The theoretical description of the energy loss of heavy ions in fully ionized matter is considered, where we focus on the many–body and plasma physics aspects of the stopping of point like projectiles with a fixed charge by free electrons, disregarding the atomic physics of the projectile and the target ions. This starts by identifying different coupling regimes for a heavy ion which passes through an electron plasma, and continues with a discussion of the available and appropriate analytical and numerical treatments of the energy loss and their applicability in these various regimes. Special attention is given to a nonlinear coupling regime with significant strong coupling effects on the projectile-target energy transfer where standard perturbative approaches cease to be valid. More advanced theoretical treatments, which are required for this regime, are presented, discussed and evaluated by comparison with simulation results.
