Effects of plasma turbulence on electron collection by a high-voltage spherical probe in a magnetized plasma

We study the effects of electron trapping and plasma turbulence on the current-voltage relation for a positively charged high-voltage spherical probe in a magnetized plasma. In a force field consisting of an attractive radial electric field and a uniform magnetic field, the electric field provides a potential well in which electrons can be bound if they have insufficient energy to escape and cannot be captured by the sphere (by virtue of angular momentum conservation and/or the effects of the magnetic field). Electrons entering such a well from infinity may become trapped if they lose energy as a result of some scattering process acting within the well, such as inelastic collisions with neutral atoms or wave-particle interactions due to plasma collective effects. When the neutral density is low enough so that ionization can be ignored, our results indicate that the sheath structure and the current-voltage relation of a charged sphere configured as in the originally planned SPEAR I experiment (with an operating plasma contactor) would be substantially influenced by the combined action of trapped electrons and plasma instabilities. Our method is a modification of Linson's (1969) method in which potential contours are taken to be elliptical rather than cylindrical, space charge is not assumed to be constant within the sheath, and the controlling parameter is a scattering rate. We find reduced levels of current collection relative to Linson's model. Further, variation of the scattering parameter over the whole range of physically realizable values results in a range of predicted current collection values which is a small fraction of the interval between the Parker-Murphy and Langmuir-Blodgett limits.