Plasma beta in magnetized target fusion systems is sometimes much greater than 1, and the plasma may be in direct contact with the imploding liner. Plasma processes are strongly dominated by inter-particle collisions. Under such conditions, the plasma microturbulence, behaviour of α-particles, and plasma equilibria are very different from conventional fusion systems. This paper contains the most comprehensive analysis of the corresponding phenomena to date. Two-dimensional numerical simulations of plasma convection in the targets of a diffuse pinch type demonstrate an onset of convection in this configuration.