Microwaves in fusion plasmas
In a magnetically confined plasma the ions and electrons experience a Lorenz force from the externally applied magnetic field which gives rise to gyromotion of the particles. The Lorenz force is equated with the centrifugal force and from this simple force balance it is found that, in the case of electrons, the gyration frequency is 28 GHz/T. The magnetic field in large fusion devices as JET, ITER and W7-X is of the order of 3 to 5 T, placing the 1st harmonic of the Electron cyclotron (EC) frequency in the range of 100 to 200 GHz. Microwaves with similar frequencies are used extensively as a tool for both heating and diagnosing the plasma.
In a tokamak or stellarator the strength of the magnetic field decays with a 1/R dependence, with R the radius measured with respect to the center of the machine. Therefore, the EC frequency decreases with 1/R as well. By launching microwave power at the EC frequency, referred to as Electron Cyclotron Waves (ECW), the power of the waves can be transferred to the electron population at this specific resonance location. By selecting the frequency (or the magnitude of the B-field) one has thus a mechanism of localized heating. See figure 1.
Fig. 1. A simplified scheme of an Electron Cyclotron Heating system. Due to the 1/R dependence of the magnetic field that contains the plasma, the cyclotron frequencies also fall off with a 1/R dependence, with the high frequencies to the left and the low frequencies to the right. Microwaves are injected, in this example, by a double mirror arrangement inside the vacuum vessel. The microwaves travel through the plasma and are absorbed at the cyclotron resonance frequency. Localization in vertical direction is obtained by shaping the microwave beam, for simplicity drawn as a straight line in the cartoon.
The power is launched into the plasma using Gaussian beam optics which can focus to a spots size down to the order of 1.5 cm (note: figure shows a line, not a Gaussian beam). Powerful sources are available, gyrotrons with a total beam power of 1 MW, resulting in extreme power densities at the focus of up to a GW/m2. Increase of local conductivity, and / or injection under a toroidal angle, also enables to drive net current.
For diagnostic purposes high power as well as low power microwaves are used. In passive systems, such as e.g. Electron Cyclotron Emission (ECE) diagnostics, the electromagnetic radiation that the electrons emit as they gyrate around the magnetic field lines is picked up. The frequency is a measure for the location in the plasma while the intensity of ECE is a measure of the electron temperature. See figure 2 for a cartoon of the situation.
Fig. 2. A simplified scheme of an Electron Cyclotron Emission receiver. Traversing the cord from right to left the frequencies drop from high to low. This spectrum is coupled into a microwave receiver by means of transmission line, a waveguide in the case of the figure. The receiver separated the frequencies and at each frequency the microwave power is measured, which is by means of the Planck function a measure of the electron temperature.
Compared to gyrotron power, the power of the ECE is extremely small. For instance, for a plasma at 100 million K the ECE power in a localised volume - say corresponding to a few cm3 in the plasma - is of the order of several 100 nW. But at very high electron temperatures, such as expected at ITER, the total synchrotron radiation (integrated over the whole spectrum and vessel volume), is still expected to be considerable. Other microwave diagnostics are e.g. reflectometers that exploit reflection of waves depending on local density, or Collective Thomson Scattering, where photons of a microwave probing beam are scattered of electrons in the plasma.