# Plasma engine calculator

Date: Wed Mar 21 2001 - 23:16:57 MST

So I finished before the weekend...

The following is for a space transport vehicle whose sole propulsion is a plasma engine constructed as follows:

• Main engine is a cylinder ("exhaust bell") consisting of one wide winding of some low-resistance conductor. (This is as opposed to the standard solenoid practice of having one long wire with many windings; this significantly lowers total conductor resistance, and thus power needed to induce the necessary current.)
• Every so often along the circular part of the cylinder, there is a break in the conductor to interrupt it with a bank of batteries, or other electric power storage devices. These devices provide current through the conductor, as well as power to RF heaters pointed at the bell's interior.
• Fuel is injected from one end of the bell and heated until it becomes a plasma. Current passing through the conductor creates a magnetic field that leaves this plasma nowhere to go except out the other end of the bell. (This is the only source of thrust, as opposed to ion engines which add in electric fields to further accelerate the exhaust.)
Note the following potential inaccuracies in this model:
• The RF heaters are assumed to be of negligible mass.
• Cooling systems for the conductor are neglected.
• Mass of the fuel injector, fuel storage tanks, and injector end of the bell, is neglected. (Though, if the bell is made more cone-shaped than cylindrical, there need be no "injector end of the bell". Fuel injector and storage tanks can be subsumed under "structure", though they are not strictly dependant on the overall vehicle mass.)
• No maneuvering thrusters are included, and only one main engine is assumed.
• Control electronics' mass and power requirements are assumed to be negligible for fly-by-wire systems (fly-by-wire is assumed).
• Thrust lost due to plasma hitting the engine edge is not accounted for.
• Bell is calculated as if it were not interrupted by batteries; magnetic field from default values is strong enough so that plasma escaping through breaks in the bell is assumed to be negligible.
• "Payload" includes any crew and life support systems.
Default values are from the following sources:
• Plasma temperature, total vehicle mass at start, exhaust bell length and internal volume - arbitrary (and therefore most freely adjustable)
• Exhaust bell thickness - large enough to ensure that loss of thickness due to damage from the plasma is negligible during the ~10 minutes of thrust that the other default values give
• Structural mass fraction - multiple sources: composite airframes seem to take about 9%, plus another 3% for landing gear, plus another 3% for avionics
• Molar values of fuel - multiple sources (most standard physics and chemistry references should corroborate), fuel is 100% helium
• Delta V - NASA and other sources for effective delta V when going Earth-to-LEO, including allowance for drag
• Acceleration - 1.5 Gs, reccomended for human launch by multiple sources
• Exhaust bell resistance and density - "Niobium Nb-1Zr (Wah Chang WC-1Zr; Fansteel 80)" from http://www.matweb.com/
• Plasma beta and heating efficiency - ITER and other fusion projects; a lower beta means less plasma impacting engine edge (and thus less thrust, plus less damage to engine)
• Power storage density - Black Light Power, Inc., at http://www.blacklightpower.com/
NameUnitsValue
Plasma TemperatureK
Molar Mass Of Fuelkg/mol
Molar Heat Capacity Of FuelJ/mol * K
Total Vehicle Mass At Startkg
Structural Mass Fraction(none)
Delta Vm/s
Accelerationm/s^2
Plasma Beta (thermal pressure to magnetic pressure ratio measured at exhaust bell edge)(none)
Exhaust Bell Thicknessm
Exhaust Bell Lengthm
Exhaust Bell Internal Volumem^3
Exhaust Bell Resistanceohm/m
Exhaust Bell Densitykg/m^3
Plasma Heating Efficiency (1 watt input generates X watts of heat)(none)
Power Storage Max. Power DensityWh/kg
Power Storage Max. Current DensityAh/kg
Exhaust Velocitym/s
Mass Of Fuel Consumedkg
Total Time To Achive Delta Vs
Rate Of Fuel Consumptionkg/s
Exhaust Bell Circumferencem
Exhaust Bell Masskg
Current To Contain PlasmaA
Power To Contain PlasmaW
Energy To Heat PlasmaJ
Power Storage Mass (current, ampere-hour limited)kg
Power Storage Mass (heat and containment, watt-hour limited)kg
Power Storage Mass (actual: maximum of above two)kg
Structure Masskg

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