  A recent paper [Phys. Plasmas 20, 032304 (2013)] considered the forced linear
Vlasov equation as a model for the quasi-steady state of a single stable plasma
wavenumber interacting with a bath of turbulent fluctuations. This approach
gives some insight into possible energy flows without solving for nonlinear
dynamics. The central result of the present work is that the forced linear
Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all
orders under a detuning of the forcing frequency and the characteristic
frequency associated with particle streaming. We first prove this by direct
calculation, tracking energy flow in terms of certain exact conservation laws
of the linear (collisionless) Vlasov equation. Then we analyze the steady-state
solutions in detail using a weakly collisional Hermite-moment formulation, and
compare with numerical solution. This leads to a detailed description of the
Hermite energy spectrum, and a proof of no dissipation at all orders,
complementing the collisionless Vlasov result.
