A lower hybrid heating system is to be installed on a tokamak whose edge

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 lower hybrid heating system is to be installed on a tokamak whose edge, where the wave is launched, has

B = 2.2\,\mathrm{T}

, electron density

n_e = 2.0\times10^{19}\,\mathrm{m^{-3}}

, and deuterium ions (

m_i = 2.0\times1.67\times10^{-27}\,\mathrm{kg}

, charge

+e

). The wave frequency is

f = 3.7\,\mathrm{GHz}

. ((a)) Compute the electron plasma and cyclotron frequencies,

f_{pe}

and

f_{ce}

, at the launch point. ((b)) Compute the ion plasma frequency

f_{pi}

and the ratio

(\omega_{pi}/\omega)^2

. ((c)) Use

n_{\parallel,\mathrm{acc}} = \frac{\omega_{pe}}{|\Omega_e|} + \left[1 + \left(\frac{\omega_{pe}}{\Omega_e}\right)^2 - \left(\frac{\omega_{pi}}{\omega}\right)^2\right]^{1/2}

to find the minimum parallel refractive index the launcher must impose. ((d)) State the launched

n_\parallel

you would specify, allowing a practical margin of about ten per cent above the minimum, and explain in one sentence why access only gets harder deeper in the plasma.

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