In the rotating plasma frame of reference, beam ions are born with less energy than in the lab frame. Consequently, in the rotating lab frame there is less beam power available to collisionally heat the thermal ions and electrons. Where does the extra power go?
The answer is very simple: the beam ions exert a toroidal force (per unit volume) on the rotating fluid--which is precisely the force needed to sustain the rotational velocity against viscous damping forces. We can calculate from the usual Coulomb collisions between beam ions and the thermal electrons, and impurities. Since the plasma is moving, the toroidal beam force does `work' on it at the rate (per unit time and unit volume). The total power thus delivered as `work' to the plasma over some volume is just the volume integral of all the terms. Some of this power is converted to thermal energy by viscous heating (), but the remainder flows out radially and is no longer available to heat the plasma inside the volume under consideration.
Goldston  has analyzed the energy balance in a rotating plasma. His formalism has been implemented in the SNAP\ code.