An asymptotic solution has been obtained for the electron heat transfer to a spherical body immersed in a weakly ionized, quiescent plasma. Dimensional analysis of the governing equations shows that the problem can be divided into two regions: charge-separated and quasi-neutral. For the charge-separated region, the equations must be solved numerically, whereas the quasi-neutral solution can be expressed in closed form. From these studies it was found that the extent of the charge-separated region (i.e, sheath) is of the order of Λ2/3. Within the sheath the effects of ionization and recombination are of the order of Λ4/3. The results include the variation of electron flux, electron heat transfer, and current as a function of body potential. The results are presented in a form to permit the easy determination of the electron heat transfer to a body immersed in a quiescent, weakly ionized plasma over a wide range of operating conditions. Furthermore, the electrical characteristics presented here can be used in conjunction with electron heating data to treat the body as a probe for diagnostic purposes.
Nonlocal Electron Heat Transport in Magnetized Dense Plasmas