Figure 9.14: Anodic thrust e ciency against discharge power HT-5k computed map and comparison with experimental results (diamonds)
As it is evident from the maps the agreement between the computed maps and the experi- mental data is extremely good, less than a 5% error is found on every operation point.
The greatest dierences, observing Figure 9.14, are found for the computation of the anodic thrust e ciency. This is likely caused by the large error bars in the experimental data concerning the e ciency that is calculated a posteriori over other experimental data (the thrust, input power and mass ow rate), therefore the experimental data on the e ciency intrinsically present a large error. As a matter of fact, while the prediction for the e ciency against the power have a very clear and expected trend, the experimental data don't, underlining their poor precision.
9.3 Model capabilities and limitations
The presented results show how, if properly calibrated, the 1D model with ideal radial magnetic eld, is capable of catching the essence of the working principle of current HETs, predicting with an extremely good accuracy the thruster operation, also away from the nominal operation con- ditions.
it can only simulate thrusters in which the magnetic eld is mainly radial, so it can't be used to study the bene ts and the behavior of non-standard thrusters, in example thrusters with magnetically shielding magnetic eld topology (see Chapter 3);
to accurately predict the operation points of speci c HETs previous experimental data on that same HET, or a thruster of similar characteristics, are needed to calibrate the free parameters. If no data is available, constant values of the parameters can be used, or the ones available for other thrusters, but the model will loose its great accuracy;
Part V
Conclusions
Chapter 10
Conclusions
10.1 Summary
The complete work here presented yields some important gains into the eld of rst order mod- elization of the plasma behaviour inside a Hall eect thruster, giving contributions in the analysis of both standard and non-standard HETs con gurations.
A complete research of the state-of-the-art modelization of the plasma wall interaction and ero- sion was presented, analyzing various models along with their advantages and drawbacks. The analysis of the interaction between plasma and walls lead us to develop an original sheath model that allows a general inclination of the magnetic eld line with respect to the wall. This model was analytically solved, obtaining closed form expressions of the oating potential and the velocities at the plasma edge of the sheath, and their simpli ed dependence on the local plasma properties. While classical sheath models are suitable to study the insulating walls eect on the plasma inside the channel of standard HETs, the discussed generalization is needed when particular magnetic eld topologies are under analysis, like in the case of magnetically shielded HETs.
Then a one-dimensional model of a Hall eect thruster was developed. With the assumptions we made, this rst model is capable of simulating the operative conditions of current HETs with ideal, quasi-radial magnetic eld topologies. The main additions with respect to previous models are:
the complete problem was at rst faced and a sensitivity analysis on the relevance of the electron pressure and the ion's boundary condition at the anode was performed. Ultimately we were able to demonstrate their irrelevance on the solution. Thus we were able to neglect the pressure and to apply a positive ion velocity at the anode, greatly simplifying the
problem, without loosing accuracy;
a general study also on the neutral mean motion was performed and the neutrals velocity was physically linked with the operation condition and in particular on the anode temperature; the radial behavior of the plasma was analyzed and a simpli ed, closed form solution for both the wall particle and energy losses was found. The uncertainties on the radial model were accounted for with a free parameter f that ultimately was found to be in close proximity to 1 for all operation conditions, validating the simpli ed radial model for a rst order description;
a general dependance of the anomalous diusion parameter αB on the operation condition
was allowed, and upon solution, we found a clear dependance of the anomalous diusion parameter on the discharge voltage;
Then the model was validated against the experimental data available for the Alta HT-5k thruster. After calibration the model predictions showed a remarkable agreement with the experimental data, generating results on the performance that, for the case of the thruster's nominal operation condition, were less than a 1% away from the actual experimental performance. When o design conditions were studied, very low errors were found and therefore a reliable computed operation map for the thruster was built. Moreover the analysis of the plasma properties trends in the chan- nel and the near plume, along with the formulated plasma-wall interaction models, highlighted the fundamental relevance that the presence of the wall has on the plasma regime in the thruster. In particular from the temperature pro le it is evident how the walls are the primary energy sink in the thruster, and how the temperature peak, when the input power increases, tends to move outside of the thruster.
The model is, therefore, validated, and gives now a toolbox to predict the operation of standard HETs with very low computational eorts and very good accuracy.
After that the rst steps in the modelization of non standard HET con gurations were performed. In order to ful ll the rst theoretical work foreseen in ESA's Long Life Low Erosion Hall Eect Thruster TRP, commissioned to Alta S.p.A (now Sitael S.p.A.), the concept of magnetic shielding was studied, qualitatively justi ed and discussed, and a second model, that should be able to analyze non standard HETs con gurations with complex 2D magnetic eld topologies, formulated. In this model the anisotropy induced by the presence of the magnetic eld was used assuming that the plasma properties gradients in the direction orthogonal to the magnetic eld were dominant, allowing for a rst order, one-dimensional, description of a general HET, not constrained by the assumption of ideal, quasi-radial magnetic eld.
10.2. FUTURE WORK 177