In a double-plasma device two identical electron beams

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

Plasma Physics, Ch Hot plasmas and free energy: beam instabilities, cyclotron damping and Bernstein waves

Problem

In a double-plasma device two identical electron beams, each a Maxwellian at temperature

T = 5.0\,\mathrm{eV}

, counter-stream at

\pm u

along the same line, giving a combined distribution symmetric about

v=0

. For this exact distribution the Penrose integral has been evaluated numerically and is positive (unstable) only for

u > 1.31\,v_t

, where

v_t = (T/m_e)^{1/2}

. ((a)) Find

v_t

. ((b)) The beams are separated by

u = 1.30\times10^{6}\,\mathrm{m\,s^{-1}}

. Decide, giving the ratio

u/v_t

, whether the combined distribution drives growing electrostatic waves.

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