Processes in a dense long-pulse electron beam focused on a solid target

Recently a number of applications appeared where a long- pulse (duration more then 0.1 ms) electron beam had to be focused on a solid surface to obtain energy density 1 kJ/cm² or more [1,2]. It is well known that in these conditions a jet of partially ionized sputtered target matter propagates into the beam and shields, to some extent, the surface from the energy flux. But the self-consistent process is too complicated to obtain reliable values of jet parameters, shielding efficiency and surface etching rate otherwise then experimentally.