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HALL THRUSTER

DIMENSIONING

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Hall thruster design is an empirical science at this time,since it is not possible to design a thruster with acceptableperformance levels based solely on basic principles.

Instead, it is necessary to build on years of designexperience, most of which has been conducted byRussian scientists and engineers.

This research only has been done on SPT Hall thrusters,no such data has been collected on TALs.

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Consider This Diagram For All Dimensioning Parameters

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A set of design equations that relate dimensions of a SPTsuch as the discharge chamber width and depth to itsdiameter were presented at an electric propulsion seminargiven at the Massachusetts Institute of Technology in

1991 by Russian Hall thruster designers. These equationswill provide the basis for our Hall thruster. I extractedthese equations from:

Gulczinski, F. S., "Examination of the Structure and Evolution of Ion Energy Properties ofa 5 kW Class Laboratory Hall Effect Thruster at Various Operational Conditions," Ph.D.

Dissertation, University of Michigan, 1999.

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Dimensioning Equations

= 0.3

= 6 + 0.375 []

= 0.32

= 2 1.1

Butwe need one thing!

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Discharge Chamber Diameter

Discharge Chamber Diameter can be referred tointerchangeably with when describing a Hall thruster. i.e.one can say a so-and-so diameter Hall thruster, or,equivalently, a so-and-so kW Hall thruster

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It turns out to be best to design a Hall thruster for anominal power level

Since mission requirements are most directly driven bythe specific impulse of a thruster, it is best to begin bydetermining a relationship between the nominal specificimpulse and nominal power level of the thruster.

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Here it is:

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By finding the desired Isp, the thruster efficiency can beestimated:

=

1 +

Where a is the theoretical maximum efficiency based onengineering losses (particle collisions with walls, electricalcircuit resistance, PPU losseset cetera)

b relates to the discharge energy required for productionof an ion.

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a is approximated to be = 0.8

b is approximated from this relationship:

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Then we can determine the mass flow rate:

=2

Since = , one expects that the mass flow rate islinearly proportional to the area of the injection area,which would imply a linear proportionality between thediameter squared and the mass flow rate.

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And it is!