Calculating thrust pressure from ion thruster for rocket thrust equation

So recently i have been very interested in the possibilities of using ion thrusters as power interstellar propulsion units, however when it comes to calculating ISP it have absolutely zero idea how you calculate the mass flow rate of the ionised particles or the pressure in the thrust beam. I am guessing the mass flow rate depends on the method of ionisation but it is there a way to work this out? Thank you very much!

2 Answers

If by "pressure in the thrust beam" you mean the force on the vehicle from the beam, that's just called thrust. (The pressure of the plasma itself is minuscule, and not really of interest.)

Then the three things you're talking about are related simply: $$T=g_n I_{sp}{dm\over dt}$$, where $$g_n$$ is the standard gravitational acceleration at the surface of the Earth, which by convention is exactly $$9.80665\,\mathrm{m/s^2}$$.

So for example if you are flowing 60 milligrams of propellant per minute into your ion engine, that's a mass flow rate $${dm\over dt}$$ of $$1\times 10^{-6}$$ kg/sec. If your mass-specific impulse $$I_{sp}$$ is 5,000 seconds, then your Thrust $$T$$ = $$(9.81) \times (5 \times 10^{3}) \times (1\times 10^{-6}) \approx 0.049$$ Newtons of force.

• please double check; I've worked through a simple example for the OP.
– uhoh
Dec 16, 2018 at 20:05
• Though it's not obvious unless you go look at the edit history, also thanks to @uhoh for the example. Dec 17, 2018 at 18:33

To add to Mark Adler's right-on-the-money (as usual!) answer: although ionization method doesn't explicitly enter into the classical performance equations, this paper discusses the non-unity efficiencies involved in propellant ionization and their effects on electric propulsion system performance. The effects aren't huge: the paper quotes up to 6% loss of efficiency.