Two approaches to enhancement of the Q (energy gain) factor of mirror systems are under study at Livermore. These include the Tandem Mirror and the Field Reversed Mirror. Both of these new ideas preserve features of conventional mirror systems as far as plasma-wall interactions are concerned. Specifically in both approaches field lines exit from the ends of the system and impinge on walls located at a distance from the confinement chamber. It is possible to predict some aspects of the plasma/surface interactions of TM and FRM systems from experience obtained in the Livermore 2XIIB experiment. In particular, as observed in 2XIIB, effective isolation of the plasma from thermal contact with the ends owing to the development of sheath-like regions is to be expected. Studies presently underway directed toward still further enhancing the decoupling of the plasma from the effects of plasma surface interactions at the walls will be discussed, with particular reference to the problem of minimizing the effects of refluxing secondary electrons produced by plasma impact on the end walls.