The electron-retarding range of the current–voltage characteristic of a flat Langmuir probe perpendicular to a strong magnetic field in a fully ionized plasma is analysed allowing for anomalous (Bohm) cross-field transport and temperature changes in the collection process. With probe size and ion thermal gyroradius comparable, and smaller than the electron mean free path, there is an outer quasineutral region with ion viscosity determinant in allowing non-ambipolar parallel and cross flow. A potential overshoot lying either at the base or inside the quasineutral region both makes ions follow Boltzmann's law at negative bias and extends the electron-retarding range to probe bias eϕP∼+2T∞. Electron heating and cooling occur roughly at positive and negative bias, with a Te-minimum around eϕP∼−2T∞; far from the probe heat conduction cools and heats electrons at and radially away from the probe axis, respectively. The potential overshoot with no thermal effects would reduce the electron current Ie, making the ln Ie versus ϕP graph downwards-concave, but cooling further reduces Ie substantially, and may tilt the slope upwards past the temperature minimum. The domain of strict validity of our analysis is narrow in case of low ion mass (deuterium), breaking down with the ion Boltzmann law.
Electric fields and currents in front of a biased electrode (flush mounted probe) and the I - V characteristics of the electrode for various mechanisms of transverse conductivity