A laboratory maintains

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

Plasma Physics, Ch Waves that need pressure or tension: Langmuir, ion-acoustic, Alfven and magnetosonic

Problem

A laboratory maintains, in turn, a helium discharge and a xenon discharge, both fed by the same electron source so that the electron temperature

T_e

is expected to be the same in both. A time-of-flight measurement gives the ion-acoustic speed

c_s=6.9\,\mathrm{km\,s^{-1}}

in helium (

m_i=4.0026\,\mathrm{u}

) and

c_s=1.2\,\mathrm{km\,s^{-1}}

in xenon (

m_i=131.29\,\mathrm{u}

), each quoted to

\pm10\%

. The ions are cold enough that

T_i\ll T_e

in both gases. ((a)) Using

c_s=(T_e/m_i)^{1/2}

, find the electron temperature (in eV) implied by each measurement. ((b)) State whether the two values are consistent with a single electron temperature, given the quoted uncertainty, and explain in one sentence why the ion-acoustic speed is the right quantity to compare across two different gases rather than, say, the ion thermal speed.

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