I would like to ask about the thrust in PPT (Pulsed Plasma Thrusters) which uses solid propellants such as Teflon.
We know that the thrust force is given as F= T= d(m ve)/dt = m dve/dt + ve dm/dt. We know that both the mass and also the exhaust velocity ‘ve’ are not constant, the velocity usually fairly similar to the trend of the discharge current signal.
The question is:
Why the most (or ALL) of researches consider that the exhaust velocity 've' as constant value and neglect the second term of the equation? Is because the experimental measurements do not allow detecting the variation or something else?
Secondly,
If so, How about the theoretical calculations? Should we consider the variation of ‘ve’ or just take the constant value? and which one? is it the peak or the average velocity on the exit muzzle? average of peak velocity along the discharge tube?
Also, How about the specific impulse ‘Isp’ in both cases? Is it just as Isp = T/(g*m_dot) or ve/g and which ve?
For a propulsion device, the thrust it generates comes from the mass and velocity of the particle ejected from the nozzle (or electrode), where this velocity should be that of the particle at the moment it flies out of the nozzle (or electrode).
In a PPT, the arc ablates the solid propellant to produce neutral gas, part of which is ionised into plasma and accelerated by the electromagnetic force then ejected out of the electrode to produce thrust. Therefore, there are many types of charged and neutral particles produced by a single discharge of PPT using PTFE as propellant.
In general, the impulse generated by a single discharge of a PPT can be classified as neutral gas-generated or plasma-generated. However, in experiments, it is difficult to obtain the amount of plasma produced by a single discharge, and the velocities of different components and clusters in the plasma are also different. So, as you say, dm in the equation 1 is hard to measure by experiment.
In addition, since the plasma velocity (generally more than 20km/s) is much more higher than the neutral gas velocity (about 5km/s), it is generally assumed in the calculations that the entire source of thrust is from the plasma and the contribution of the neutral gas is ignored, but this assumption can only be used if the PPT is electromagnetic type rather than electrothermal type.
I hope my answer is useful to you.
Dear Tianyi Hu
Thank you so much for your comprehensive comment.
From an energy efficiency standpoint, a pulsed plasma thruster can be much more efficient than a constant one. However, I'll explain why the variation of exhaust velocity (ve) is often neglected in the equation
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