Plasma Properties Inside a Small Hall Effect Thruster

Transcription

1 Plasma Properties Inside a Small Hall Effect Thruster IEPC Presented at the 33 rd International Electric Propulsion Conference, The George Washington University, Washington, D.C., USA Maziar Dabiri Michel Dudeck Université Pierre et Marie Curie, Institut d Alemebert, 4, Place Jussieu, 75005, Paris, France Marcel Guyot Université de Versailles-St.Quentin en Yvlines(UVSQ), 45 av. des Etats-Unis, Versailles, France Serge Barral, Jacek Kurzyna Institute of Plasma Physics and Laser Microfusion, 23, ul.hery, Warsaw, Poland Hall effect thrusters, with a typical power of about 1.5 kw, are especially well suited for stationkeeping geostationary satellites for telecommunication applications or for future interplanetary missions. In the present study, the plasma properties of different PPI Hall effect thrusters have been determined using the IPPLMs HETMAn code. A small innovative PPI thruster was designed and built in France in The plasma properties inside the discharge channel of the PPI were calculated using the HETMAn 1-D simulation code. The simulation has been performed for various PPI channel sizes keeping constant the ration of the radii of the channel to anticipate the operating conditions of a miniaturized PPI type thruster. I. Nomenclature A B r e E I d J i J e m e m i N e N i ṁ n r Le R i = discharge column cross section = radial magnetic field = elementary charge = axial electric field = discharge current = ionic current = electron current = electron mass = ion mass = density of electrons = density of ions = anode neutral mass flow rate = electron Larmor radius = inner radius of the channel Student of M.Sc in Mechanical Engineering, University of Pierre et Marie Curie, maziar.da@gmail.com Professor, University of Pierre and Marie Curie, Institut d Alembert 1

2 R e T e T T U d V i = outer radius of the channel = total electron temperature = electronic temperature perpendicular to B lines = electronic temperature along B lines = discharge voltage = axial velocity of ions II. Introduction Afirst PPI (small Hall effect thruster, laboratory model) using permanent magnets was designed and constructed in France in ,2. The plasma properties inside its annular discharge channel have been studied using a fluid 1D simulation (HETMAn code) developed at IPPLM in Warsaw, Poland 3,4. The code allows the calculation of the non stationary plasma properties along the discharge channel with two electron temperatures and two populations of neutral xenon. Plasma density, electron temperatures, neutral xenon, electron and ion current are determined as functions of time along the axis of the annular channel. The plasma frequency of the breathing mode is deduced from the oscillations of the parameters. The global performances as thrust, specific impulse and, efficiency are calculated for the nominal operating conditions (discharge voltage: 300V, xenon mass flow rate: 1mg/s, maximum value of radial magnetic field: 270G). With the objective of studying versions of the smaller PPIs, the code HETMAn was used while conserving the same magnetic profile, the same channel length and the same discharge voltage. However, the channel size has been modified, while keeping an identical ratio for radii (R e /R i =1.3). The mass flow rate per unit of cross channel section of neutral xenon injected into the channel is kept constant. The first PPI (PPI-0) is used as the reference and the three other PPIs(PPI-1,2,3) have been studied based on this reference, using the HETMAn simulation code. For each PPI, the plasma properties have been calculated and the global performances (thrust, specific impulse and efficiency) have been compared with PPI-0. It is shown that the efficiency can be increased by modifying the maximum value of the radial magnetic field at the channel exit while keeping the same Gaussian shape for the magnetic field. The difference with Ref. 5 is in the objective, which is miniaturization of PPI for this paper and optimization of performances by changing the channel width (R e -R i ) for the same mean diameter. III. Hall effect thrusters Due to its weak ionization potential, its mass as well as its lack of toxicity, Xenon is chosen as the propellant. It is injected into an annular channel surrounded by isolating ceramic (BNSiO 2 ). The gas distributor is generally used as the anode, but the anode and the distributor can be separated in some thrusters like for ATONs (MIREA Institute, Moscow). An external hollow cathode emits electrons which move towards the anode through the channel but the low pressure in the channel (104 to 105 mbar) leads to a electrons-neutrals mean free path which is much larger than the channel length L ( λ e n >> L), which prevents the ionization of the gas. An electron trapping will be obtained by a magnetic lens formed by coils located on either side of the channel. The magnetic field is mostly radial and the maximum intensity ( B r ) is situated in the vicinity of the exit plane of the channel. It is therefore necessary that the Larmor electronic radius (r Le ) is less than the channel length L (r Le << L). Trapping electrons will therefore increase their residence time in the channel and allow ionizing collisions. In the region with high magnetic field, discharge current conservation imposes the creation of an axial electric field in order to compensate the drop in electron mobility. This axial electric field will accelerate the ions and eject them with high speed (15-20 km.s 1 ) creating the propulsion effect without needing accelerating grids as in a GID category plasma thruster. Ions with large Larmor radius (r Le > 1m) are not very sensitive to the magnetic field Br and only electrons are magnetized. The plasma is created in the presence of an crossed electromagnetic field E B causing azimuthally electron drift (Hall current of tens of amperes). Electronic high-frequency oscillations azimuthally (1-10MHz) are considered likely to explain the electron transport transverse to the magnetic lines, rather than the electron-neutral collision volume (because the number of collisions at low pressure is insufficient) or the parietal transportation suggested by Prof. AI Morozov (electron transport of field lines 2

3 in the magnetic field lines, heading towards the anode by collisions with the walls) 6. IV. PPI-0 nominal version The nominal version of the PPI is running with 200 W input electric power and 1 mg s of xenon mass flow rate. This PPI uses permanent magnets to generate the required magnetic field and a porous ceramic made of Al 2 O 3 ring for the gas injection and operating as electric insulation. Moreover, a gap in the magnetic circuit moves the magnetic lens toward the channel exit and to focus the ionization zone so that the PPI thrusters would not need magnetic screens. The magnetic field is created by permanent magnets made of samarium-cobalt (SmCo) set in each part of the channel. The magnetic field is realized by a set of small cylindrical permanent magnets in order to easily change the amplitude and the profile of the magnetic field. The PPI properties, in its nominal version functioning with xenon, have been calculated using the HETMAn fluid simulation. The mass flow rate of xenon is 1 mg s and the interior and exterior radii of the annular channel are respectively 16mm and 21mm. The channel length is 25mm and the maximum value of the magnetic field, created by the permanent magnets is of 270G in the vicinity of the exit. The discharge voltage of cathode-anode is 300V. Figure.1 represents the evolution of the discharge current I d as a function of time. The oscillations are between I min = 0.74A and I max = 0.94A with an average value of I av =0.82A. These low frequency oscillations are usual in Hall effect thrusters 7,8 and are due to an effect called the breathing mode. Figure.2 shows the evolution of the electric power P d of the plasma discharge (P d = U d I d ). The power is between P d,min =222W et P d,max =282W with an average value of P d,av =246.5W. Figure 1. Discharge current as a function of time Figure 2. Electric power as a function of time The evolution of the ionic and electronic density is a variable of time t and z-coordinate where x = 0 is defined as the exit of the channel. The discharge current is essentially electronic in the vicinity of anode (x=-0.025m) and it breaks up into an ionic current and an electronic current throughout the channel. Both currents follow the fluctuations of the breathing mode of low frequency plasma. The evolution of the electronic density at the exit of the channel is represented in Fig.3. The electronic density is between n e,min = el cm. 3 el cm and n 3 e,max = el cm with an average value of n 3 e,av = 6.5 The electronic parallel and perpendicular temperatures, respectively shown as T e and T e are represented in Fig.4 and Fig.5. The maximum value of T e is 12.5eV and that of T e is 68.1eV. The average electronic temperature is defined by 3T e = T e + 2T e The 1-D simulation allows the calculation of thrust T and thus the specific impulse I sp as well as the 3

4 Figure 3. Electronic density in the channel as a function of time and x-coordinate Figure 4. Parallel electronic temperature as a function of time and x-coordinate Figure 5. Perpendicular electronic temperature as a function of time and x-coordinate global efficiency of the thruster. I sp is calculated using the Eqn.1 : I sp = T mg 0 (1) where g 0 is the intensity of the gravity at the surface of Earth. This equation shows that the specific impulse is approximately the ejection velocity divided by 10. The fuel consumption to carry out a change of orbit asking for a velocity variation of V is more lower, the more specific impulse and thus the speed of ejection are higher (Tsiolkovski formula, 1905).The thrust and the specific impulse have the average values of respectively 13mN and 1326s. V. PPI-1, PPI-2, PPI-3 miniaturized versions based on PPI-0 The plasma properties of xenon in channel of miniaturized versions of PPI thrusters have been studied. Different channel dimensions have been considered while keeping the ratio R e /R i =1.3 as a constant. This condition makes h/d a constant ratio where h is the width and d the average diameter of the channel. The values chosen for the interior radius are 14mm (PPI-1), 11mm (PPI-2) and 9mm (PPI-3). The mass flow rate of the neutral xenon injected into the channel is proportional to the surface of the section as to maintain a constant flow per unit of area, whatever the size of the channel. The magnetic field profile is the same for 4

5 all channel geometries with a value of B r,max = 270G. The parallel and perpendicular temperatures go through negligible variations for different versions of the PPIs studied ( Fig.6 ). The average thrust goes through values of 10mN for PPI-1, 5mN for PPI-2 and 3mN for PPI-3 and the specific impulse has values of 1323s for PPI-1, 1080s for PPI-2 and 968s for PPI-3. Figure.7 shows the specific impulse of the PPIs as a function of global efficiency. The efficiency is between 21% and 35% for different PPIs. The consumed electric power is only that of the plasma discharge in the channel, due to lack of reel in order to create the magnetic field. The mass flow rate of xenon is that of the anode. Figure 6. Parallel and perpendicular temperatures as functions of time Figure 7. Specific impulse as a function of efficiency 5

6 Figure 8. Frequency as a function of inner radius R i Figure.8 shows the low frequency of the plasma oscillations. This frequency is quasi linearly increasing from 12.1 khz to 18.1kH. This result is obtained keeping the same magnetic field and the same density of mass flow (per unit of section) and the same discharge voltage. This increase could be explained by.. (Serge?) As shown in the Fig.10, the thrust decreases starting from a value of R i. The thrust is a result of T = n i AM i V 2 i (2) so if we admit that the axial ejection velocity of ions V i stays the same, then the product of N e A goes through a maximum as a function of interior radius Ri ( Fig.9). This explains the thrust reduction starting 17 el from R i = 11mm due to the reduction of electronic density which passes from 6.5 m for R 3 i = 11mm to 17 el 2.2 for R i = 16mm. m 3 Figure 9. N ea product as a function of R i 6

7 Figure 10. Thrust and specific impulse as functions of inner radius R i Figure.9 shows the origin of thrust decrease, starting from R i =12mm. The solution to this phenomenon is to modify the magnetic field amplitude for different sizes of the PPIs. The maximum value of the magnetic field at the channel exit has been modified (keeping the two parameters defining the Gaussian shape of B r as constants), in order to find greater values for the thrust during strong flow operations. The thruster of larger size requires a magnetic field of smaller amplitude. The magnetic field amplitude of B r,max = 230G is thus chosen for the two PPI-0 and PPI-1 (R i 11mm). The results are shown in the Fig.11. Figure 11. Thrust and specific impulse as functions of R i after modifying the B r VI. Conclusion The properties of four PPI Hall effect thrusters, which differ by the channel dimensions have been studied. The parallel and perpendicular electronic temperatures and the electronic density have been calculated for each model. Global parameters such as the thrust, the specific impulse and the global efficiency have been calculated. A reduction in the thrust is appeared due to a reduction in the ionic density, which can be compensated by modifying the magnetic field. The numerical results, despite of the detailed plasma descriptions, should be validated by experimental studies in order to examine the interpretation and the progress of PPIs. 7

8 Acknowledgments The present work benefited from the input of prof.dudeck from the University of Pierre and Marie Curie of Paris and prof.barral, head of research at the Institute of Plasma Physics and Laser Microfusion of Warsaw, who both provided valuable comments, ideas and assistance to the writing and undertaking of the research summarized here. References Proceedings 1 M. Guyot, P. Renaudin, V. Cagan, C. Boniface, patent FR (2007) 2 M. Guyot, New concepts for magnetic field generation in Hall effect thrusters, proceeding of the 5th Int. Spacecraft Propulsion Conference, Heraklion, Greece (2008) 3 S. Barral, Numerical studies of Hall thrusters based on fluid equations for plasma, IPPT Polish Academy of Sciences, Warsaw April 25th, J. Kurzyna, S. Barral, 25 Symposium on Plasma Physics and Technology, Prague, Czech Republic, June 18-21, S. Mazouffre, K. Dannenmayer, G. Bourgeois, M. Guyot, S. Denise, P. Renaudin, V. Gagan, M. Dudeck, Effect of channel geometry on discharge properties and performances of a low-power Hall effect thruster Space Propulsion conference, San Sebastian, Spain (3-6 Mai 2010). 6 A.I. Morozov, V.V. Savelev, Plasma Physics Reports, Vol. 27, 7, 570, (2001) 7 J.-P. Boeuf, L. Garrigues, Low frequency oscillation in a stationary plasma thrusters, Journal of Applied Physics 84 (7), 3541 (1998) 8 L. Garrigues, Modlisation dun propulseur plasma stationnaire pour satellites, University of Paul Sabatier Toulouse, October 28th,