Total current to cylindrical collectors in collisionless plasma flow

A theory is presented for charged-particle collection by a cylindrical conducting object, such as a spacecraft or an electrostatic probe, which is moving transversely through a collisionless plasma, such as those in the upper atmosphere and space. The calculation is approximate, using symmetric potential profiles which are exact for the infinite-cylinder stationary case. Theoretical current predictions are presented for ratios of collector potential to electron thermal energy eφ c / kT e from 0 to −25, for ion-to-electron temperature ratios T i / T c = 1 and 0.5, ratio of collector radius to electron Debye length r c / λ D from 0 to 100, and ratio of flow speed to ion thermal speed S i = U/(2kT i/m i 1 2 ) from 0 to 10. Comparisons with existing exact calculations by other authors show that none of these fulfil all of the requirements for nontrivial comparison. Appropriate parameter ranges for future exact calculations are thereby suggested. These are as follows: (a) r c / λ D should be large enough that the collector not be in or near orbit-limited conditions; (b) the ratio S i 2/¦χ c, i¦ of ion directed energy to potential energy change in the sheath, should be close to unity or if S i 2/¦χ c,i¦⪡ 1, then S i ⪢ 1 .