Theory of a cylindrical probe in a collisionless magnetoplasma

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Abstract
A theory is presented for a cylindrical electrostatic probe in a collisionless plasma, when the probe axis is inclined at an angle ϑ to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit when probe radius rp≪ Debye length λD. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if rp/λD and rp/ā, where ā is the mean gyroradius, are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for ϑ from 0° to 90°, and for rp/ā from 0.1 to ∞. For ϑ=0°, the end‐effect current is calculated separately.