Conventional 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. This paper revisits 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 that 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.

描述等离子推进器性能（包括推力，比冲和推进器效率）的常规表达式和定义均假定稳态等离子流具有恒定流速。然而，对于这些推进器，等离子体表现出不稳定的行为是非常普遍的，这导致推力和排气速度随时间变化。例如，在霍尔推力器中，电离的不稳定性会导致放电电流的剧烈振荡（所谓的呼吸振荡），等离子体密度，离子能量以及由此产生的离子流。本文重新研究推力和推力效率的公式，以解决离子参数随时间变化的问题，包括离子能量和离子流之间的相移。对于正弦振动，发现推力可能会变化超过20％。结果表明，通过以特定幅度调制离子能量，可以在这种情况下使推力最大化。最后，推导了调节推进器的推进器效率表达式，以显示这种推进器效率低下的机制。