  Traditional expressions and definitions describing performance of plasma
thrusters, including the thrust, specific impulse, and the thruster efficiency,
assume a steady state plasma flow with a constant flow velocity. However, it is
very common for these thrusters that the plasma exhibits unstable behavior
resulting in time-variations of the thrust and the exhaust velocity. For
example, in Hall thrusters, the ionization instability leads to strong
oscillations of the discharge current (so-called breathing oscillations),
plasma density, ion energy, and as a result the ion flow. In this paper, we
revisit the formulation of the thrust and the thrust efficiency to account for
time variations of the ion parameters including the phase shift between the ion
energy and the ion flow. For sinusoidal oscillations it was found thrust can
potentially change more than 20%. It is shown that by modulating ion energy at
specific amplitudes, thrust can be maximized in such regimes. Finally, an
expression for the thruster efficiency of the modulating thruster is derived to
show a mechanism for inefficiencies in such thrusters.
