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
6.3.6. Electron cyclotron transmission line and antenna design
Power generated in the ECH frequency range, typically by gyrotrons, must be transmitted to the confinement device by transmission lines of typical length 50–100 m. The most common method is use of a waveguide. The fundamental mode of a waveguide in which the transverse dimensions are of the order of a half-wavelength (a few mm) is unsuitable for frequencies above a few tens of GHz due to excessive dissipation in the waveguide and likely breakdown caused by extremely high electric fields when operated at high power. Instead, a highly overmoded waveguide propagating a low order mode is used. Modern fusion related systems [6.229, 6.230] use circular waveguides with diameters 10–50 times the wavelength, propagating the very low loss HE11-mode (see Ref. [6.229]) that propagates in waveguides with corrugated walls; for ITER conditions of 170 GHz and a 63.5 mm diameter corrugated waveguide, the theoretical loss is 0.02 dB/100 m. The dominant loss in waveguide transmission lines is at mitre bends, where 0.1–0.3% of the propagated power is ohmic loss on the mirrors and there is an additional mode conversion loss of 0.1–0.3%, depending on the design [6.231].
Transmission lines can suffer electrical breakdown, but the high frequencies of EC systems help to avoid it. The reliable power handling capability of corrugated waveguides, above 105 Wãcm–2 in practice, comes from the low energy excursion of a collisionless electron in a waveguide. The peak electric field at the centre of a waveguide propagating the HE1/2 11-mode is
2 1/2
32 EC / ( 0 ) 60 EC /
E P c d P d, where c is the speed of light and d is the waveguide diameter. For the ITER waveguide diameter, the peak electric field is of order 1 MVãm–1 for 1 MW of power. An unmagnetized electron in this field will oscillate with a peak energy W 16 /e2 0m c Pe EC /2 2d .
Again for the ITER waveguide example, this energy is only about 0.1 eV, which is far below the ionization energy. The only way the electron can be accelerated to ionization energies is through a decorrelation process like collisions. Keeping the collision frequency either much smaller (evacuated waveguide) or much larger (pressurized waveguide) than the applied frequency will avoid this random walk in energy, which must take place in a time less than the time for the electron to drift to a waveguide wall or lose energy through excitation of the background gas. In practice, power at the MW level at 60 GHz and above has been robustly transmitted in waveguides of a few cm diameter, either evacuated or at atmospheric pressure.
The polarization of the electric field of the incident wave at the plasma boundary must be set in the transmission line to match the polarization of the desired mode, ordinary or extraordinary. This can be done using grooved mirrors in the bends of the transmission line [6.232]. In the local Stix coordinate system at the plasma boundary, the low density limit of the cold plasma dispersion relation provides the target polarization. An example diagram of a waveguide transmission line is shown in Fig. 6.65.
FIG. 6.65. Schematic drawing of the waveguide transmission line for the JT-60U tokamak [6.233]. Some components of the system are described in Ref. [6.231].
An alterna tive to the waveguide transmission line is the quasi-optical transmission line [6.234], which has been developed for the stellarator W-7x.
This approach, shown in Fig. 6.66, uses free-space propagation of Gaussian beams with periodic focus mirrors in a confocal arrangement. Beams from up to seven 1 MW 140 GHz gyrotrons are transmitted to the stellarator by each of two such transmission systems. Each gyrotron beam has a pair of beam conditioning mirrors and a pair of polarizing mirrors before the beams enter the common mirror system (mirrors M5-M11 in Fig. 6.66(a)). This system has demonstrated robust alignment in tests with two gyrotrons operating each at 0.9 MW for 30 minutes.
Overall efficiency is 90% for the Gaussian beam fraction of the power.
FIG. 6.66. Schematic design of the 140 GHz, 10 MW transmission system for ECH on W7-X.
Shown is (a) a vertical cross-section and (b) a top view. Reprinted from Ref. [6.234]. Copyright (2011), American Nuclear Society.
Launchers for ECH systems are relatively simple, due to the feature that the EC wave propagates in vacuum. This means that the launcher need not be close to the plasma in order to have good coupling. And because the launching structure is many wavelengths in dimension, there are other advantages. First, where the wave exits a highly overmoded waveguide there is little reflected power, since the wave phase velocity is very nearly the same (namely c) in the waveguide and outside it. Second, the beam emerging from a waveguide can have small
angular divergence even without additional focusing optics. For example, for the ITER case of the HE11-mode at 170 GHz in a 63.5 mm diameter waveguide the radiation pattern from an open-ended waveguide is down 10 dB at 1.8 .
Diffraction-limited divergence is of order 1.6°. The small angular divergence is very suitable for objectives requiring highly localized heating or current drive, like NTM control. Narrower deposition profiles may be obtained by using focusing mirrors, but diffraction is always a limit.
The simplest launcher is a terminated waveguide pointed at the plasma.
This approach has been used successfully in many experiments. However, as the experiment objectives became more sophisticated, more flexible launchers were developed so that power could be directed with different poloidal and toroidal angles. Typically this has been done with articulating mirrors [6.233–6.235]
so that aiming in the poloidal and toroidal directions can be accommodated.
This front steering approach can launch very narrow beams over a wide range of angles. An alternative technique, which was developed to avoid the galling or seizing problems to which mirrors that move or slide in the high vacuum of tokamak vessels are subject, is the remote steering launcher [6.236, 6.237]. In this approach, waves are launched into a waveguide of tuned length such that the waveguide modes reconstruct at the end of the waveguide into a beam propagating at an angle to the axis of the waveguide. In this way, the steering mechanism can be relocated to the input end of the waveguide rather than the output end near the plasma, but the beam may not be as narrow as for the front steering system.
The ECH system for ITER will have the capability of 20 MW incident on the plasma from 24 gyrotrons of 170 GHz and 1 MW. Two front steering launcher systems are planned, an equatorial launch and a top launch [6.238].
These launchers are shown in Fig. 6.67. Extensive modelling has shown that this combination of launchers is capable of a wide range of physics objectives for the ITER scenarios.
FIG. 6.67. Schematic diagram of the two types of ECH launchers designed for ITER. Reprinted from Ref. [6.238].