Low velocity ion stopping of relevance to the US beam-target program

We focus attention on the stopping mechanisms involved in the recently proposed US beam-target program devoted to the production of warm dense matter through pulsed ion beams linearly accelerated and impacting thin solid foils in Bragg peak conditions.We concentrate on moderate or low ion projectile velocities Vp $<$ Vth, target thermal electron velocity. Ion projectile energy loss in the very low and Vp- linear regime is investigated in a novel and statistical physics approach in terms of particle diffusion coefficients. Beam target interaction in the presence of an arbitrarily strong magnetic field is also considered.