Two problems related to alpha particle physics in magnetized target fusion (MTF) systems are briefly discussed. First, we evaluate the pressure and density of alpha particles under the assumption that they are perfectly confined and have a classical slowing-down distribution. It turns out that because of a comparatively low plasma temperature in MTF systems, the relative pressure and density of alpha particles are more than an order of magnitude less than in fusion reactors based on ITER-type tokamaks. Therefore, one may expect that even in the extreme case of a perfect confinement of alpha particles, their presence will have a much weaker (than in the case of tokamaks) effect on plasma stability and transport. Second, we discuss the kinetics of plasma burn under the opposite extreme assumption that all the alpha particles are instantaneously lost, without leaving any energy in a plasma. It turns out that even in this case, the plasma energy yield in batch-burn systems is only weakly affected by burnout effects.