Scattering of suprathermal ions by partially ionized impurities

The pitch-angle scattering rate of suprathermal ions has been used as a diagnostic to measure Z_eff in tokamak plasmas. The interpretation of these measurements is made somewhat obscure, however, by the presence of partially ionized impurities. Beam ions can penetrate the electron clouds of impurity ions, and experience a scattering potential intermediate between the unshielded nuclear potential and the reduced field observed well outside the electron cloud. This problem is treated by using the Thomas-Fermi statistical model for the charge density of the electron cloud of the impurities and the impulse approximation for the angular deviation resulting from a collision. An analytic approximation to the exact Thomas-Fermi potential for an ion of arbitrary charge state is found, and is used to calculate the addition required to the classical Coulomb logarithm for 10%-90% ionized impurities and for incident energies in the range (10^-2-10³) keVxZ _n^4/3, where Z_n is the nuclear charge of the impurity. The correction can be comparable in magnitude to the classical result, e.g., for 40 keV protons incident on 30 times ionized tungsten ions, the addition to 1nΛ is approximately 30%.