A tokamak with major radius and on-axis field is heated by a electron cyclotron beam…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Fusion plasmas

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

Problem

A tokamak with major radius

R_0 = 2.96\,\mathrm{m}

and on-axis field

B_0 = 3.45\,\mathrm{T}

is heated by a

140\,\mathrm{GHz}

electron cyclotron beam aimed at the fundamental resonance (

\ell=1

). The field varies as

B(x) = B_0R_0/(R_0+x)

, where

x

is the horizontal distance from the magnetic axis (positive outward). ((a)) Find the magnetic field

B_{\rm res}

at which the wave frequency equals the electron gyrofrequency. ((b)) Find the position

x

of the resonance layer.