# Need help modeling a Pulsed plasma thruster discharge circuit using matlab

1. Mar 13, 2009

### Dankul

Hi everyone,

I'm not sure if this is a basic EE problem as I'm in aerospace and I would like to apologize if i posted in the wrong forum. I've attached a circuit diagram of my design. The capacitors and the 2 higher resistors are of variable values. The switch and the lower resistor represents the thruster where it behaves as an open circuit charging the capacitors until a breakdown voltage is obtain. Then which, a plasma arc closes the circuit, discharging the capacitors for a duration of about 10 microsec. The process then repeats.

I've derived the differential equation for the circuit and was able to plot the charging cycle but I'm having some difficulties with the discharge. There is a discontinuity where the voltages across the capacitors suddenly drop from the breakdown voltage as the thruster fires because a different equation is used to account for the added thruster resistance. I am thus unable to use any of the charging circuit initial conditions at the time of breakdown. I think might have to model it with the capacitors discharging at it's pulse rise time according to the data sheet of the capacitors. However, i'm not sure how to incorporate that with the differential equation for discharging.

Do you have any recommendations? Please tell me if you need any additional info or clarification. Thank you

#### Attached Files:

• ###### pptc.jpg
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2. May 12, 2010

### PeterShaw

Hi Dankul,

I did my PhD in pulsed plasma thrusters, the modelling of the discharge is not a trivial matter as the circuit acts as an LCR circuit, of which the capacitor and wire inductance is missing from your circuit.

For a full description of a more complex 1 dimensional circuit model i'd point you to the Thesis of David Lapierre at the Worchester Polytechnic Institute. Although he makes some assumptions on the a non variable plasma mass or plasma resistance it's a good place to start. If you want a more detailed 1 dimensional circuit analysis model on the PPT discharge than a paper written by myself will help out, 'Pulsed Plasma Thrusters: Simple Design, Complex Matter.' Space Propulsion Conference 2010, San Sebastian.

Regards

Pete