An engineer designing electron cyclotron heating for a compact tokamak with at the…

PHYSICS · Subjective · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Waves in a non-uniform plasma: rays, reflection, mode conversion and radiofrequency heating

Problem

An engineer designing electron cyclotron heating for a compact tokamak with

B_0 = 1.8\,\mathrm{T}

at the magnetic axis

R_0 = 0.9\,\mathrm{m}

(so

B(R) = B_0R_0/R

) plans to launch a

50\,\mathrm{GHz}

fundamental X-mode beam from the low-field side (large

R

, outboard midplane). The core electron plasma frequency is

f_{pe} = 32\,\mathrm{GHz}

. The engineer argues: 'The X mode has a lower cutoff density than the O mode, so it will penetrate further into the plasma. Launched from the outboard side, it will cross the fundamental cyclotron resonance layer near the axis and be absorbed there.' Find the error in this reasoning, using the right-hand cutoff frequency

\omega_R = \tfrac12\left(|\Omega_e| + \sqrt{\Omega_e^2+4\omega_{pe}^2}\right)

(Chapter 9's cold-plasma dispersion, quoted here), evaluated with the axial values of

B_0

and

f_{pe}

. State what the engineer should do instead.

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