A lower hybrid wave of frequency is launched into a tokamak edge plasma with electron…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

Plasma Physics, Ch The Vlasov equation and Landau damping

Problem

A lower hybrid wave of frequency

f = 1.00\,\mathrm{GHz}

is launched into a tokamak edge plasma with electron temperature

T_e = 2.00\,\mathrm{keV}

. Ray tracing (of the kind used for mode conversion at the lower hybrid layer) shows the wave arrives at the absorption layer with a parallel refractive index

n_\parallel = c k_\parallel/\omega = 5.00

, where

k_\parallel

is the component of

\mathbf{k}

along

\mathbf{B}_0

. The steady magnetic field itself is not needed for this part of the argument; the identification of who absorbs the energy uses only the motion of particles along the field. ((a)) Compute the parallel phase speed

v_\parallel = \omega/k_\parallel

of the wave and the electron thermal speed

v_{te} = (T_e/m_e)^{1/2}

, and give their ratio. ((b)) State, in one or two sentences, which electrons take the wave's energy at this layer (identify them by their motion relative to the field and the wave), and explain why this is Landau damping by parallel resonance rather than cyclotron absorption, given that the ratio found in part (a) places these electrons on the Maxwellian's tail rather than at rest.

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