A Langmuir probe sits in an argon discharge

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Laboratory, industrial and space plasmas

Plasma Physics, Ch From particles to fluids: the distribution function, its moments and the two-fluid model

Problem

A Langmuir probe sits in an argon discharge. Biased below the plasma potential, it collects an electron current (the small ion current already subtracted) of I1=0.40 mAI_1 = 0.40\,\mathrm{mA} at bias V1=−12.0 VV_1 = -12.0\,\mathrm{V} and I2=3.6 mAI_2 = 3.6\,\mathrm{mA} at V2=−7.6 VV_2 = -7.6\,\mathrm{V}, both in the retarding region. Above the plasma potential the electron current saturates at Isat=20 mAI_{\rm sat} = 20\,\mathrm{mA}. ((a)) Starting from the Boltzmann relation, explain why ln⁡I\ln I is a straight line against bias in the retarding region, and find TeT_e in electronvolts from the two readings. ((b)) Taking the exponential to hold right up to the plasma potential VpV_p, where it meets the saturation current, find VpV_p. ((c)) Along a magnetic field line in the same discharge, the electron density at a point near the wall is 0.300.30 times its value at the centre. Find the potential difference between the two points, and state the two conditions along the field line under which your answer holds.

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