1. Click to edit Master subtitle style Professor, Department of Aerospace Engineering, University of Pisa, Italy Chairman, Alta S.p.A, Via A. Gherardesca 5, 56121 Ospedaletto, Pisa, Italy e-mail: m.andrenucci@alta-space.comm.andrenucci@alta-space.com IEPC-2005-187 Francesco Battista and Pietro Piliero Mariano Andrenucci Hall Thruster Scaling Methodology

2. 2 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Introduction Expansion of human activities in space will certainly pose the need to develop high power propulsion systems HETs will certainly play a major role in that scenario But power range of devices developed so far relatively narrow limited power levels affordable in laboratory experiments modest power levels typical of past and current space systems At the opposite end of the power gamut, growing case emerging for the application of HET technology to very low power levels (less than 200 W) This would grant access to the mini/micro-satellite market, a potentially large market already expressing a significant demand for thrusters in the performance range suitable for Mini-HETs Issue: How to extrapolate sizing criteria worked out for thrusters developed to date to different scales, or different operating conditions

3. 3 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Introduction sequel to previous paper mainly focussing on methodology more refined modelling of processes involved

4. 4 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 General approach We are concerned with the way in which the different parameters characterizing a device of a given family will vary as a result of a change of size (defined by the value of any suitable parameter) This will result from the interplay of different physical processes, which will generally obey different scaling laws Each scaling law will consist of a simple power-law relation between the involved parameters Other physical magnitudes resulting from the combination of different processes will be calculated as a function of those pertaining to each of the costituent processes

5. 5 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Scaling Model

6. 6 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Scaling modes

7. 7 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Scaling mode algebra

8. 8 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Calculation of scaling parameters

9. 9 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 HET scaling Model: efficiency Standard description adopted

10. 10 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 HET scaling Model: efficiency Loss factor Exhaust velocity from discharge voltage and loss factor and therefore

11. 11 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 HET scaling Model: efficiency Other effects considered plume divergence spread of ion velocities Overall thrust efficiency usually assumed

12. 12 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 HET scaling Model: other factors ionization diffusion length wall losses anode and ionization losses lifetime, heat loads, etc. (see paper)

13. 13 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Scaling Exponent Matrix

14. 14 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Reference thruster: SPT-100 Suppose we want to design a thruster with 50 kw power 369 mm average diameter 88 mm channel width With respect to the reference thruster this means P’/P=37.037 d m ’/d m =4.341 b’/b=5.867 or ln(P’/P)=3.612 ln(d m ’/d m )=1.468 ln(b’/b)=1.769 We need to use three independent transformations; we choose to use a combination of SL, L, R. (1) Use of the model

15. 15 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Use of the model From the general exponent matrix we extract which means that so that by matrix inversion we find (2)

16. 16 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Use of the model We thus obtain so that the values of the scaling factors for the involved transformations are We can hence determine the equivalent overall scaling factor and the relative weights of the component transformations (3)

17. 17 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Use of the model We can thus generate the exponent vector for the equivalent transformation, where and accordingly determine all other parameters such as (4)

18. 18 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 50 kW Thruster

19. 19 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 5kW variants

20. 20 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 5 kW Thruster

21. 21 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Alta’s 5 kW HET  Operating power: nominal 5 kW, maximum efficiency 7 kW.  Axially symmetric magnetic coil arrangement, three separate windings  Maximum recorded efficiency: 49% at 4.1 kW, including cathode and magnetic circuit  Thrust: 200 mN, I sp : 1850 s.

22. 22 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 100 W variants

23. 23 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 100 W Thruster

24. 24 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Alta’s HT-100 Mini-HET

25. 25 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Comparison with data Power levels > 5 kW

26. 26 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Comparison with data Power levels > 5 kW

27. 27 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Comparison with data Power levels > 5 kW

28. 28 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Comparison with data Power levels < 500 W

29. 29 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Comparison with data Different operating points

30. 30 Hall Thruster Scaling Methodology 29th International electric propulsion Conference - Princeton University, October 31 - November 4, 2005 Conclusions Despite simplicity of model adopted, fairly good approximation of the scaling behaviour of experimental devices easily obtained by careful combination of a few basic scaling modes Useful preliminary design tool, allows quick evaluation of impact of design choices or operating conditions Possibility to improve predictive capability by more refined modelling of involved processes Intrinsic interest of methodology