16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 1 of 25 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 13-14: Electrostatic Thrusters Outline Page No. 1 Introduction…………………………………………………………………………………… 2 2 Principles of Operation………………………………………………………………….. 2 3 Ion Extraction and Acceleration……………………………………………………. 3 4 Ion Production………………………………………………………………………………. 9 4.1 Physical Processes in Electron Bombardment Ionization Chambers………………………………. 9 4.2 Nature of the Losses……………………………………………………….. 10 4.3 Electron Diffusion and Confinement……………………………….. 11 4.4 Particle Production Rates…………………………………………………. 13 4.5 Lumped Parameter Performance Model…………………………… 15 5 Propellant Selection ………………………………….………………………………….. 15 References………………………. 16 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 2 of 25 Lecture 13-14 Electrostatic Thrusters 1 Introduction Electrostatic thrusters (“ion engines”) are the best developed type of electric propulsion device, dating in conception to the ‘50’s, (1) and having been demonstrated in space in 1964 on a suborbital flight of the SERT I spacecraft (2) . The early history and concepts are well documented (1),(3) , and evolved through progressive refinements of various types of ion beam sources used in Physics laboratories, the improvements being essentially dictated by the needs for high efficiency, low mass and long life for these sources to be used in space. Of the various configurations discussed for example in Ref. 3 (ca. 1973), only the electron bombardment noble gas type, plus (in Europe) the radio-frequency ionized thruster (4) and (in Japan) the Electron Cyclotron Resonance thruster, have survived. Other interesting concepts, such as Cesium Contact thrusters and duo-plasmatron sources have been largely abandoned, and one new special device, the Field Emission Electrostatic (5) thruster has been added to the roster. The electron bombardment thruster itself has evolved in the same time interval from relatively deep cylindrical shapes with uniform magnetic fields produced by external coils and with simple thermoionic cathodes, to shallow geometrics using sharply nonuniform magnetic field configurations, produced by permanent magnets, and with hollow cathode plasma bridges used as cathode and neutralizer. Where a typical ion production cost was quoted in Ref. (3) as 400- 600 eV for Hg at 80% mass utilization fraction, recent work with ring-cusp thrusters has yielded for example a cost of 116 eV in Xenon at the same utilization (6) . Such reductions make it now possible to design for efficient operation (above 80%) with environmentally acceptable noble gases at specific impulses below 3000 sec, a goal that seemed elusive a few years back. The major uncertain issues in this field seem now reduced to lifetime (measured in years of operation in orbit) and integration problems, rather than questions of cost and physical principle or major technological hurdles. Extensions to higher power (tens of kW) and higher specific impulse (to 7,000 – 8,000 s) are now being pursued by NASA for planetary missions requiring high ?V . 2 Principles of Operation Electrostatic thrusters accelerate heavy charged atoms (ions) by means of a purely electrostatic field. Magnetic fields are used only for auxiliary purposes in the ionization chamber. It is well known that electrostatic forces per unit area (or energies per unit volume) are of the order of 2 1 E 2 0 ε , where E is the strength of the field (volts/m) and 0 ε the permittivity of vacuum 12 Farad 8.85 10 m ? 0 ?? ε= × ?? ?? . Typical maximum fields, as limited by vacuum breakdown or shorting due to imperfections, are of the order of 10 6 V/m, yielding maximum force densities of roughly 2-5 5 Nm =5×10 atm.This low force density is one of the major drawbacks of electrostatic engines, and can be compared to force densities of the order of 10 4 N/m 2 in self-magnetic devices such as MPD thrusters, or to the typical gas pressures of 10 6 -10 7 N/m 2 in chemical rockets. Simplicity and efficiency must therefore compensate for this disadvantage. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 3 of 25 The main elements of an electrostatic thruster are summarized in Fig. 1. Neutral propellant is injected into an ionization chamber, which may operate on a variety of principles (electron bombardment, contact ionization, radiofrequency ionization…). The gas contained in the chamber may only be weakly ionized in the steady state, but ions are extracted preferentially to neutrals, and so, to a first approximation, we may assume that only ions and electrons leave this chamber. The ions are accelerated by a strong potential difference V a applied between perforated plates (grids) and this same potential keeps electrons from also leaving through these grids. The electrons from the ionization chamber are collected by an anode, and in order to prevent very rapid negative charging of the spacecraft (which has very limited electrical capacity), they must be ejected to join the ions downstream of the accelerating grid. To this end, the electrons must be forced to the large negative potential of the accelerator (which also prevails in the beam), and they must then be injected into the beam by some electron-emitting device (hot filament, plasma bridge…). The net effect is to generate a jet of randomly mixed (but not recombined) ions and electrons, which is electrically neutral on average, and is therefore a plasma beam. The reaction to the momentum flux of this beam constitutes the thrust of the device. Notice in Fig. 1 that, when properly operating, the accelerator grid should collect no ions or electrons, and hence its power supply should consume no power, only apply a static voltage. On the other hand, the power supply connected to the neutralizer must pass an electron current equal in magnitude to the ion beam current, and must also have the full accelerating voltage across its terminals; it is therefore this power supply that consumes (ideally) all of the electrical power in the device. In summary, the main functional elements in an ion engine are the ionization chamber, the accelerating grids, the neutralizer, and the various power supplies required. Most of the efforts towards design refinement have concentrated on the ionization chamber, which controls the losses, hence the efficiency of the device, and on the power supplies, which dominate the mass and parts count. The grids are, of course, an essential element too, and much effort has been spent to reduce their erosion by stray ions and improve its collimation and extraction capabilities. The neutralizer was at one time thought to be a critical item, but experience has shown that, with good design, no problems arise from it. Following a traditional approach (1),(3) , we will first discuss the ion extraction system, then turn to the chamber and other elements. 3 Ion Extraction and Acceleration The geometry of the region around an aligned pair of screen and accelerator holes is shown schematically in Fig. 2 (from Ref. 7). The electrostatic field imposed by the strongly negative accelerator grid is seen to penetrate somewhat into the plasma through the screen grid holes. This is fortunate, in that the concavity of the plasma surface provides a focusing effect which helps reduce ion impingement on the accelerator. The result is an array of hundreds to thousands of individual ion beamlets, which are neutralized a short distance downstream, as indicated. The potential diagram in Fig. 2 shows that the screen grid is at somewhat lower potential than the plasma in the chamber. Typically the plasma potential is near that of the anode in the chamber, while the screen is at cathode potential (some 30-60 volts lower, as we will see). This ensures that ions which wander randomly to the vicinity 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 4 of 25 of the extracting grid will fall through its accelerating potential, while electrons (even those with the full energy of the cathode-anode voltage) are kept inside. The potential far downstream is essentially that of the neutralizer, if its electron-emission capacity is adequate. This potential is seen to be set above that of the accelerator grid, in order to prevent backflow of electrons from the neutralizer through the accelerating system. In addition, by making the “total voltage”, V T , larger than the “Net voltage”, V N , the ion extraction capacity of the system is increased with no change (if V N is fixed) on the final velocity of the accelerated ions. In some designs, a third grid (“decelerator grid”) is added to more closely define and control V N , and the neutralizer is set at approximately the same potential as this third grid. It is difficult to analyze the three-dimensional potential and flow structures just described. It is however, easy and instructive to idealize the multiplicity of beamlets as a single effective one-dimensional beam. The result is the classical Child-Langmuir space charge limited current equation. The elements of the derivation are outlined below: a) Poisson’s equation in the gap: 2 i 20 end =- dx φ ε (1) b) Ion continuity ii env j = constant= (2) c) Electrostatic ion free-fall: () i i 2e - v= m φ (3) Combining these equations, we obtain a 2 nd order, nonlinear differential equation for ( )xφ . The boundary conditions are () ( ) a 0=0, x=d=-Vφφ (4) In addition, we also impose that the field must be zero at screen grid: x=0 d =0 dx φ?? ?? ?? (5) This is because (provided the ion source produces ions at a sufficient rate), a negative screen field would extract more ions, which would increase the “in transit” positive space charge in the gap. This would then reduce the assumed negative screen field, and the process would stop only when this field is driven to near zero (positive fields would choke off the ion flux). At this point, the grids are automatically extracting the highest current density possible, and are said to be “space charge limited”. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 5 of 25 Since three conditions were imposed, integration of the equations (1) to (3) will yield the voltage profile and also the current density j. The result is 12 32 0 2 i 42 e Va j= 9md ?? ε ?? ?? (6) and also () 43 x x=-Va d ?? φ ?? ?? (7) () 13 4Va x Ε x=- 3d d ?? ?? ?? (8) Equation (8) in particular shows that the field is zero (as imposed) at x=0, and is 4Va - 3d at x=d (the accelerator grid). This allows us to calculate the net electrical force per unit area on the ions in the gap as the difference of the electric pressures on both faces of the “slab”: 2 2 2 F1 4Va 8Va = A2 3d 9 d 00 ?? = ?? ?? εε (9) and this must be also the rocket thrust (assuming there is no force on ions in other regions, i.e., a flat potential past the accelerator). It is interesting to obtain the same result from the classical rocket thrust equation. The mass flow rate is i mm =j Ae i , and the ion exit velocity is i 2eVa c= m , giving i i mFm 2eVa c= j AA e m = i Using Child-Langmuir’s law for j (Equation 6), this reduces indeed to Equation (9). For a given propellant (m i ) and specific impulse (c/g), the voltage to apply to the accelerator is fixed: 2 i mc Va = 2e (10) 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 6 of 25 and, from (9), increasing the thrust density requires a reduction of the gap distance d. As noted before, this route is limited by eventual arcing or even by mechanical shorting due to grid warping or imperfections. For thruster diameters of, say, 10-50 cm., gap distances have been kept above 0.5-1 mm. The only other control, at this level of analysis, is offered by increasing the ion molecular mass, m i . This allows increased voltages V a (Equation 10), and, provided d can be kept small, higher thrust (Equation 9). In addition to increasing thrust density, higher molecular mass also reduces the importance of a given ion production cost ?φ (See lecture 3), and hence increases the thruster efficiency. The effect of ion deceleration past the accelerator grid (either through the use of a “decel” grid, or by relative elevation of the neutralizer potential) can be easily incorporated in this 1-D model. For the usual geometries, the screen-accelerator gap still controls the ion current (Equation 6 with V a replaced by V T , and d by d a ). This is because the mean ion velocity is high (and hence the mean ion density is low) in the second gap, between the accelerator and the real or virtual decelerator, so that no electrostatic choking occurs there. This is schematically indicated in Figure 4 by a break in the slope of the potential at the decelerator. More specifically, it can be shown that Equation (6) still controls the current provided that ()() 12 12 12d N aT d V >1-R 1+2R ; R= dV (11) (for equal gaps, this is satisfied for all R between 0 and 0.75, for instance; at higher R, the second gap limits current). Accepting, then, Equation (6), the thrust is again given by Fm c AA = i , where m A i has not changed, but c is proportional to 12 N V . Hence we obtain instead of (9) 22 32 12 12 -32TN T N 2 aaa VV V VF8 8 8 =RR A9 9 d 9 dd 00 0 ?? ?? == ?? ?? ?? ?? εε ε (12) The last form shows that for a given specific impulse (hence given V N ), reducing R=V N /V T increases thrust. It does so by extracting a higher ion current through the flux-limiting first gap. Returning to Equation (6), if we imagine a beam with diameter D, we would predict a total beam current of 12 2 32 32 0TT i 42 e D Ι V=PV 49 m d = ?? ?? ?? ?? ?? ?? π ε (13) where P is the so-called “perveance” of the extraction system. Equation (13) shows that this perveance should scale as the dimensionless ratio 2 2 D d , so that, for example the same current can be extracted through two systems, one of which is twice the size of the other, provided diameter and grid spacing are kept in the same ratio. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 7 of 25 While the one-dimensional model is important in identifying many of the governing effects and parameters, its quantitative predictive value is limited. Three-dimensional effects, such as those of the ratio of extractor to accelerator diameter, the finite grid thicknesses, the potential variation across the beam etc. (see Fig. 2) are all left out of account. So are also the effects of varying the properties of the upstream plasma, such as its sheath thickness, which will vary depending on the intensity of the ionization discharge, for example. Also, for small values of R=V N /V T , the beam potential (averaged in its cross-section) cannot be expected to approach the deep negative value of the accelerator, particularly for the very flattened hole geometry prevalent when d/D is also small. Thus, the perveance per hole can be expected to be of the functional form aa s D ssss T Dt t Vd P=p ,,,,R, DDDD V ?? ?? ?? (14) where the subscripts (s) and (a) identify the screen and accelerator respectively, t is a grid thickness, and V D is the discharge voltage, which in a bombardment ionizer controls the state of the plasma. These dependencies were examined for a 2-grid extractor in an Argon-fueled bombardment thruster in Ref. 7. Some of the salient conclusions of that study will be summarized here: (1) Varying the screen hole diameter D s while keeping constant all the ratios (d/D s , D a /D s , etc.) has only a minor effect, down to s D0.5≈ mm if the alignment can be maintained. This confirms the dependence upon the ratio d/D s . (2) The screen thicknesses are also relatively unimportant in the range studied ( s t/D 0.2 - 0.4≈ ). (3) Reducing R=V N /V T always reduces the perveance, although the effect tends to disappear at large ratios of spacing to diameter (d/ D s ), where the effect of the negative accelerator grid has a better chance to be felt by the ions. The value of d/ D s at which R becomes insensitive is greater for the smaller R values. (4) For design purposes, when V N and not V T is prescribed, a modified perveance 32 N I V ?? ?? ?? (called the “current parameter” in Ref. 7) is more useful. As Equation (13) shows, one would expect this parameter to scale as R -3/2 , favoring low values of R (strong accel-decel design). This trend is observed at low R, but, due to the other effects mentioned, it reverses for R near unity, as shown in Fig. 5. This is especially noticeable at small gap/diameter ratios, when a point of maximum extraction develops at R ~ 0.7-0.8, which can give currents as high as those with R ~ 0.2. However, as Fig. 5 also shows, the low – R portion of the operating curves will give currents which are independent of the gap/diameter ratio (this is in clear opposition to the 1-D prediction of Equation 13). Thus, the current, in this region, is independent of both d and D s . This opens up a convenient design avenue using low R values: Fix the smallest distance d compatible with good dimensional control, then reduce the diameter D s to the smallest practicable size (perhaps 0.5 mm). This will 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 8 of 25 allow more holes per unit area (if the hole spacing varies in proportion to their size), hence more current per unit grid area. Due to this circumstance, Ref. 7 recommends low R designs. (5) The perveance generally increases as D a /D s increases, with the exception of cases with R near unity, when an intermediate as D/D 0.8≈ is optimum. (6) Increasing V D /V T , which increases the plasma density, appears to flatten the contour of the hole sheath (8) , which reduces the focusing of the beam. This results in direct impingement on the screen, and, in turn, forces a reduction of the beam current. Some appreciation for the degree to which Child-Langmuir’s law departs from the observed current extraction capacity of real devices can be obtained from the data for the 30 cm. J-series thruster, as reported for example in Ref. (9). In this case, we have d=0.5 mm, t a =t s =0.38 mm, D s =1.9 mm, D a =1.14 mm, and a total of 14860 holes. We will refer to data in X e , for V NET /V T =0.7 and V D =31.2 Volts. V Beam =1200 v. Table III of Ref. (9) then gives a beam current J B =4.06 A. The correlation given in the same reference for various propellants is () 2.2 T B 17.5 V 1000 J= +-25% Mα (15) where αis a double-ion correction factor, given as 0.934 for this case, and M is the molecular mass in a.m.u.. The power of 2.2 instead of 1.5 for the effect of extraction voltage is to be noticed. This correlation yields for our case I B =5.4 A, on the outer boundary of the error band. For these data, if we apply the Child-Langmuir law (Equation 13) to each hole (diameter D s ), and use directly the spacing d=0.5 mm, we obtain a hole current of 3.83 mA, or, in total I B =57.1 A, i.e., 14 times too high. An approximate 3-D correction (Ref.’s 10a, b) is to replace d 2 by 22 ss (d + t ) + D /4 in Child-Langmuir’s equation. This gives now I B =8.4 A, still twice the experimental value. It is of interest to see how well the data of Rovang and Wilbur (Ref. 7) can be extrapolated to the J- thruster. We first use the data in Fig. 6a of Ref. (7), which are for D s =2mm., R=0.8 D a /D s =0.66 (lowest value measured), and V D /V T =0.1. Corrections for the actual D a /D s =0.6 and V D /V T =0.018 can be approximated from Fig.’s 5 and (6a) of the same reference. The effects of R=0.7 instead of 0.8, as well as of the slightly different D s , should be small, according to Ref. 7. We obtain in this manner I B =5.2 A., which is indeed as accurate as the correlation of Equation (15). Additional data on grid perveance are shown and assessed Ref. (10c) in the context of ion engine scaling. To complete this discussion, two limiting conditions should be mentioned here: (a) Direct ion impingement on screen: At low beam current, the screen collects a very small stray current, which is due to charge-exchange ion-neutral collisions in the accelerating gap: after one such collision, the newly formed low speed ion is easily accelerated into the screen. The screen current takes, however, a strong upwards swing when the beam current increases beyond some well defined limit. This is due to interception of the beam edges, and, 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 9 of 25 since the high energy ions are very effective sputtering agents, results in a very destructive mode of operation. All the perveance values reported in Ref. (7), for instance, are impingement-limited, i.e., correspond to the highest current prior to onset of direct impingement. (b) Electron back-streaming: For R values near unity, the barrier offered by the accelerator negative potential to the neutralizer electrons becomes weak, and beyond some threshold value of R, electrons return up the accelerator potential to the chamber. This results in screen damage, space charge distortion, and shorting of the neutralizer supply. Kaufman (10a) gave the theoretical estimate max a aa 0.2 R=1- tle exp DD ?? ?? ?? ?? ?? ?? (16) which was confirmed experimentally in Ref. 7, except that it was found to be a somewhat conservative estimate. 4 Ion Production 4.1 Physical Process in Electron Bombardment Ionization Chambers In an electron bombardment ionizer, the neutral gas is partially ionized by an auxiliary DC discharge between conveniently located electrodes. Of these, the anode is the same anode which receives the electrons from the ionization process (see Fig. 1). The primary electrons responsible for the ionization of the neutral gas are generated at a separate cathode, which can be a simple heated tungsten filament, or for longer endurance, a hollow cathode. The cathode-anode potential difference V D is selected in the vicinity of the peak in the ionization cross-section of the propellant gas, which occurs roughly between three and four times the ionization energy (i.e., around 30-50 Volts for most gases). The structure of the potential distribution in the discharge is very unsymmetrical: most of the potential difference V D occurs in a thin sheath near the cathode, and the body of the plasma is nearly equipotential, at a level slightly above that of the anode (typically the anode current density is below the electron saturation level, and so an electron-retarding voltage drop develops). Ionization is due both to the nearly mono-energetic primary electrons (with energies of the order of eV D ) and to the thermalized secondary electrons themselves. These have typically temperatures (T m ) of a few eV, so that only the high energy tail of the Maxwellian energy distribution is above the ionization energy and can contribute to the process, but their number density greatly exceeds that of the primaries, and both contributions are, in fact, of the same order. It is therefore desirable to maximize the residence time of both types of electrons in the chamber before they are eventually evacuated by the anode. This is achieved by means of a suitable distribution of confining magnetic fields. Fig.’s 6 (a), (b) and (c) show three types of magnetic configurations, of which only the last two are today of practical importance. These will be discussed in more detail later, but we note here that magnetic field strengths can vary from about 10 to 1000 Guass, depending on type and location. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 10 of 25 The ions generated in the active part of the discharge chamber are only weakly affected by the magnetic field, and so they wander at random, colliding rarely with neutral atoms before reaching any of the wall surfaces. Since these walls (or the cathode itself) are all negative with respect to the plasma, the ions penetrate the negative sheaths at a velocity of the order of the so-called Bohm velocity, or isothermal ambipolar speed of sound, e B i KT V= m (17) and are then further accelerated in the sheath proper. Those that happen to arrive at one of the extractor hole sheaths become thus the ion beam, but those arriving at solid walls collide with them at an energy corresponding to that of the sheath, which often leads to sputtering, and are neutralized. They then return as neutrals to the plasma, where they are again subject to ionization or excitation processes. 4.2 Nature of the Losses Since electron-ion recombination, even if it did happen in the beam, would contribute nothing to the engine thrust, the ionization energy per beam ion is the minimum energy expenditure required. This would amount to 10.5 eV in Hg, 15.8 in Argon or 12.1 eV in Xenon. In reality the energy loss per beam ion ranges from about 100 to 400 or more eV. The sources of the additional losses can be identified from the description of processes in the previous section: (a) Some primary electrons reach the anode and surrender their high energy. (b) The thermal electrons arrive at the anode with energies of a few eV. (c) Ions that fall to cathode-potential surfaces lose their kinetic energy to them. In addition, they also lose the energy spent in their ionization. (d) Metastable excited atoms surrender the excitation energy upon wall collision. (e) Short-lived excited atoms emit radiation, which is mostly lost directly. Of a different nature are the energy losses required to heat the cathode emitters or, in the case of Hg, the vaporizers and chamber walls. Finally, not all the injected gas leaves in the form of ions (only a fraction η u , called the “utilization factor” does). At the best conditions, η u ranges from 75 to 95%. It is of interest to examine the relationship between η u and the degree of ionization, α, in the chamber plasma. If n e is the electron (and ion) density, the flux of ions being extracted is approximately () 1 - 2 2 ieBs = n v × e ions/m /secΓφ (18) 1 - 2 s include e in φ where v B is as in Equation (17) and φ s is the open area fraction of the screen grid. The flux of neutrals through the same overall area is n nn c =n 4 Γφ (19) 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 11 of 25 where 12 n i 8KTg c= m ?? ?? π ?? is the mean thermal speed of the heavy particles, and φ is an open-area fraction for the combination of grids, reflecting the fact that neutrals, unlike ions, are not focused into the accelerator grid holes, if φ s and φ a are the geometrical open-area fractions of the screen and accelerator grids, we have sa 111 =+-1 φφφ (20) The ratio of (18) and (19) gives, after rearrangement, g u eu s T = 1- T 1- 2 ηαφ αη φπ (21) where () ee n =n n +nα and ( ) uiin =+ηΓΓΓ. As an illustration (using once again the J-series Xenon data of Ref. 9), if φ s =0.67, φ a =0.24 (hence φ=0.215), and if we take T e =70,000 K=6.03 eV, Tg=400 K (wall temperature), and u 0.8η = (a common operating point) we obtain =0.0372α , i.e., a 3.7% ion density fraction gurantees an 80% ion flux fraction. 4.3 Electron Diffusion and Confinement For the same example, using B i 2 J = eD 4 Γ π , with J B =4.06 A. and D=28.3 cm, Equation (18) can be used to calculate 17 3 e n =2.85 10 m ? × , and hence, from α, 18 3 n n =7.38 10 m ? × . If we estimate the effective collision cross-section between ions or electrons and neutrals at Q in =10 A 2 =10 -19 m 2 , the mean free path for a charged particle would then be () i,e n in =1 nQλ =1.36 m, so that collisions with neutrals are indeed infrequent. The e-e or e-i cross-section is approximately () -17 2 18 2 ei Q = 6.5×10 E eV =1.79×10 m ? , so that the e-i mean free path is in this case 1.96 m. and charged-charged particle collisions are about equally infrequent. The gyro radius (Larmor radius) for an electron in a magnetic field B is L mv r= eB (22) For a 6 eV electron in a field of B=100 Gauss=0.01 Tesla, this is about 1 mm. Primary electrons, with energies of 30-50 eV have gyro radii of 2-3 mm in the same field. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 12 of 25 With a Samarium-Cobalt magnet, the B level could reach ~0.2-0.4 Tesla near the cusp. The ion Larmor radius is then comparable to the cusp size, and ions are also confined partially. Example: ie B=0.2 T, v 250ms, X :null i L 0.13×250 r = = 0.0017 m =1.7 mm 95000×0.2 The picture that emerges from these figures is that of the electrons being very tightly guided by the magnetic field lines, but with very large mobility along such lines, except at their ends, where extractor or cathodic sheaths reflect the electrons back along their guiding magnetic line. Lines terminating at the anode can be “drained”, with only low energy electrons being typically reflected. As a result, one can speak about a “virtual anode” formed by the outermost magnetic surface which intersects the anode (see Figure 6(b)), since electrons reaching such a surface have a high probability of anode capture. Similarly, there are “critical field lines” (Figure 6(b)) which bound the region directly accessible to cathodic (primary) electrons. Secondary electrons are generated in the shaded area of Figure 6(b) by primaries diffusing out of the confines of this directly accessed region, and then, both, primaries and secondaries must diffuse further to the virtual anode surface prior to collection. Similar concepts apply, to cusped magnetic configurations, such as that of Figure 6(c). Here, it is clear that only the areas very near the cusp lines can serve as active anodes, and the “virtual anode” has a complex, scalloped configuration. Diffusion across the magnetic lines would be extremely slow if it were controlled by the classical collisional mechanism. For 6 eV electrons, in a 100 Gauss field, we found a ratio β ≈ 1000 between the m.f.p. and the Larmor radius. The scalar diffusivity e o,classical e 1 D c 3 ≈ λ is about 52 5×10 m /sec, and the cross-field diffusivity would then be o,class class 2 D D β = , i.e., 2 clas. D0.5 m/sec≈ . An electron would then diffuse through l=1 cm in a time 2-4 t l 2D 10 sec≈≈ . For comparison, the time between ionizing collisions for a primary electron () -202 6 19-3 ioniz n Q10 m, v6×10msec,10 m≈≈ ≈is ( ) 1 -6 ioniz ioniz n tQ n v1.5×10sec ? ≈≈ , and so this would represent a very good confinement indeed. However, experiments indicate that the microturbulence which accompanies the discharge has the effect of greatly increasing the rate of electron scattering, and hence the cross-field diffusion. Bohm (11) first proposed the widely used empirical formula e KT D 16eB ⊥ = (23) which amounts to replacing the mean free path by roughly 1/16 (more exactly, 128 =13.5 times 3π ) of the Larmor radius. The validity of (23) was confirmed for ion engine conditions in Ref.’s (12) and (13), although Ref. (13) found that best results can be obtained if an additional factor of 0.44 is included in Equation (23). Using 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 13 of 25 (23) for 6 eV electrons and B=100 Gauss gives 2 m D=40 sec ⊥ , i.e., 80 times the classical value. The diffusion time through 1 cm is then about 10 -6 sec, which is of the same order as the ionization time. As the contours in Figure 6(c) show, the 100 Gauss level is exceeded in the outer parts of the chamber in cusped designs (levels as high as 3000 Gauss are reached on the surface of the Sa-Co permanent magnets used). Thus, electrons may diffuse rapidly throughout the “ion producing core” of the discharge, but their diffusion is considerably slowed down near the outer walls, which leads to efficient ionizer operation. 4.4 Particle Production Rates The Ion production rate per unit volume can be expressed as a sum over the various ionizable excited states, involving rate coefficients for both primary and thermalized electrons. This is discussed, for instance in Ref. (14). The result is mi n υ , where the ionization frequency i υ is () () exc.states, j iiP ijjPjm m n nPE+QT n ?? υ= ?? ?? ∑ (24) Here n m and n P are the densities of thermalized (Maxwellian) and primary electrons, respectively, and ii jj P, Q are rate coefficients for ionization from the j th state by, respectively, primary and maxwellian electrons. Expressions for these factors are given in Ref. (14), in terms of the various cross-sections. For overall modeling purposes, it is convenient to define an “ion production current” by PmiP J=en Vυ (25) where V P is the active ion production volume. Similar atomic calculations can be made for the production rates of each of the excited states, and also of multiple ions (14),(12) . Ref. (12) gives a predictive correlation for the double-ion current in various propellants, and compares to data. Both data and theory indicate that the ratio r=J ++ /J + of the fluxes of double and single ions is a function of only the propellant utilization efficiency u η for a given propellant. Additional data, for the ring-cusp geometry first introduced by Sovey (15) are given in Figure 7 (from Ref. (9)), which shows that all noble gases fall nearly on the same curve, with mercury having a higher double-ion fraction. The values of u η used in Figure 7 are based on the total measured beam current B++ u TOT TOT JJ+J == JJ η TOT i e J=m m ?? ?? ?? i and may exceed unity. The actual flux ratio between charged and uncharged particles is 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 14 of 25 +++ +++ u TOT TOT 1 J+ J n+n 2 == J n η ii i so that a correction factor should be applied to the current-based utilization factor, given by r 1+ 2 = 1+r β (26) Similarly, the presence of the double ions reduces the thrust by a factor (9) : r 1+ 2 = 1+r α (27) We conclude this section with charge flux balances for the casing-cathode-screen grid (which are assumed to be all interconnected and at cathode potential) and for the anode. This will be useful for modeling purposes in the next section. The total ion production rate in the plasma was called J P (Equation 25), and an electron current of equal magnitude is also produced, which must be evacuated by the anode. In addition, the anode must also evacuate the electron current J E emitted by the cathode. The two together make up the “discharge current” DPE J=J+J (28) The discharge power supply, connected between anode and cathode at a voltage V D must handle this current J D , and hence consumes a power J D V D . Of the ions produced (J P ) a current J B is extracted into the beam, while a small current J acc is intercepted by the accelerator grid. The balance is the stray ion current that goes to the cathode-potential surfaces (cathode-screen-casing): CPBac J=J-J-J (29) Electrons are returned to the cathode-potential structure by the discharge power supply, at the rate J D . Electrons are also removed from it by the cathode itself (J E ), by the neutralizer power supply, which must send to the neutralizer an electron current equal to the ion beam current J B , and, to a small extent, by the accelerator power supply to neutralize the intercepted ion current J acc . Setting the total rate of positive charge gain to zero, ( ) P B acc D E B acc J-J-J -J+J+J+J =0 which agrees with (28). 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 15 of 25 4.5 Lumped Parameter Performance Model For design purposes, as well as for characterization of existing engines, it is useful to develop aggregate physical models of the performance of ionization chambers, where temperatures, densities, etc., are either assumed to be constant or are given their average value. 5 Propellant Selection As implied by many points of the preceding discussion, the ideal propellant for an ion thruster would have a high molecular mass, low first ionization potential and high maximum cross-section for 1 st ionization (but the reverse properties for 2 nd and higher levels of ionization), and it should also be easy to store and handle and be benign in terms of materials compatibility and human safety. Mercury has many of these attributes, except for its low 2 nd ionization threshold and its toxicity and chemical aggressivity in general. The same can be said to a greater extent about Cesium, which, because of its handling difficulty, has been only used in contact ionization thrusters (3) . Concerns about spacecraft contamination by condensation of plume-derived atoms on external surfaces has led to a shift away from Hg (and any other liquid metals) and towards alternative, safer propellants. Molecular gases tend to be rejected because of the multiplicity of ionic and excited species their discharges can generate, and thus the noble gases are the natural choice, especially Xenon, which is the heaviest (and easiest to ionize) of the naturally occurring noble gases. Argon has also been considered due to its low cost. Table 2.1 gives a compilation of physical and operational properties of these propellants, with some comments as to their impact on thruster operation. Much of the material comes from the excellent discussions in Refs. (30) and (9). The overall performance with Xe is very similar to that with Hg, although the efficiency at a given thrust level is slightly better in Hg (30) . The same was also found in Ref. (9), which also showed that the efficiency correlated uniquely with the product of the specific impulse, the square root of the molecular mass and the double-ion factor α (Equation 27), although this depends to some extent upon the choice of other parameters. Thus, the simplified performance modeling based upon the “loss velocity” (lecture 2) appears justified. Table 2.1 SPECIES PROPERTY Hg A Xe IMPACT 1 st ionization potential (eV) 10.43 15.8 12.13 Hg best, lower ionization losses 2 nd ionization potential (eV) 29.2 27.6 33.3 Higher 2 nd leads to fewer 2 nd ions 3 rd ionization potential (eV) 63.4 45 65.5 High enough in all 1 st excitation potential (eV) 4.8 11.7 8.39 More radiation from Hg 2 nd excitation potential (eV) 4.6 (Metast.) 13.2 8.28 (Metast.) More effective Hollow Cathodes in Hg 3 rd excitation potential (eV) 5.4 (Metast.) 14.1 9.4 (Metast.) More effective Hollow Cathodes in Hg Atomic Mass (AmU) 200.59 39.9 131.3 Lowest acceleration voltage for an Isp in Hg. Lowest current for a given thrust in Hg. Boiling Point ( o C) 356.58 -189.2 -107 +/- 3 Only Hg storable as liquid Storage Condition Liquid 3 = 13.6 g/cmρ Compr. Gas or Cryogenic Liq. Near Critical 3 =0.5 g/cmρ at 35 o c, 60 Bar Hg and Xe both compact tanks. A bulkier. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 16 of 25 Chemical Activity (Toxicity) High None A, Xe safer. Cu, Al, common brazes can be used. Cost Moderate Low High May be issue in large systems (Relative) Sputtering yield 1 4 2 Higher erosion in A, Xe, despite fewer 2 nd ions. Propellant Flow Control Simple, through vaporizer T-cont. More Complex through plenum, control or servo-needle valve Heavier propellant system in A, Xe (despite elimination of heaters) Power Processing No need for heaters on fuel lines, vaporizer Higher reliability with A, Xe. Also, some loss reductions. Chapter 2 References (1) Stuhlinger, E. Ion Propulsion for Space Flight McGraw-Hill Book Co., New York, NY, 1964. (2) Cybulski, R.J. et al. “Results from SERT-I Ion Rocket Test”, NASA Tech. Note D-2718, 1965. (3) R. L. Jahn “Physics of Electric Propulsion” McGraw-Hill, 1968, Ch. 7. (4) Groh, K.H., Loeb, H.W., Mueller, J., Schmidt, W., and Schuetz, B., “RIT-35 RT-Ion Thruster-Design and Performance”. Paper AIAA-87-1033, 19 th Int. Electric Propulsion Conference, Colorado Springs, May 1987. (5) Petagna, C., Van Rohden, H., Bartoli, C. and Valentian, D., “Field Emmission Electric Propulsion (FEEP): Experimental Investigation of Continuous and Pulsed Modes of Operation”. Proc of the 20 th International Electrical Propulsion Conference, paper 88-127. Garmisch-Partenkirchen, W. Germany, Oct.1988. (6) Beattie, J.R., Matossian, J.N. and Robson, R.R. “Status of Xenon Ion Propulsion Technology”, Paper AIAA ’87, 19 th International Electrical Propulsion Conference, Colorado Springs, May 1987. (7) Rovang, D.C. and Wilbur, P.J. “Ion Extraction Capabilities of Two-Grid Accelerator Systems”. J. Propulsion, Vol. 1, No. 3, pp. 172-179 (1985). (8) Kaufmann, H.R. “Ion Source Design for Industrial Applications” AIAA J., Vol. 20, June 1982, pp. 745-760. (9) Rawlin, V.K. “Operation of the J-Series Thruster Using Inert Gas”. NASA TM- 82977. Also AIAA 82-1929 (1982). (10a) Kaufman, H.R. “Accelerator System Solution for Broad-Beam Ion Sources”, AIAA J., Vol. 15, July 1977, pp. 1025-1034. (10b) Wilbur, P.J., Beattie, J.R. and Hyman, J. “An Approach to the Parametric Design of Ion Thrusters” Proc. of the 20 th Int. Electrical Propulsion Conference, Garmisch-Partenkirchen, W. Germany, Oct. 1988. Paper 88-080. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 17 of 25 (10c) Martin, A.R., Bond, A., Lavender, K.E., Harvey, M.S. and Lathem, P.M. “A UK Large Diameter ion Thruster for Primary Propulsion”. 19 th Int. Electrical Propulsion Conference, Colorado Springs, May 1987. Paper AIAA-87-1031. (11) Bohm, D. “Qualitative Description of the Arc Plasma in a Magnetic Field”. In The Characteristics of Electrical Discharges in Magnetic Fields. A. Guthrie and R.K. Wakerling, editors. McGraw-Hill, NY 1949. (12) Kaufman, H.R. and Robinson, R.S. “Plasma Processes in Inert-Gas Thrusters”. J. Spacecraft, Vol. 18, no. 5, Sept. 1981, pp. 470-476. (13) J.R. Brophy and P.J. Wilbur, “Electron Diffusion Through the Baffle Aperture of a Hollow Cathode Thruster”. Progress in Aeronautics and Astronautics, Vol. 79, pp. 159-172. Also AIAA Paper 79-2060 (1979). (14) Longhurst, G.R and Wilbur, P.J. “Plasma Properties and Performance Prediction for Mercury Ion Thrusters” AIAA Paper 79-2054, Princeton, NJ, 1979. (15) Sovey, J.S., “Improved Ion Containment Using a Ring-Cusp Ion Thruster”, AIAA Paper 82-1928, Nov. 1982. (16) Brophy, J.R. and Wilbur, P.J. “Simple Performance Model for Ring and Line Cusp Ion Thrusters”, AIAA Journal, Vol. 23, Nov. 1985, pp. 1731-1736. (17) Brophy, J.R. and Wilbur, P.J. “An Experimental Study of Cusped Magnetic Field Discharge Chambers”, AIAA J., Vol. 24, Jan. 1986, pp. 21-26. (18) Wilbur, P.J. and Brophy, J.R., “The Effect of Discharge Chamber Wall Temperature on Ion Thruster Performance”. AIAA Journal, Vol. 24, No. 2, Feb. 1986, pp. 278-283. (19) Wilbur, P.J., Beattie, J.R. and Hyman, J. Jr. “An Approach to the Parametric Design of Ion Thrusters”. 20 th International Conference on Electric Propulsion, Paper IEDC 88-080. Garmisch-Partenkirchen, W. Geramany, 1988. (20) Matossian, J.N. and Beattie, J.R. “Plasma Properties in Electron Bombardment Ion Thrusters”. Paper AIAA-87-1076, Colorado Springs. CO, 1987. (21) Hyatt, J.M. and Wilbur, P.J. “Ring Cusp Discharge Chamber Performance Optimization”. Paper AIAA-85-2077. Alexandria, VA, 1985. (22) Collett, C.R. and Poeschel, R.L., “A 10,000 hr. Endurance Test of a 700- Series 30-cm Engineering Model Thruster”. AIAA Paper 76-1019, 1976. (23) Bechtel, R.T., Trump, G.E. and James, E.L. “Results of the Mission”Profile Life Test, AIAA Paper 82-1905, 1982. (24) Rock, B.A., Mantenieks, M.A. and Parsons, M.L., “Rapid Evaluation of Ion Thruster Lifetime Using Optical Emission Spectroscopy”, NASA TM 87103, 1985. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 18 of 25 (25) Beattie, J.R. “A Model for Predicting the Wearout Lifetime of the LeRC/Hughes 30-cm Mercury Ion Thruster”, AIAA Paper 79-2079, 1979. (26) Mantenieks, M.A. and Rawlin, V.K., “Sputtering in Mercury Ion Thrusters”. AIAA Paper 79-2061, Oct. 1979. (27) Rawlin, V.K. and Mantenieks, M.A., “Effect of Facility Background Gases on Internal Erosion of the 30-cm Hg Ion Thruster”. NASA TM-73803, 1978. (28) Garner, C.E., Brophy, J.R. and Aston, G. “The Effects of Gas Mixtures on Ion Engine Erosion and Performance”. AIAA Paper 87-1080, Colorado Springs, 1987. (29) Wilbur, P.J., “A Model for Nitrogen Chemisorption in Ion Thrusters”. AIAA Paper 79-2062, Princeton, NJ, 1979. Also in Progress in Aeronautics and Astronautics, Vol. 79. (30) Fearn, D.G. “Factors Influencing the Integration of the UK-10 Ion Thruster System with a Spacecraft”. AIAA Paper 87-1004, Colorado Springs, CO, 1987. (31) Beattie, J.R. and Kami, S. “Advanced Technology 30 cm. Diameter Mercury Ion Thruster”. AIAA Paper 82-1910, New Orleans, 1982. 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 19 of 25 Figure 1 Simplified Schematic of Ion Transfer Figure 2 The Two-grid Acceleration System – see Reference 7. Figure 3 Idealized One-Dimensional Extraction and Acceleration System Figure 4 Accel-Decel Geometry and Potential Profile Figure 5 Effect of grid separation on impingement-limited current parameter – see Reference 7. Figure 6(a) Early chamber design, with axial magnetic field and simple cathode Figure 6(b) Divergent-Field Chamber with magnetically shielded Hollow Cathode Figure 6(c) Ring-Cusp Chamber, with body acting as anode. Figure 7 Doubly to singly charged ion current ratios as functions of measured discharge propellant efficiencies 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 20 of 25 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 21 of 25 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 22 of 25 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 23 of 25 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 24 of 25 16.522, Space Propulsion Lecture 13-14 Prof. Manuel Martinez-Sanchez Page 25 of 25