Sizing of Hall effect thrusters with input power and thrust level: An   Empirical Approach
  Sizing methods can be used to get a first estimate of the required Hall thruster dimensions and operating conditions for a given input power and a corresponding thrust level. After a review of the existing methods, a new approach, which considers the three characteristic thruster dimensions, i.e. the channel length, the channel width and the channel mean diameter as well as the magnetic field, is introduced. This approach is based on analytical laws deduced from the physical principles that govern the properties of a Hall effect thruster, relying on a list of simplifying assumptions. In addition, constraints on the channel wall temperature as well as on the propellant atom density inside the channel are taken into account. The validity of the scaling laws is discussed in light of a vast database that comprises 23 single-stage Hall effect thrusters covering a power range from 10 W to 50 kW. Finally, the sizing method is employed to obtain a preliminary geometry and the magnetic field strength for a 20 kW and a 25 kW Hall effect thruster able to deliver a thrust of 1 N, respectively 1.5 N. 
Kathe Dannenmayer, Stephane Mazouffre