16.522, Space Propulsion Prof. Manuel martinez-Sanchez Lecture 13-14: Electrostatic Thrusters Outline No 1 Introduction 2 Principles of Operation..... 3 Ion Extraction and Acceleration 4 Ion production 4.1 Physical Processes in Electron Bombardment ionization chambers 9 4.2 Nature of the losses 4,3 Electron diffusion and confinement 11 4. 4 Particle production rates 13 4.5 Lumped Parameter Performance Model 15 Propellant Selection References 16 16.522, Space P pessan Lecture 13-14 Prof. Manuel martinez Page 1 of 25
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
Lecture 13-14 Electrostatic Thrusters 1 Introduction Electrostatic thrusters c ion engines")are the best developed type of electric propulsion device, dating in conception to the 50's, )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(),(3), and evolved through progressive refinements of various types of ion beam sources used in Physics laboratories, the and long life for these sources to be used in space. Of the various configurations improvements being essentially dictated by the needs for high efficiency, low mas discussed for example in Ref. 3(ca. 1973), only the electron bombardment noble gas type, plus(in Europe) the radio-frequency ionized thruster 4and(in Japan)th 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 by permanent magnets, and with hollow cathode plasma bridges used as cathode ed shallow geometrics using sharply nonuniform magnetic field configurations, prod 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 o. 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 =c E, where e is the strength of the field(volts/m)and E, the permittivity of vacuum E,=8.85x10-12 Farad ypical maximum fields, as limited by vacuum breakdown or shorting due to imperfections are of the order of 10 V/m, yielding maximum force densities of roughly 5N/m2=5x105 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 N/m in self-magnetic devices such as MPD thrusters, or to the typical gas pressures of 10-10'N/m in chemical rockets. Simplicity and efficiency must therefore compensate for this disadvantage. 16.522, Space Propulsion Lecture 13-14 Page 2 of 25
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 1 2 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 106 V/m, yielding maximum force densities of roughly 2 -5 5 N m = 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 104 N/m2 in self-magnetic devices such as MPD thrusters, or to the typical gas pressures of 106 -107 N/m2 in chemical rockets. Simplicity and efficiency must therefore compensate for this disadvantage
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 va 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 tive 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 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 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 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 Page 3 of 25
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 Va 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
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 grid, in order to prevent backflow of electrons from the neutralizer through the or capacity is adequate this potential is seen to be set above that of the accelera accelerating system. In addition, by making the total voltage", VI, larger than the Net voltage",VN, the ion extraction capacity of the system is increased with no on lerated a third grid ( decelerator grid") is added to more closely define and control VN, 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 s 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)Poissons equation in the gap: dφ b) Ion continuity en v,=]= constant (2) c) Electrostatic ion free-fall: 2e(- Combining these equations, we obtain a 2n order, nonlinear differential equation for 9(x). The boundary conditions are 中(0)=0,中(X=d)= (4) In addition, we also impose that the field must be zero at screen grid This is because(provided the ion source produces ions at a sufficient rate) 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 automaticall extracting the highest current density possible and are said to be space charge limited 16.522, Space P pessan Lecture 13-14 Prof. Manuel martinez Page 4 of 25
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”, VT, larger than the “Net voltage”, VN, the ion extraction capacity of the system is increased with no change (if VN 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 VN, 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 2 0 d en = - dx φ ε (1) b) Ion continuity en v j = constant i i = (2) c) Electrostatic ion free-fall: ( ) i i 2e - v = m φ (3) Combining these equations, we obtain a 2nd order, nonlinear differential equation for φ (x ). The boundary conditions are () ( ) 0 = 0, x = d = -Va φ φ (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
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 4 ana aso 4 Va x d Equation(8)in particular shows that the field is zero(as imposed )at x=0, and 3 d 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 A=2(3d丿=9na 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 m and the ion exit velocity is F mc=e A Using Child-Langmuir's law for j(Equation 6), this reduces indeed to Equation(9) For a given propellant(mi) and specific impulse(c/g, the voltage to apply to the accelerator is fixed 16.522, Space P pessan Lecture 13-14 Prof. Manuel martinez Page 5 of 25
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 1 2 3 2 0 2 i 4 2 e Va j = 9 m d ⎛ ⎞ ε ⎜ ⎟ ⎝ ⎠ (6) and also ( ) 4 3 x x = -Va d ⎛ ⎞ φ ⎜ ⎟ ⎝ ⎠ (7) ( ) 1 3 4 Va x Ε x =- 3d d ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (8) Equation (8) in particular shows that the field is zero (as imposed) at x=0, and is 4 Va - 3 d 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 F 1 4 Va 8 Va = A 2 3d 9 d 0 0 ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ε ε (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 m = j mi A e i , and the ion exit velocity is i 2eVa c = m , giving i i F m 2eVa m 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 (mi) and specific impulse (c/g), the voltage to apply to the accelerator is fixed: 2 m ci Va = 2e (10)