Energy loss of heavy ions in dense plasma. I. 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 ${\mathit{v}}_{\mathit{p}}$, below the electron thermal velocity ${\mathit{v}}_{\mathrm{th}}$, and on solutions nonlinear in the coupling parameter scrZ=${\mathit{Z}}_{\mathrm{eff}}$/(${\mathit{n}}_0$ ${\lambda }_{\mathit{D}}^3$) between the heavy-ion projectile with effective charge ${\mathit{Z}}_{\mathrm{eff}}$ and the plasma with electron density ${\mathit{n}}_0$ and Debye length ${\lambda }_{\mathit{D}}$. 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∝${\mathit{v}}_{\mathit{p}}$ 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 ${\mathit{v}}_{\mathit{p}}$>${\mathit{v}}_{\mathrm{th}}$, but also describes the limit ${\mathit{v}}_{\mathit{p}}$→0 correctly.