ENERGY-LOSS OF HEAVY-IONS IN DENSE-PLASMA .1. LINEAR AND NONLINEAR VLASOV THEORY FOR THE STOPPING POWER

The plasma physics of heavy-ion stopping in fully ionized matter is developed on the basis of the Vlasov-Poisson equations with particular emphasis on small ion velocities upsilon-p, below the electron thermal velocity upsilon-th, and on solutions nonlinear in the coupling parameter Z = Z(eff)/(n(o)lambda-D-3) between the heavy-ion projectile with effective charge Z(eff) and the plasma with electron density n(o) and Debye length lambda-D. Concerning the stopping power in the low-velocity regime relevant for the Bragg peak at the end of the ion range, results on the friction term dE/dx proportional upsilon-p are presented, and an improved dE/dx formula for plasma is derived in closed form and readily applicable for stopping-power calculations; it is identical to the standard result for upsilon-p > upsilon-th, but also describes the limit upsilon-p --> 0 correctly. For upsilon-p < upsilon-th, nonlinear results are found to contribute to the stopping power with terms proportional Z5/2 for positive ions and terms proportional Z3 for negative ions in addition to the basic Z2 term; they are derived from a low-velocity expansion of a form-factor representation of dE/dx. Concerning high velocities upsilon-p > upsilon-th, the relevant coupling parameter is Z(upsilon-th/upsilon-p)3, and nonlinear corrections to the stopping power proportional Z3/upsilon-p5 are obtained by extending the work of Ashley, Ritchie, and Brandt [Phys. Rev. B 5, 2393 (1972)] to the plasma case. An interpolation between the low- and the high-velocity results is given; taking, e.g., parameters characteristic for heavy-ion beam inertial fusion the nonlinear corrections further enhance dE/dx up to 10% in the Bragg peak region. An application of the present results to heavy-ion energy loss in an electron-cooling line is also discussed. In the present paper, Z(eff) is assumed to be constant; the physics determining Z(eff) is treated in a subsequent article [Peter and Meyer-ter-Vehn, following paper, Phys. Rev. A 43, 2015 (1991)].