Fig. 6.25(a), while parts (b) and (c) of the figure show the topologies of configurations to drive a phased array of two elements.

FIG. 6.25. Schematics of simple ICRF system configurations. (a) Single antenna, single source.

Characteristic impedance of transmission line Z0 = 30–50 Ω. (b) Feeding a pair of antenna elements with a single source. (c) Feeding a pair of antenna elements with two sources.

In Fig. 6.25(a) the feedthrough defines the boundary between the pressurized transmission line and the device vacuum. The antenna’s input impedance is primarily reactive with only a small resistive part, in magnitude much smaller than the characteristic impedance of the transmission line Z0∼30 50 . In Fig. 6.25(b), the power splitting may be inside the device vacuum and only a single feedthrough would be needed. In Fig. 6.25(c) a decoupler would be needed

if arbitrary phasing is desired to compensate for mutual reactance between the antenna elements.

6.3.2.2. ICRF source technology

An important advantage of heating and current drive systems in the ICRF over other auxiliary heating methods, particularly in future reactor applications, is the highly efficient continuous wave (CW) sources that are available. Prime electric power can be converted into electromagnetic wave energy in the ICRF at an overall efficiency of about 70%, which compares favourably with presently achievable efficiencies of other frequency regimes of interest for fusion applications, as well as both positive-ion- and negative-ion-based neutral beam sources. The reason that source efficiency is of importance in reactor applications is that reactors will operate in a high Q but not ignited regime, for reasons of controllability. The efficiency of the drivers directly feeds into the overall Q of the plant at fixed levels of confinement.

Sources with these high efficiencies and at high power levels have been available for many years because of the coincidence of the ICRF for hydrogenic plasmas at magnetic fields of 3–8 T with the VHF frequency band (30–300 MHz), which has been used for decades for radio and television broadcasting and other high power commercial applications. In essentially all experiments in the ICRF that have been carried out since the late 1950s, the RF sources have been based on modified high power broadcast transmitters. As early as 1964, a 4 MW transmitter at 25 MHz was in use for ICRF experiments on the C stellarator [6.132], though pulse lengths longer than 0.005 s were not needed in those experiments. The highest power ICRF transmitter that has been used in fusion experiments to date is the 32 MW system installed on JET [6.133], which is composed of sixteen 2 MW modules. This system was specified to be able to produce full power at a pulse length of at least 20 s. The highest power CW generator for fusion research that has been demonstrated to date is the 25–100 MHz 1.6 MW transmitter developed for the superconducting Large Helical Device. This module has been tested to 5000 s pulse length at full power into test load [6.134]. Each of these high power RF sources is built as a chain of two or three gridded-tube amplifiers, each stage having a power gain of ~13 dB, as illustrated in Fig. 6.26.

The final stage amplifier is built around a high power tetrode with a typical anode dissipation rating in steady state of up to 2.5 MW [6.135]. Figure 6.27 shows a photograph of such a tetrode made by EIMAC in the USA. At a typical anode efficiency of ~0.7, output power levels into a matched load of 5 MW from a single tetrode should be in principle possible. In practice, allowable maxima of anode current, of control and screen grid dissipation, and readily achievable drive power levels (at a gain of 13 dB) limit the achievable output power to somewhat lower than 3 MW from a single source. The remaining substantial

margin of maximum power output relative to what is usually produced with a single amplifier has been used to permit operation with less than perfect matching, or to widen the available instantaneous bandwidth (when frequency is used as a tuning actuator), and to maximize tube lifetime and reliability. For high power long pulse operation in the VHF band, the circuit that matches the output impedance of the tetrode to the characteristic impedance of the transmission line (typically 30 or 50 Ω) is implemented as a coaxial cavity. Such systems tend to have instantaneous bandwidths (without retuning) in the order of several hundred kHz and can be tuned between pulses in a matter of a few minutes to operating frequencies in the VHF band differing by a factor of two or more. Typical tunable frequency ranges are 25 to 50 MHz, 40 to 80 MHz, 25 to 100 MHz, or 30 to 120 MHz.

FIG. 6.27. Typical high power tetrode used in cavity amplifiers for ICRF systems in the VHF band (CPI Eimac 4CM2500KG). The structure at the top is the water jacket surrounding the anode; the cooling water inlet and outlet tubes are visible. Photograph courtesy of CPI EIMAC, Palo Alto, CA.

FIG. 6.26. Typical high power transmitter layout with three amplifier stages, the necessary power supplies and the control system.

The needs of future devices in the area of ICRF transmitters will be able to be met with a relatively small amount of further development. In particular, extension of the power that is demonstrated in true steady state (no further evolution of the temperature of any of the components in the transmitter) up to 2 MW per unit and beyond should be carried out. It should be noted that requirements on the flexibility of the system, especially in the area of tunable frequency range, are likely to be maximum on ITER and decrease for subsequent, less experimental devices. The ultimate ICRF system is likely to operate only at a single, pre-chosen frequency, or at most in a narrow band around such a specific frequency. Removal of the need for a one or two octave wide tunable band should permit significant simplification of the transmitter and may be accompanied by gains in overall system efficiency and reliability.

6.3.2.3. ICRF transmission line design

A significant advantage of RF heating methods over neutral beams is that the sources of RF energy can be located at a convenient distance from the plasma device with quite low levels of loss of power over long transmission lines. This is even more the case with waves in the ICRF than with the higher frequency ranges. In practice, distances of the sources from the plasma are measured in the hundreds of metres or even kilometres with losses of only a few per cent being typical. Since the transmission lines operate in the lowest order TEM mode, mode conversion at bends and resulting increased losses is not an issue, nor is alignment, etc. The wave launchers used in the ICRF usually involve a phased array of elements which present an impedance to their feedlines that is significantly different than the characteristic impedance of the transmission line.

Furthermore, the elements in the array often have significant levels of mutual reactive coupling to each other, and the total number of elements often does not equal the number of RF sources being used to power them. Consequently, in addition to conveying the wave energy from source to plasma device, the transmission line must perform a number of additional functions. These functions include power splitting or combining, relative phase and amplitude control and impedance matching. A quite significant challenge is to deal with the fact that in the ICRF the coupling physics of the wave launchers is such (see the next section) that the input impedance of the coupler can vary strongly on a large range of timescales, from tens of microseconds (L/H transitions, ELMs) to very slow changes due to thermal expansion of the components of the system which may be hundreds to thousands of seconds. The impedance matching system must be capable of dealing with these changes to optimize power transfer from the source to the plasma and to minimize RF voltage in the tuned sections of the lines.

The development of both sources and transmission lines has been facilitated by the environment which is fully controllable (e.g. transmission lines can be pressurized with insulating gases, water and/or air cooling is readily introduced). Many developments in the transmission line area for the ICRF have been reviewed in Refs [6.136, 6.137], with a few of the highlights being listed here:

• Demonstration in existing experiments of multiple techniques of impedance matching that allow a significant range of coupler input impedance variation and yet present the transmitter with a well matched load at all times. This includes passive-lossy schemes involving 3 dB hybrid junctions, lossless systems such as the conjugate tee matching scheme, and fast-acting matching elements such as the ‘twin stub’ with narrow band frequency modulation, fast ferrite stubs and other devices.

• Successful methods of power division and phase control for large phased arrays of up to 12 elements, including significant development of necessary decoupling schemes that are needed to permit travelling wave phasings for current drive applications in the face of strong mutual reactance between elements in the arrays. The decouplers are also an integral part of the matching schemes listed above.

• Demonstration of actively cooled ICRF transmission lines operating in a thermal steady state at high CW power levels, as will be needed for ITER and steady state devices beyond ITER.

In summary, it can be asserted that the transmission line aspect of high power steady state ICRF systems is well in hand, with only minimal further development being needed for future systems.

An example of a transmission line system in present use is the tunerless system used on the DIII-D device to power a four-element phased array at a 90° phasing [6.138]. In this case, flexibility (in operation frequency and antenna phasing) is sacrificed to gain simplicity. This configuration uses a 3 dB 90°

hybrid junction and a 2-port decoupler to provide complete isolation from reflected power to the transmitter in the face of rapidly changing antenna loading without adjustable tuning elements. Other transmission line configurations in present use employ external conjugate tees, such as on JET [6.139], to provide similar “load resilience”, or use conjugate tees internal to the antenna similarly with the added advantage of low electric fields in the vacuum coaxial feedlines (see next section and Ref. [6.140]) The latter system essentially moves part of the impedance matching system from its traditional location in the transmission line into the coupling structure, which is the topic of the next section.

6.3.2.4. ICRF wave launchers

The wave launcher (antenna) is the most critical component in a high power ICRF system for fusion applications (see Fig. 6.28). Once a propagating wave is successfully excited near the edge of the magnetically confined plasma, the fast Alfvén wave (fast wave) propagates to the core minority cyclotron resonance (or harmonic cyclotron resonance of the main species) without intervening cut-offs, as was discussed in previous sections. The launcher must efficiently excite the waves with the necessary polarization and the desired amplitude without introducing significant impurities or suffering from electrical breakdown. As discussed in previous sections, a wave of fixed wavelength along the static magnetic field (i.e. a fixed k) is evanescent in the low density region from the antenna face to the right hand cut-off density, which for typical parallel wavelengths and magnetic fields occurs at electron densities on the order of a few times 1018 m–3. At lower densities, the wave is very nearly as evanescent as it is in vacuum (zero density), where N^=i N( 2-1)1/2. The wave energy must tunnel through the evanescent layer from the antenna surface up to the cut-off density, and the wave amplitude therefore decreases exponentially in this region. The wave launcher must excite the appropriate polarization, which for a compressional (fast Alfvén) wave must have the RF magnetic field alternately parallel and anti-parallel to the static magnetic field, and the RF electric field perpendicular to the static magnetic field. In principle, this polarization could be excited by a capacitative coupler that imposes an RF electric field across the static magnetic field or by an inductive coupler that modulates the static magnetic field at the RF frequency. Of these two possibilities, for several reasons the inductive coupler has been used in all high power ICRF experiments.

FIG. 6.28. (a) Approximative schematics of an idealized single element of a loop antenna to launch fast waves (the coordinate system shown here does not correspond to the right side of the figure); reproduced Fig. 3 from Ref. [6.141]. Reprinted from Ref. [6.141]. Copyright (2011), American Institute of Physics. (b) Practical phased array of four loop antennas, as viewed from the plasma, including slanted Faraday screen elements, double poloidal straps and surrounding graphite protection tiles, from DIII-D. The height and width of the array are 0.45 m by 0.70 m.

Energy that is carried away from the coupler by fast waves in the plasma looks like a loss to the exciting circuit, and hence can be modelled as a resistive component to the termination of the transmission lines that feed the coupler. This resistance is called the loading resistance and the larger the value of the loading resistance, the larger the amount of power that is coupled to the plasma per unit of antenna current. Figure 6.29 shows the simplest possible lumped-element antenna model, in which the feedline of characteristic impedance Z0 is terminated by a resistance RL to ground in series with a reactance iX , the net reactance X representing the parallel combination of the element’s inductive reactance and capacitative reactance to ground. Such a lumped-element model is reasonable if one is not interested in the spatial dependence of fields along the radiating element. The loading resistance RL is almost always much smaller than Z0, so the current through the load resistance is a maximum, denoted by Imax. The total dissipated power is

max2

dis 1/ 2 L

P  I R (6.127)

where the factor of 1/2 is due to the use of peak amplitudes rather than root mean square and the maximum current Imax and the maximum voltage Vmax, separated by a quarter of a wavelength in the feedline, are related by the characteristic impedance of the feedline

0 max/ max

Z V I (6.128)

so

Pdis=(Vmax2 2Z02)RL (6.129)

if the net reactance X is neglected.

Since the dissipated power can readily be measured with directional couplers in the transmission line and the voltage at a maximum in the transmission line can also be readily measured with capacitative voltage probes, this relation provides a simple way to measure the loading resistance without instrumentation inside the device vacuum. In typical applications, the antenna element is indeed electrically short, so that the antenna does not radiate electromagnetic waves into vacuum (i.e. in the absence of a plasma load.) Hence the loading resistance in the absence of plasma is almost entirely due to ohmic losses (skin-current losses) in the antenna and feedlines. If this ohmic loss is modelled as being lumped into the total load resistance RL, i.e. RL is taken to be the sum of ohmic losses in the antenna and feedline, denoted by Rvac, plus the power radiated into plasma, Rp, then RL Rvac Rp (see Fig. 6.29). The power dissipated in the plasma (the power radiated from the antenna into the plasma) is

( )

2 2

max max

2 2

0 0

2 2

p V p V L vac

P R R R

Z Z

= = - (6.130)

and by comparing these equations we obtain the fraction of the total dissipated power that is coupled to plasma waves as P Pp / dis=(RL-Rvac) /RL.

FIG. 6.29. Simple lumped-element equivalent circuit of antenna, viewed as a lumped-element termination of the feedline. The total loading resistance RL, which is vacuum losses Rvac plus the plasma loading Rp, is much smaller than the characteristic impedance of the feedline.

Let us consider some typical numbers in this application. Suppose 0.5 MW is to be applied to a single antenna element, on which the loading resistance is 1 Ω. The peak antenna current would be 1 kA and if the feedline charac- teristic impedance is 25 Ω, then the peak voltage in the feedline, one quarter of a wavelength from the termination, is 25 kV. If the feedthrough is farther than one quarter of a wavelength from the termination, then this peak voltage occurs within the device vacuum, in the feedline. If the net reactance is not negligible compared with the characteristic impedance, the peak voltage is higher than in the case with X = 0; for example, if X = Z0 in magnitude in this case the peak voltage becomes about 35.5 kV. One obtains in this simple model that the peak voltage is given by

   

max 2 0 dis 1 1

V  Z P     (6.131)

and the reflection coefficient magnitude  is given by

 

 

2 2

2 0

2 2

0

Z R X

Z R X

   

  (6.132)

Since in decades of experience it has been found that high voltage electrical breakdown (‘arcing’) becomes probable if the RF electric field at any point within the device vacuum parallel to the static magnetic field exceeds a threshold value of about 1.5 MVãm–1 [6.142] and often the coaxial feedlines have spacings between the inner and outer conductors on the order of centimetres, voltages of this order often cause a coupled power limit at low values of antenna loading resistance (compared with transmission line characteristic impedances). For this reason, the two important characteristics of the loading resistance in practice are that its absolute value is low (by comparison to a reasonable value of transmission

line characteristic impedance), and tends to be highly sensitive to edge plasma conditions and hence strongly varies in time. These characteristics stem from the exponential decrease in the wave amplitude in the tunnelling region. Since it is found experimentally that in ICRF heating a parallel wavenumber spectrum peaked at N significantly larger than is needed for efficient absorption [6.47, 6.48, 6.143], the previous discussion indicates that the evanescence will be severe if the radial distance g from the antenna to the cut-off layer is such that k g ~ 0.5 or larger. A more sophisticated estimate [6.144] shows a less pessimistic number than 0.5, but of similar magnitude. To minimize deleterious plasma/wall interactions, in most high performance fusion devices the distance between the edge of the plasma and the antenna surface cannot be reduced to less than ~0.1 m and therefore the evanescence tends to be strong and the loading resistance low, approximately 1 Ω per element. Nevertheless, for multiple antenna straps with optimized spectrum, JT-60 has obtained 4 Ω loading resistance with a 0.15 m antenna–separatrix gap, sufficient for present ITER requirements [6.145]. The combination of high antenna currents needed to couple large power levels and transmission lines terminated in an impedance much different (lower) than their characteristic impedance implies high electric fields within an electrical distance of 1/4 of a vacuum wavelength away from the region of high antenna current.

Since in large devices this distance away from the current maximum is still within the torus vacuum region, these high electric fields can lead to electrical breakdown problems within the antenna structure, as discussed above.

Although the inductive launchers are designed to minimize the component of the RF electric field along the static magnetic field (E), the 3-D effects associated with current-carrying elements of finite poloidal length, radial currents from feeders, the effect of the housings in which the current carriers are located, and the impracticality of maintaining perfect alignment of the antenna elements with the perpendicular to the local static magnetic field all lead to non-zero E in the vicinity of the coupler face. Furthermore, incomplete absorption of the RF energy in the core of the plasma on the first pass may lead to non-zero RF field amplitudes everywhere near the first wall in the device. The combination of static magnetic fields intersecting conducting surfaces, non-zero (albeit very low) electron density at those points, and non-zero RF field amplitudes parallel to the static magnetic field line at the contact points are the recipe for rectified RF sheaths to appear at those locations [6.146, 6.147]. These sheaths are categorized as near-field sheaths, such as the ones driven by the antenna currents directly, and far-field sheaths, which are the ones driven by the fields arising from incomplete first-pass absorption of the RF power. The acceleration of ions into conducting surfaces by the DC component of these rectified sheaths represents a power dissipation mechanism (with the power dissipated being the product of the sheath voltage drop and the ion current to the wall), and can cause localized heating of the surface (‘hot spots’). The accelerated ions can sputter material from the