ISSN 1063780X, Plasma Physics Reports, 2009, Vol. 35, No. 9, pp. 754–767. © Pleiades Publishing, Ltd., 2009. Original Russian Text © V.I. Minakov, 2009, published in Fizika Plazmy, 2009, Vol. 35, No. 9, pp. 819–833.
PLASMA DYNAMICS
Plasma ElectronEmitting Source in a LowPressure Beam−Plasma Discharge in a Stationary Plasma Thruster V. I. Minakov Moscow State Institute of Aviation, Volokolamskoe sh. 4, Moscow, 125080 Russia Received July 23, 2008; in final form, March 17, 2009
Abstract—A new type of plasma electronemitting source capable of increasing the temperature of plasma electrons behind the edge of a stationary plasma thruster (SPT) to 7−15 eV has been developed and investi gated experimentally. For the same parameters of the main discharge, the thrust, the thrust efficiency, the mass use factor, and the lifetime of the “SPT anode unit−plasma electronemitting source” assembly are found to increase substantially as compared to a thruster equipped with a conventional cathode compensator. Simultaneously, the neutral particle pressure required for the existence of selfconsistent distributions of the electric field and charged particle density in the drift space of the neutralized ion beam decreases appreciably. It is shown that the volume of the region in which primary slow ions are produced increases with increasing ionization frequency. Three additional channels for discharge control are implemented. The ranges in which the discharge parameters can be controlled are extended. PACS numbers: 52.40.Mj, 52.80.Sm DOI: 10.1134/S1063780X09090049
1. INTRODUCTION Progress in the development of electrostatic thrust ers (ESTs) [1], such as the ion plasma thruster (IPT) and plasma Hall thrusters—a thruster with an anode layer (TAL) and a stationary plasma thruster (SPT) [2], is based on studies of physical phenomena occur ring in a stationary lowpressure beam−plasma dis charge (BPD). Lowpressure BPD is also used in ion sources [3] and plasma optical systems [4]. Experimental data [5] show that the density of neu trals is more than one order of magnitude higher than that of ions even in the SPT acceleration region. In [6], a high density of slow ions in the “shadow” near the axial magnetic conductor was noticed. These observations indicate that the degree of ionization of the intense neutralized ion beam is low (β = ni/(ni+na) ~ 0.02−0.1), which limits the characteristics of an SPT equipped with a conventional cathode compensator. On the other hand, results of calculations [7, 8] dem onstrate that xenon atoms are burnt out almost com pletely over the acceleration length—an argument in favor of the model in which the ion beam is considered in the approximation of a fully ionized plasma [9]. Thus, there is an obvious discrepancy between the experimental data and the existing theoretical models. The new method for arrangement of a lowpressure EST discharge considered in the next section allows one to find the reason for such a discrepancy and par tially eliminate the constraints imposed on the improvement of the thruster characteristics. The practical goal of the present work is to increase the mass use factor of the working medium (xenon) by
increasing the electron temperature in the ion beam drift space, just behind the EST edge. The problem is solved using a newly developed plasma electronemit ting source (PEES) [10, 11]. 2. ARGUMENTS IN FAVOR OF CHANGING THE ARRANGEMENT OF DISCHARGE IN AN EST To a large extent, the EST quality is determined by the mass use factor ηu. The possibility of increasing ηu by using conventional methods, e.g., by increasing power deposited in the plasma of the acceleration channel of the “SPT anode unit−conventional cath ode compensator” assembly [9], is exhausted almost completely. Attempts to increase power deposition above a certain critical level lead to the development of crisis phenomena.1 An increase in ηu at a fixed mass flow rate is related to a decrease in the density of neu trals in both the region in which the ion flux forms and accelerates and the space in which the plasma beam produced by the thruster propagates. It can be shown [12] that, at high densities of fast ions that are achieved in regimes in which the input power is close to its critical value, the degree of ioniza tion of the ion beam behind the edge of the accelera 1 Crisis
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phenomena manifest themselves in a decrease in the thrust efficiency due to increased power losses, an increase in the fluctuation level, the development of discharge instabilities leading to rearrangement of the discharge, and an increase in the erosion rate of the channel walls. These phenomena are typical of the SPT, TAL, and some types of IPT.
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tion channel is always limited from above. Such limi tations are caused by the necessity of satisfying condi tions for plasma existence behind the EST edge [12], specifically, the plasma quasineutrality condition (see [3], p. 92) and conditions for the establishment of self consistent steadystate distributions of the electric potential and charged particle densities (see [3], p. 273). In what follows, these conditions will be referred to as conditions 1*. Stable operation of a lowpressure discharge can be provided only if the density of neutrals in the critical region2 of an EST equipped with a conventional cath ode compensator is at least one order of magnitude higher than the density of charged particles. The max imum achievable ratio between the densities of charged and neutral particles in this region is deter mined by the mechanisms and conditions of ioniza tion of neutral particles and the kind of working medium. In the plasma just behind the EST edge, as in any plasma with charged particle densities of ne ≈ ni > 106 cm−3, an electron temperature of Te = 1−10 eV, and a characteristic size of L ~ 1−10 cm, ambipolar fluxes of electrons and slow ions arise. In an axially symmetric configuration, these fluxes are mainly accelerated in the radial direction under the action of the selfconsistent electric field created by the gradient of electron pressure. The velocities of slow ions are one to two orders of magnitude lower than those of fast ions. The fluxes of fast ions are primarily oriented along the longitudinal axis, in the vicinity of which they are localized. The momentum of fast ions is fairly large, so that the weak selfconsistent field insignifi cantly affects their spatial distribution. In this sense, fast ions, unlike slow ones, do not directly participate in the formation of selfconsistent distributions of the electric field and charged particle densities. At the same time, the contribution of fast ions to the total positive space charge created by both fast and slow ions, is proportional to the mass use factor ηu. The contribution of slow ions depends on ηu in a more complicated manner and decreases faster than 1 − ηu with increasing ηu. An increase in the discharge power leads to an increase in the mass use factor; in this case, the space charge of fast ions increases, while that of slow ions decreases. As ηu increases, the electric field 2 The
critical region is a region behind the thruster edge in which the density of neutral particles cannot be lower than a certain threshold value, below which conditions 1* are violated, which leads to the development of crisis phenomena. In the ion beam, the electron temperature Te and the densities of neutral and charged particles, na and ne, decrease with increasing distance |r| from the thruster edge, each according to its own law. The ion ization rate ϕ(r) = ϕ(Ee, na, ne), which determines the density of slow ions, decreases with increasing |r| no less slowly than na. Therefore, if the discharge parameters are changed in such a way that only the density of neutral particles decreases behind the thruster edge, there will always be such r at which conditions 1* cease to be satisfied. PLASMA PHYSICS REPORTS
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produced by the total space charge of ions and elec trons should also remain selfconsistent even if the spatial distribution of the major fraction of ions (i.e., the distribution of fast ions) does not depend on this field. The ratio between the space charges of fast and slow ions increases with increasing power deposited in the discharge. When this ratio reaches the value at which conditions 1* are violated, crisis phenomena develop. Crisis phenomena will only not develop if the space charge density of slow ions creating selfconsis tent distributions of the electric field and charged par ticle densities is comparable with or larger than the space charge density of fast ions. In the limiting case in which the mass use factor reaches its maximum value and, therefore, the densities of fast and slow ions become comparable, the total flux of slow ions deter mined by the ratio between the characteristic veloci ties of fast and slow ions amounts to ~2−5% of the xenon flux supplied to the thruster. When the effi ciency of formation of primary slow ions is low, which is typical of SPTs equipped with conventional cathode compensators, the total flux of neutrals leaving the accelerator is always much higher than the flux of slow ions and reaches ~20% of the xenon flow rate. From a functional standpoint, the ion beam poten tial just behind the EST edge, which is mainly deter mined by the operating regime of the cathode com pensator or cathode neutralizer, is maintained by the plasma consisting of electrons and slow ions. For Hall thrusters, this plasma may be considered as one of the “capacitor plates” (the other “plate” being the anode plasma), between which a longitudinal electric field accelerating ions is produced. The plasma conductiv ity behind the thruster edge must be high enough for electrons to enter the accelerating channel in amounts required to neutralize the space charge of fast ions and the current of ions escaping onto the channel wall. The spatial configuration of the plasma in the acceleration region and near it is determined by the consistent action of the electric and magnetic fields, the reactive forces of the accelerated plasma flows, and the gradient of the electron pressure. The minimum xenon flow rate through a conven tional cathode compensator that is necessary to pro vide the required discharge parameters of an SPT is ~10% of the total xenon flow rate [9]. The necessity of supplying an appreciable fraction of the working gas to the conventional cathode compensator leads to a decrease in the mass use factor, because the velocities at which xenon ions and atoms escape from the cath ode are one to two orders of magnitude lower than the velocities of fast ions leaving the acceleration channel of the SPT anode unit. Therefore, it is reasonable to compare the xenon flow rates through the SPT cath ode compensator and the cathode of the IPT gasdis charge chamber (GDC). For the same discharge cur rents, the minimum admissible xenon flow rate through the conventional SPT cathode compensator is
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Table 1. Rate constant of xenon ionization by electrons with a Maxwellian distribution function, ki(Те) ≡ 〈σi (Те)ve〉 [15–17] Te , eV
ki, cm3/s [15]
ki, cm3/s [16]
ki, cm3/s [17]
Te , eV
ki, cm3/s [15]
ki, cm3/s [16]
ki, cm3/s [17]
1 2 3 4 5 6
– 6 × 10–10 4 × 10–9 9 × 10–9 1.3 × 10–8 1.8 × 10–8
– 1.1 × 10–10 1.1 × 10–9 3.4 × 10–9 7.5 × 10–9 1.2 × 10–8
2.9 × 10–13 1.5 × 10–10 1.3 × 10–9 4.1 × 10–9 8.4 × 10–9 1.4 × 10–8
7 8 9 10 15 20
2.3 × 10–8 2.8 × 10–8 3.3 × 10–8 3.8 × 10–8 5.2 × 10–8 6.1 × 10–8
1.85 × 10–8 2.4 × 10–8 3.1 × 10–8 3.8 × 10–8 – –
2.0 × 10–8 – – 3.9 × 10–8 6.8 × 10–8 9.1 × 10–8
a factor of 3−5 larger than the optimal flow rate through the GDC cathode in the most efficient IPT operating regimes. Let us show that such a difference in the flow rates is partially due to the more efficient arrangement of the discharge in the GDC as compared to that in the SPT cathode region. The GDCs of modern IPTs operate with a low pressure constricted reflective arc discharge in a horn magnetic configuration [13]. Discharge constriction is achieved by adjusting the xenon flow rate through the cathode cavity, while the major fraction of xenon is supplied to the GDC through the gasdistributing col lector. The current−voltage characteristic of such an arc discharge is ascending with a tendency toward sat uration. This allows one to obtain plasma with an elec tron temperature of Te ≈ 12−15 eV. For a discharge voltage of Ud = 40−50 V, magnetic induction of Bmax ≈ 0.015 T, charged particle density in the GDC axial region of ne = ni = 1011 − 1012 cm −3 , and neutral parti cle density in the GDC of no higher than namax = 5 × 1013 cm−3, the electron energy distribution function has two maxima. The first maximum corresponds to the electron temperature and is located in the energy range 12−15 eV. The second maximum lies in the energy range 25−30 eV, which indicates the presence of a group of fast electrons. The measurements were performed in the plasmas of three IPT GDCs with characteristic ionoptics sizes of 5, 10, and 20 cm. The control parameters corresponding to the optimal regimes were nearly the same for all three GDCs. The obtained values of the local plasma parameters were also close to one another and lay within the above ranges. This allowed us not to perform such measure ments in the subsequent tests of the PEES [10, 11]. The preparation of a discharge with increased mean electron energy made it possible to achieve stable operation and high efficiency of this type of IPT. The plasma electron temperature behind the edges of the conventional cathode compensator and the SPT acceleration channel is Te ~ 3 eV [14]. At this temper ature, the rate of electronimpact ionization of xenon is one to two orders of magnitude lower than that in the main ionization region of modern ESEs, where Te ~ 10 eV (see Table 1).
In what follows, for electron temperatures in the range 2−7 eV, we used the data from [16, 17]. The low ionization rate in the ion beam propaga tion region is one of the main factors due to which an enhanced flow rate of neutral xenon is required to achieve optimum discharge parameters in an SPT equipped with a conventional cathode compensator. In turn, the increase in the density of neutrals in this region leads to an increase in electron energy losses [16] and a decrease in their temperature. Therefore, simple replacement of the conventional SPT cathode compensator with an IPT GDC cathode unit results in neither a reduced flow rate through the cathode, which is typical of an SPT discharge, nor the improve ment of SPT characteristics. Note that the electron temperature of Te ~ 3 eV is typical of a lowpressure arc discharge with a descend ing current−voltage characteristic. Electrons with energies higher than 7−10 eV can be generated in the arc plasma only in gasdischarge devices satisfying specific requirements. These requirements (which will be further referred to as conditions 2*) were formu lated in [12, 13] as applied to the IPT GDC: the elec tron current emitted by the arc hollow cathode is lim ited, electrons escape behind the edge of the cathode cavity with appropriate energies, and the magnitude and configuration of the magnetic field are such that it prevents the loss of fast electrons. The set of control parameters should satisfy conditions 2*, because elec trons with an increased temperature and a two humped energy distribution function can appear only in the narrow parameter range corresponding to opti mal regimes. In modern IPD GDCs, these conditions are satisfied. The axial distributions of the electric potential in the IPT GDC plasma and the PEES [10, 11] are shown in Fig. 1. 3. PLASMA ELECTRONEMITTING SOURCE The above considerations allow us to expect that the satisfaction of conditions 2* directly behind the edge of the hollow cathode (the EST cathode compen sator or EST cathode neutralizer) will result in the enlargement of the region in which the discharge sta bly operates, the expansion of the range in which its PLASMA PHYSICS REPORTS
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757 〈Ee〉
U, В 45 30 15 0
z
–15
Magnetic field line
Fig. 1. Profiles of the electric potential and energy of fast electrons on the axis of the IPT GDC and PEES (the notation of the structural elements is indicated in the caption of Fig. 2).
We performed three series of PEES experiments [12]. The first series included performance tests, adjustment of the PEES [10, 11], the determination of PLASMA PHYSICS REPORTS
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Xenon
4. TESTING METHODS AND EXPERIMENTAL RESULTS
8
Xenon
main parameters can be varied, a decrease in the xenon flow rate through the cathode unit, and the appearance of the selfthrust of the cathode unit. The device in which conditions 2* are satisfied should be similar in some respects to the end Hall thruster (EHT) [2] operating as an electron source. At the same time, the operating regime of such an EHT and its plasma parameters should be close to those of an IPT GDC [13]. These considerations lay the basis for the development of a PEES [10, 11]. As compared to the conventional EST cathode compensator [9, 18], the PEES [10, 11] (see Fig. 2) has an additional discharge stage consisting of main anode 6, a magnetic system (pole caps 5 and 8 and solenoid 7, which is a source of magnetomotive force), and gasdistributing collector 4 of the additional xenon supply system. In contrast to devices studied in [9, 18], the PEES under certain conditions is capable of increasing the energy of electrons entering the pos itive column plasma. This imparts a number of new features to gasdischarge devices equipped with such a cathode unit. Under optimal operating conditions, the main parameters of the PEES discharge almost coin cide with those in the IPT GDC. Therefore, the con cepts elaborated in studying the processes occurring in the IPT GDC can well be applied to the PEES.
Fig. 2. Schematic of the PEES: (1) cathode, (2) starting heater, (3) igniting electrode, (4) gasdistributing collec tor, (5, 8) pole caps, (6) main anode, and (7) solenoid.
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Table 2. Parameters of PEESs Country Type of cathode Operating mode Magnetic induction Вmax , T Current extraction through a hole Potential of the main anode Ua, V Current to the main anode Ia, А Current to the outer anode Iout , А Total mass flow rate m· , mg/s s
Electron cost W/Iout, W/A Extraction efficiency Iout /Ia Gas efficiency Iout /I m.
Russia [10, 11] Hollow arc Steadystate 0.03–0.04 in the anticathode 40–60 0.3–1.5 1–5 0.03–0.3 10–16 2.5–5 27–45
its optimal geometric parameters, and measurements of the discharge characteristics in the vicinities of the expected working points. The main parameters of the additional discharge stage were chosen in the course of autonomous tests of a model transformer that allowed us to vary the geom etry of the magnetic system, the diameter of the output aperture, and its position on the PEES axis. In these tests, the outer anode was an ~10cmdiameter perfo rated molybdenum disk located at a distance of 6− 8 cm from the PEES edge. The gas pressure in the chamber corresponded to that in the SPT tests. The PEES [10, 11] parameters achieved in the first series of experiments, as well as the parameters of the prototype device [19, 20], are presented in Table 2. Here, I m = em i /M, e is the electron charge, m i is the mass flow rate of the working medium, and M is its atomic mass. In the second series of experiments, the “SPT50 anode unit−PEES” assembly was adjusted and its inte gral characteristics in standard operating regimes were measured. It is found that the discharge has a peculiar configuration: a weakly glowing electron−ion beam with a small divergence appears behind the PEES edge. The axis of this beam is a continuation on the PEES axis and is parallel to the axis of the main ion beam. The total mass flow rate in the PEES that is necessary to achieve the required parameters of the main discharge is two to three times lower than that in the conventional cathode compensator. It is also found that, with the PEES, the discharge becomes more sta ble and the thrust increases appreciably (up to 25%). To verify the above results, we performed a third series of experiments with SPTs equipped with a con ventional cathode compensator and a PEES [10, 11]. In these experiments, the main discharge operated in the regimes optimal for the “SPT50 anode unit−con ventional cathode compensator” assembly [12]. In the experiments with both the conventional cathode com
USA [19, 20] Hollow arc Steadystate No data in the main anode 50–100 1–15 0.1–0.6 No data 1250 0.04–0.07 No data
pensator and the PEES, the xenon flow rate through the anode unit was 1.2 or 2 mg/s. The parameters of the main discharge (the discharge current and voltage and the magnetic field in the SPT acceleration chan nel) were maintained at a constant level by adjusting the PEES parameters. The following parameters were varied: the mass flow rates through the cathode and the PEES collector, the magnetic induction in the main anode cavity, and the voltage at the main anode. The angular distribution of the ion current density ji(α) and the ion energy distribution function were measured using a multielectrode probe that could be moved over the azimuth at a distance of ≈0.4 m from the thruster edge. The amplitude−frequency characteristics of current oscillations in the circuit of the main dis charge were measured using a spectrum analyzer. The pressure in the discharge chamber was p = (3−4) × 10 ⎯5 Torr. In all three series of experiments, the total mass flow rate through the PEES collector and the PEES cathode did not exceed 35−50% of the mass flow rate through the conventional cathode compensator. In optimal regimes, the increase in the mean electron energy in the PEES to 7−15 eV was accompanied by an increase in the thrust of the “SPT50 anode unit− PEES” assembly, improvement of the discharge stabil ity, and a decrease in the oscillation level and diver gence of the ion beam (see Table 3). For the same parameters of the main discharge, the thrust of the “SPT50 anode unit−PEES” assembly was higher by 10−25% and the total xenon flow rate was lower by 3−5% than those of an SPT equipped with a conventional cathode compensator. With the PEES, the ion beam current density near the longitu dinal axis increased by 5−25% within the angle α = ±(10°−12°) and remained practically unchanged at the beam periphery. In the regimes illustrated in Fig. 3, the ion beam current density near the longitudinal axis of the SPT anode unit increased by 7−15% and the beam divergence decreased by 3°−4°. The maximum PLASMA PHYSICS REPORTS
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Table 3. Results of testing the “SPT50 anode unit conventional cathode compensator” and the “SPT50 anode unit PEES” assemblies in two different regimes Operating mode Discharge voltage, V Discharge current, A Xenon flow rate through the gasdistributing anode, mg/s Xenon flow rate through the conventional cathode compensator, mg/s Total mass flow rate through the “SPT50 anode unit conventional cathode compensator” assembly, mg/s Thrust of the “SPT50 anode unit conventional cathode compensator” assembly, mN ηu of “SPT50 anode unit conventional cathode compensator” assembly, % Xenon flow rate through the PEES, mg/s Total mass flow rate through the “SPT50 anode unit PEES” assembly, mg/s Thrust of the “SPT50 anode unit PEES” assembly, mN ηu of the “SPT50 anode unit PEES” assembly, %
of the ion energy distribution function at the axis of the anode unit (Fig. 4) and both edges of this function were found to shift by approximately 10 eV toward higher energies. In the present paper, the mass use factor ηu (see Table 3) is defined as the ratio between the measured thrust Fexp and the theoretically achievable thrust Fth. This definition was introduced in [12]. The theoreti cally achievable thrust was calculated under the assumption that the entire gas flux (corresponding 100% of the total gas flow rate m s through all the units of the thruster) possesses the same projection of the average mass velocity vz onto the thrust vector as the actually accelerated fraction of the working gas. In other words, the mass use factor is defined as the ratio of the fraction of the mass flow rate spent on creating the thrust m i to the total mass flow rate m s through the thruster [1]. Then, we have ηu = m i /m s = m i vz/m s vz = Fexp/Fth.
(1)
The velocity of a xenon ion that has passed the potential difference U is vi [km/s] = 1.21U1/2 [V]; i.e., its momentum increases rather slowly with increasing voltage. Taking this into account and assuming that, for optimal SPT operating regimes and a discharge voltage Ud of 200−400 V, the average energy of fast ions at the output from the accelerator is 〈εi〉 ~ (0.82− 1/2
0.86)eUd [5], we find that vz ≈ 1.11 U d
and Fth ≈
1/2 1.11m s U d .
Thus, to within ±1.2%, for a thruster operating with xenon, we obtain ηu = m i /m s = m i vz/m s vz = Fexp/Fth ≈ 0.9Fexp/m s Ud1/2,
(2)
where the thrust Fexp is in mN, the total mass flow rate m s in mg/s, and the discharge voltage Ud in V. For an SPT100 equipped with a conventional cathode com PLASMA PHYSICS REPORTS
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No. 1 310 1 1.2 0.1 1.3 18 71.6 0.04 1.24 20 83
No. 2 220 1.67 2 0.1 2.1 24 70 0.04 2.04 30 89
pensator [21], we have Fexp = 80 mN, m s = 5.2 mg/s, Ud = 300 V, and ηu = 0.8. Thus, unlike the “SPT50 anode unit−conven tional cathode compensator” assembly, the “SPT50 anode unit−PEES” assembly possesses the following features: a new arrangement of the working process due to the presence of a magnetic field in the cavity of the PEES main anode and the additional power released in this cavity; a change in the discharge con figuration; a two to threefold decrease in the total mass flow rate through the cathode unit; an increase in the current of fast ions, the thrust, and the mass use factor by 10−25%; an increase in the thrust efficiency by a factor of 1.2−1.6; an increase in the specific momentum by 10−30%; an improvement of the dis charge stability; a decrease in the level of discharge current oscillations in the entire frequency range under study, due to which the parameter range of admissible operating regimes and the range in which the discharge parameters can be varied expand signifi cantly; a decrease in the ion beam divergence; a change in the energy distribution function of beam ions; and the appearance of three additional channels for discharge control. Note that the discharge can be controlled by varying the following parameters: the power deposited in the cavity of the main anode, the magnetic induction, and the ratio between the mass flow rates through the cathode and the PEES collec tor. 5. DISCUSSION OF EXPERIMENTAL RESULTS The substantial difference between the data obtained in the experiments with the “SPT50 anode unit−PEES” and “SPT anode unit−conventional cathode” assemblies is due to the presence of the mag netic field in the cavity of the PEES main anode and the 4−5% additional power (of the total discharge
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MINAKOV ji, mA/cm2 1.2
f(ε), arb. units 6 (a)
1.0
5 1
0.8
2
4
0.6
3
0.4 2 0.2 1 –80
–40
0 –0.2
40 80 Angle, degree
0
50
100
150
200
250
300
350
mA/cm2
ji, 1.4 1.2
(b)
400 ε, eV
Fig. 4. Ion energy distribution function for SPTs with the (1) conventional cathode and (2) PEES (U d = 310 V).
1.0 0.8 0.6 0.4 0.2 –80
–40
0 –0.2
40 80 Angle, degree
Fig. 3. Angular distribution of the ion current density ji(α) (a) in regime no. 1 of Table 3 (the discharge voltage is U d = 310 V, and the discharge current is I d = 1 A) and (b) in regime no. 2 (the discharge voltage is U d = 220 V, and the discharge current I d = 1.67 A). The dashed and solid lines refer to SPTs with the conventional cathode and the PEES, respectively.
power) released in this cavity. A significant decrease in the total mass flow rate through the new cathode unit was achieved. The factors characterizing the processes occurring in the IPT GDC and the PEES and the geometry of these devices are almost the same (the same shape of the current−voltage characteristic, the same discharge voltage, the same flux densities of charged and neutral particles, nearly the same config uration and magnitude of the magnetic field, the closeness of the ranges of these control parameters and their narrowness in optimal regimes, and the geomet rical similarity of the devices). All this, as well as a decrease in the mass flow rate through the new cath ode unit, indicates the similarity of the processes in these devices—in particular, the closeness of their local parameters, the existence of a group of fast elec trons, and a considerable increase in the temperature of thermal electrons in the cavity of the PEES main
anode. Taking this into account, it may be supposed that the conclusions drawn in [13, 16] also apply to the processes in the PEES [10, 11]. In optimal regimes, the plasma parameters near the maximum of the elec tric potential on the axis of the cavity of the PEES main anode are as follows: the density of charged par ticles is 1011−1012 cm−3, the bulk electron temperature is Te = 12−14 eV, and the energy of fast electrons is ε = 25−30 eV. As in the IPT GDC [13], electrons between the maximum of the electric potential and the PEES edge move against the electric field force under the action of the electron pressure gradient. The distribu tions of the magnetic and electric fields in the cavity of the additional PEES stage are such that a significant fraction of generated ions are accelerated toward the output aperture to energies of a few tens of electron volts. An electron−ion beam (Ie Ⰷ Ii) forms at the PEES output. In this beam, the electron gas expands quasiadiabatically. During expansion of a single beam, the electron temperature generally decreases. However, for the appropriately chosen PEES parame ters, regions with close densities of neutral and charged particles can form during the interaction of two beams created in the PEES and the SPT anode unit. The initial electron temperatures in these regions can differ considerably; so, under certain conditions (see below), they begin to exchange thermal energy. The energy is transferred from the electron gas of the PEES cavity to the electron gas of the colder main ion beam. The increase in Te in the critical region of the main ion beam from 3−4 to 7−10 eV corresponds to the increase in the rate constant ki of electronimpact ionization of xenon by one order of magnitude (see Table 1). Let us show that this growth changes the for mation mechanism of primary slow ions: ionization of neutral particles due to resonant charge exchange with the flux of fast ions with the density nih is changed with PLASMA PHYSICS REPORTS
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the combined process of chargeexchange and direct electronimpact ionization. Let us estimate the production frequency of pri mary slow ions for each of the above mechanisms. The frequency of ionization caused by charge exchange of fast xenon ions with neutral atoms for the ion velocity v ih = 2 × 106 cm/s, which corresponds to the energy εi = 272 eV and chargeexchange cross sec tion σia ≈ 5 × 10−15 cm2 [22], is νia = nih σiav ih ≈ 10−8nih s−1. The frequency of direct electronimpact ionization of neutral particles for the electron density ne and velocity ve is νi = ne〈σi(ve)ve〉 ≡ neki . For Te = 3 and 7 eV, we have ki ≈ 10−9 and 2 × 10−8 cm3/s, respectively (see Table 1). In the optimal regimes in which the mass flow rate of neutral particles reaches its lower limit, the density of slow ions nis in the ion beam drift space is compara ble with the density of fast ions nih and is close to the minimum admissible value. Then, the electron density is ne ≈ nih + nis ≈ (1.1−2)nih .
periphery are filled with slow ions via both ambipolar fluxes and direct electronimpact ionization, which goes efficiently in both the beam core and the shadow regions. Thus, as the electron temperature Te behind the edge of the acceleration channel increases above 7 eV, electronimpact ionization begins to play an important role not only in the region where fast ions propagate, but also beyond this region. A considerable increase in the production rate of slow ions with increasing electron temperature behind the thruster edge makes it possible to produce slow ions in the amount required for conditions 1* to be satisfied even at a relatively low density of neutrals. The ionization rate ϕ(r), i.e., the number of ions produced per unit volume per unit time in the vicinity of the point r via both resonance charge exchange and direct electronimpact ionization is
For the velocity of fast ions =2× cm/s and h h Te = 3 eV, we have νia/νi = ni σiav i /ne〈σive〉 = nih σiav ih /(1.1−2)nih 〈σive〉 = 5−9, i.e., the frequency of resonance charge exchange of xenon atoms with fast ions exceeds the frequency of direct electronimpact ionization by a factor of 5−9. For the same velocity of fast ions and Te = 7 eV, we have νia/νi ≡ nih σiav ih /ne〈σive〉 = 0.25−0.45. Thus, in regimes with a high mass use factor, Te = 3−4 eV, and fast ion velocity of v ih = 2 × 106 cm/s, slow ions in the ion beam are generated mainly due to res onance charge exchange of fast ions with neutral par ticles. In regimes with a high mass use factor, Te ≥ 7 eV, and fast ion velocity of v ih = 2 × 106 cm/s, the fre quency of direct electronimpact ionization of neutral particles exceeds the frequency of their charge exchange with fast ions by a factor of 2.2−4. Therefore, the appearance of a plasma with Te ≥ 7 eV behind the channel edge increases the production rate of slow ions in the ion beam via both of the above channels at least threefold. The generation of slow ions due to resonance charge exchange of fast ions with neutral particles is localized within the ion beam drift space. In regimes with a high mass use factor ηu and Te = 3−4 eV, when the inequality νia νi is satisfied in the beam core, the shadow region near the axial magnetic conductor and the ion beam periphery are filled with slow ions mainly via ambipolar fluxes. In regimes with a high mass use factor ηu and T e ≥ 7 eV , when νia ≤ νi in the beam core, the shadow regions and the ion beam
As the mass use factor tends to unity, the generation of slow ions terminates and conditions 1* cannot be sat isfied. Therefore, the following relationships are always satisfied: ηu ≤ ηmax < 1, where ηmax is the max u u imum mass use factor determined by ionization con ditions and the type of working medium. For all devices operating with a steadystate low pressure beam−plasma discharge, the assumption of full plasma ionization is invalid. The PEES [10, 11] creates its own neutralized beam of accelerated ions. This leads to a change in the discharge configuration and the appearance of the selfthrust of the cathode unit. Let us estimate this thrust. As in the case of plasma acceleration in a small size EHT [2], the average velocity of ions escaping from the PEES can be substantially higher than the velocity corresponding to the potential drop between the cathode and anode due to both electron−ion colli sions and the Boltzmann acceleration mechanism. For a cathode−anode potential drop of ≈50 V and Te = 10−15 eV, the velocity of xenon ions at the exit from the PEES is vi ~ 10 km/s. For a mass use factor of ηu = 0.7−0.8 and total mass flow rate of ≈0.04 mg/s, the thrust of a PEES operating as a part of the “SPT 50 anode unit−PEES” assembly is FPEES ~ 0.3 mN. The total increase in the thrust of the “SPT50 anode unit−PEES” assembly is 2−6 mN. Thus, 85− 95% of this increase is due to the interaction of two neutralized beams, one of which is produced by the PEES, while the other, by the SPT anode unit. Such a considerable increase in the thrust cannot be attributed exclusively to the shift of the maximum and edges of the ion energy distribution function (Fig. 4) toward higher energies by approximately
v ih
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ϕ(r) = na(nih σiav ih + ne〈σive〉) ≡ na(νia + νi).
(3)
If the background neutral particle density is negligible, then na is proportional to (1 − ηu) and we have ϕ(r) ~ (1 − ηu)(νia + νi).
(4)
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10 eV, i.e., by 3−4% of the average energy of fast ions. First, the velocity of these ions increases as the square root of the energy, so that the increase in the momen tum cannot exceed 1.5−2%. Second, along with addi tional acceleration of the beam ions due to an increase in Te, such an increase in the velocity can be caused by a decrease in the effective thickness of the gas target between the probe and the edge of the anode unit. A decrease in the density of neutrals in this region leads to a decrease in the frequency of elastic ion−neutral collisions and, accordingly, the momentum loss caused by the escape of ions onto the collector of the multielectrode probe. An increase in the current of fast beam ions at a constant discharge current can be caused only by a decrease in “the anomalously large through electron current,” which is defined as the difference between the first two currents. Formally, the electron current from the cathode compensator (which is equal to the current of the main discharge) is redistributed between the enhanced current of fast ions and the electron cur rent to the SPT gasdistributing anode. The fraction of the current of fast ions in the total discharge current is 65−80%. Accordingly, the fraction of the through elec tron current is 20−35% of the total discharge current. Therefore, the increase in the current of fast ions, e.g., from 68 to 75%, corresponds to the decrease in the through electron current from 32 to 25%; i.e., the cur rent of fast beam ions and the anomalously large through electron current are interrelated: an increase in one component of the discharge current is exactly equal to a decrease in the other component. This interrelation indicates the existence of a specific chargetransfer mechanism in the region of the maxi mum magnetic field; such a mechanism was not previ ously taken into account [12]. The motion of electrons along the axis of the SPT ring dielectric acceleration channel is limited by the radial magnetic field. When the discharge is ignited, this results in the appearance of a longitudinal electric field accelerating ions toward the channel edge. Let us consider ions generated in the region with a high elec tric potential. As these ions move under the action of the electric field toward the output of the acceleration channel into the region with a low potential, they practically do not interact with the magnetic field, because the ion Larmor radius is larger than the char acteristic scale length of the problem. When such an ion leaves the acceleration channel, the charge trans ferred by it contributes to the ion beam current. If an ion generated together with an electron near the place where the first ion was generated does not pass through the edge of the acceleration channel, but falls on the channel wall near the output aperture, it recombines on the dielectric surface with a probability close to 100%. The electron required to neutralize the charge of the ion that has escaped onto the wall is extracted from the ambient plasma. In this case, the electron is generated in the plasma volume in the region with a
high potential near the gasdistributing anode and falls onto the wall in the region with a low potential near the edge of the acceleration channel. The generation of each ion−electron pair and the subsequent ion− electron recombination on the dielectric surface is accompanied by the transfer of a positive elementary charge from the vicinity of the gasdistributing anode to the thruster edge over a distance equal to the axial projection of the ion path from the generation point to the point of recombination on the wall. The current density of ions falling onto the wall near the edge of the acceleration channel is 0.2−0.5 of the current density of beam ions (see [5], p. 109). The areas of the edge and the side wall of the acceleration channel onto which ions mainly escape are compara ble. In view of the steadystate character of the prob lem, the current of ions falling onto the channel wall is equal to the current of electrons extracted from the ambient plasma. Variations in the latter are quite suffi cient for an increase in the current of fast ions to be equal to a decrease in “the anomalously large through electron current.” The high density of the ion current onto the output part of the wall of the SPT acceleration channel equipped with a conventional cathode compensator leads to the appearance of a local maximum of the neutral particle density (see [5], p. 115). The high den sity of this current is caused by the necessity of pre serving the neutral particle density in the critical region at the level required to satisfy conditions 1*. The replacement of the conventional cathode com pensator with the PEES [10, 11] leads to an increase in the temperature and pressure of the electron gas at the output from the accelerating channel. As a result, the interdependent distributions of the electric field and the charged particle density change in such a way that a fraction of ions previously falling onto the wall of the acceleration channel near its edge leave the channel, thereby increasing the fraction of the ion beam current in the total discharge current and decreasing the num ber of electrons extracted from the plasma volume. Since the SPT lifetime is determined, first of all, by the erosion of the insulator near the edge of the accelera tion channel under the action of ions falling onto the insulator surface, the decrease in the current of ions falling onto the wall by a factor of 1.3−3.0 results in the corresponding increase in the thruster lifetime. The possibility of increasing the lifetime is also indirectly confirmed by the increase in the thrust efficiency: the fraction of the power carried away by ions onto the wall of the acceleration channel, i.e., spent on the destruc tion of the structural elements of a thruster in which the SPT anode unit is equipped with a PEES, is now expended on increasing the ion beam power. The high density of the ion current onto the output part of the wall of the SPT acceleration channel equipped with a conventional cathode compensator allows one to consider this part of the insulator surface PLASMA PHYSICS REPORTS
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as an additional source of neutral atoms leaving the thruster. The axial width of this part is determined by the necessity of creating the required flux of neutral particles and is comparable with the path length of an atom before ionization. We assume that neutral parti cles leave the channel wall in the positive and negative directions of the longitudinal axis of the thruster with equal probabilities and that the character of their motion is free molecular. Under these assumptions, the flux of particles generated on the wall and moving from the edge inside the acceleration channel is either equal to the flux of neutral particles leaving the chan nel or, taking into account that the flux going beyond the thruster edge is partially ionized, exceeds it. Therefore, the flux of ions recombining on the chan nel wall near the thruster edge is two to four times larger than the flux of neutral particles going beyond the edge. This is equivalent to the scheme in which, due to mutual transformations of atoms and ions, a fraction of the mass flow in the acceleration channel moves along a closed trajectory and carries all the power acquired in the discharge onto the channel wall, thereby destroying it. Thus, the conclusions drawn in [7, 8] from the analysis of numerical results are gener ally correct: the atom path length before ionization is much smaller than the characteristic channel size; the xenon flow supplied to the gasdistributing anode is almost completely ionized; and the atom can be ion ized and then recombined on the wall once, twice, or even three times. As a result, since an appreciable frac tion of the flow leaves the thruster in the form of neu tral particles that are necessary to produce slow ions, the density of the ion current onto the wall of the acceleration channel near the thruster edge increases considerably. Therefore, in an SPT equipped with a conventional cathode compensator, the neutral parti cle flow comprises a substantial fraction of the total mass flow rate. As a result, the total discharge current is considerably higher than the ion beam current, which leads to a decrease in the efficiency and lifetime of the thruster. This also explains an inconsistency between the current and mass balance: the current flowing between the cathode and anode, unlike the fluxes of atoms and ions undergoing mutual transfor mations, does not form closed circuits. In our experiments with an SPT equipped with either a conventional cathode compensator or a PEES, the thrust efficiency changes primarily at the expense of the thrust. In this case, the parameters of the main discharge and the xenon flow rate through the gasdistributing anode remain practically unchanged. The increase in the discharge stability, as well as the extension of the region of admissible oper ation regimes and the ranges in which the discharge parameters can be varied, indicates that the threshold for the development of crisis phenomena in an SPT equipped with a PEES is shifted toward higher dis charge powers Wd. Taking into account this circum stance and the increase in the lifetime and thrust effi PLASMA PHYSICS REPORTS
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ciency, the parameters of a thruster equipped with a PEES can be further increased by increasing the spe cific discharge power, i.e., the power per unit mass flow rate. Indeed, if we assume that the thrust is fixed and the discharge power is at least not reduced, then the thrust efficiency may be increased only by reduc ing the mass flow rate. It can easily be shown that, in this case, the ratio between the discharge current and voltage must change. Since the discharge current decreases nearly in proportion to the mass flow rate, the condition that Wd is at least not reduced yields that the discharge voltage grows either inversely propor tional to the decrease in the mass flow rate or even faster if the discharge power is increased. Simulta neously, the exhaust velocity of fast ions and, accord ingly, the specific momentum increase in proportion to the square root of the discharge voltage. In order for the thrust to remain unchanged, the mass flow rate should be further reduced. The subsequent “itera tions” will result in a new working point with the same thrust and somewhat higher (e.g., by 5−25%) dis charge power, but with a much higher discharge volt age, a higher thrust efficiency, and a mass flow rate reduced by a factor of 1.3−1.5 as compared to its initial value. “In space, energy is cheaper than mass; hence, switching to thrusters with higher exhaust velocities is quite justified” [9]. Due to a decrease in the mass flow rate and the simultaneous increase in the exhaust velocity, the space charge of fast ions decreases. Since it is desirable to preserve the optimal ratio between the space charges of fast and slow ions and since the resi dence time of slow ions near the points at which they were generated changes insignificantly, the mass expenditure in the form of neutral particles decreases not only due to a decrease in direct mass losses of the working medium, but also due to an increase in the discharge voltage. Energy losses for ionization are almost independent of the discharge voltage, so the substantial increase in the specific power results in an increase in the kinetic energy of the ion beam. There fore, as the discharge voltage increases, the thrust effi ciency increases also due to the relative decrease in ionization losses. Since, in this case, not only the life time, but also the discharge voltage can be increased, the discharge voltage in an SPT approaches that in IPTs and TALs. The combination of such basic factors as the increase in the lifetime and thrust efficiency at a fixed thrust and fixed amount of xenon implies that the time of active operation of the thruster (and, therefore, of the spacecraft) increases to the same extent to which the mass flow rate is reduced. The newly devel oped PEES [10, 11] provides such capabilities due to the higher discharge power at which crisis phenomena develop and the reduced interaction of the plasma flow with the wall of the acceleration channel. As a result, the fraction of the electron current in the total dis charge decreases by a factor of 1.3−3.0 and the thruster lifetime increases accordingly. For an SPT equipped with a conventional cathode compensator, a transition
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to such a working point is impossible, because, even at a reduced mass flow rate, an increase in the discharge voltage will lead to an increase in the energy released in the acceleration channel and, accordingly, a decrease in the thruster lifetime. Let us consider a lowdensity xenon plasma jet interacting with the same sort of neutral gas filling the vacuum chamber [21]. We will search for twodimen sional distributions of the electric field and charged particle density behind the edge of the SPT accelera tion channel. The set of model kinetic equations con taining the components of the selfconsistent electric field is supplemented with the following equation describing the behavior of plasma electrons in the adi abatic approximation: 2
kT 0 ⎛ n (r)⎞ 3 U(r) = U0 + 5 e ⎜ i 0 ⎟ , 2 e ⎝ ni ⎠
(5)
where U0, Te0 , and ni0 are the potential, electron tem perature, and ion density at a certain characteristic point of the discharge. Equation (5) relates the electric potential to the charged particle density in the adia batic approximation. The results of calculations demonstrate an increase in the ion current density ji at the periphery of the jet as the background pressure of neutral xenon in the vacuum chamber increases from 2 × 10−6 to 10−4 Torr. Therefore, the beam divergence depends on the den sity of neutrals beyond the edge of the acceleration channel. The distributions of the plasma density and electric potential, as well as the corresponding radial and inverse ion fluxes, were found. The measured ion current density [23, 24] agrees satisfactory with the calculated one on the beam axis, while at the periphery of the jet, the measured ion cur rent density is higher than the calculated one by at least one order of magnitude. This is because the actual density distributions of neutral particles leaving the acceleration channel were not taken into account in [21]. It is worth noting the smoothness of the mea sured angular distributions of the ion current density ji = ji(α) (see [23, 24] and Fig. 3). Taking into account that the ion energy and, accordingly, the ion velocity vi decrease with increasing angle between the ion veloc ity vector and the thruster axis (see [5], p. 109) and that ne ≈ ni = ji/evi, we may conclude that the correspond ing angular distributions of the charged particle den sity are even smoother. Thus, conditions 1*, the smoothness of the gener alized solutions to elliptic equations [25], and the assumption on the applicability of Eq. (5) to a low pressure beam−plasma discharge yield the following fundamental conclusions, which are confirmed by the results of PEES experiments. (i) In the absence of external electric and magnetic fields, the plasma generated in a certain region of a
vacuum chamber tends to occupy the entire available space. In this case, the gradient of the electric poten tial does not exceed the value | ∇ U | ~ kTe/eL, where L is the characteristic scale length of the problem. In view of Eq. (5), the gradient of the plasma density is determined by the electron temperature and the gradi ent of the electric potential. Therefore, the stationary neutralized beam of fast charged particles has no sharp boundaries that could be determined from the drops in the density and/or velocity of charged particles. (ii) Let there be two inhomogeneous plasma objects separated by a region with low densities of neutral and charged particles in the vacuum chamber, and let there be no thermal insulation in the form of external elec tric or magnetic fields between them. We assume that, in each object, there are domains 1 and 2 with close densities of neutral and charged particles and with close conditions of thermal insulation of the electron gas by the magnetic field from the nearest wall. Let the electron temperatures and, accordingly, electric potentials in these domains be different at the initial instant. Then, after the ambipolar flows of charged particles are established, the plasma objects begin to exchange heat and, in the course of this exchange, the electron temperatures of the domains and the poten tials in them equalize in view of Eq. (5). Energy is transferred from the electron gas of domain 1, where the temperature is higher, to the electron gas of domain 2, where the temperature is lower. The tem perature in domain 2 increases gradually, because this process is related to the slow decrease in the density of neutrals caused by the increase in the partial pressure of the electron gas. A specific feature of heat exchange in a plasma with an increased electron temperature is the possibility of the electron temperature changing nonmonotonically, as follows directly from Eq. (5). Electrons that have left domain 1 with the highest energy move against the electric field force under the action of the electron gas pressure gradient; as a result, their kinetic energy transforms into the potential energy. At the periphery, where the potential energy of electrons reaches its maximum, the electrons chaotize and return to domain 1 or 2, due to which their potential energy transforms back into the kinetic one. In this case, the electron density and temperature at the periphery are low and the electric potential with respect to objects 1 and 2 is negative. The temperature and plasma poten tial in domain 2 continue to increase until energy losses from this domain become equal to the energy influx. There are four reasons by which the electron tem perature and plasma potential behind the edge of the acceleration channel grow: (i) there is no thermal insulation in the form of external electric and/or mag netic fields between the objects, (ii) the electron tem perature in the cavity of the PEES main anode is fairly high, (iii) the densities of neutral and charged particles PLASMA PHYSICS REPORTS
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near the PEES edge are comparable with those near the edge of the acceleration channel of the EST anode unit, and (iv) the electron gas in the cavity of the PEES main anode and near the edge of the acceleration channel of the EST anode unit is thermally insulated by the magnetic field tangential to the anode surface. According to Eq. (5), the electron temperature and plasma potential behind the edge of the acceleration channel of the “SPT anode unit−PEES” assembly increase in the region where the densities of charged and neutral particles become comparable with those in the cavity of the PEES main anode and near its edge. Since the magnetic induction behind the edge of the acceleration channel decreases much faster than does the charged particle density in the core of the ion flow, the magnetic field ensures electron thermal insulation only near the wall, i.e., at the boundary of the region in which the plasma density is maximum. In this sense, the “SPT anode unit−PEES” assembly may be con sidered as a peculiar magnetic mirror system the mag netic mirrors of which are oriented in the same direc tion. Electrons with an increased energy are emitted from the mirror located on the cathode side. In the other mirror, which is located near the anode, the neu tral particle flow in the main ionization region trans forms into the ion flow at Te ~ 10 eV. Electrons in this region are thermally insulated from electrons of the cathode region by strong magnetic and electric fields. The electron temperatures in the acceleration channel and beyond it are comparable; therefore, a relatively small number of neutral particles that have left the anode unit efficiently transform into slow ions. The increase in the electron temperature corresponds to an increase in the electron Larmor radius ( RL ~ Te1/2 ), electric conductivity (σ ~ Te3/2 ), and electron pressure (Pe ~ neTe ) near the edge of the acceleration channel. Along with a decrease in the ion and electron fluxes onto the wall of the acceleration channel, the first two factors favor the neutralization of the ion space charge in the channel. Due to a decrease in the excess space charge of ions in the channel, as well as to an increase in the electron pressure near the channel edge, the longitudinal component of the electric field increases, the acceleration zone shortens, and the ratio between the longitudinal and radial ion fluxes enlarges. The above experimental data and the consequences follow ing from them indicate that a new potential distribu tion is established in the BPD plasma. Since, in this case, there is no necessity of maintaining the high neu tral particle density in the critical region, the new potential distribution possesses a higher focusing capability. The thrust, the thrust efficiency, and the thruster lifetime increase accordingly. In [26], the dependence of the neutral particle den sity on the electron temperature in the cylindrical pos itive column of a lowpressure discharge was deter PLASMA PHYSICS REPORTS
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mined. The balance equation for the electron density yields
1.075( Te/ M )1/2 cm−3, (6) R0 ki( Te) where R0 is the characteristic scale length of the prob lem and M is the atomic mass. As Te increases from 3 to 7 eV, the ionization rate constant ki(Te) for xenon increases from ki(Te = 3 eV) = 1.1 × 10−9 cm3/s to ki(Te = 7 eV) = 2 × 10−8 cm3/s (see Table 1), i.e., by approximately a factor of 20, and the neutral particle density, according to formula (6), decreases by one order of magnitude. Formula (6) was derived under the assumption that selfconsistent dis tributions of the electric field and charged particle density and the corresponding ambipolar flows of ions and electrons have been established in plasma. Leav ing aside the magnetic field (which substantially increases the time during which electrons reside in the plasma volume), chargeexchange processes, and fast ions, the neutral particle density predicted by this for mula agrees qualitatively with the results of the present paper. Since there are no fast ions in the positive col umn of the low pressure discharge, the density of the generated ions is not limited by any condition. There fore, if the neutral particle density corresponds to that predicted by formula (6), no crisis phenomena occur. The difference between the electron temperatures in the main ionization region of an SPT equipped with a conventional cathode compensator and behind its edge is determined by many factors. In particular, in all ESTs, these regions are thermally insulated from one another either by a strong electric field (in IPTs) or a superposition of electric and magnetic fields (in TALs and SPTs) present at the interface between these regions. Another important factor is the shape of the current−voltage characteristic of the discharge. The current−voltage characteristic of an arc discharge, including that in the conventional cathode compensa tor, is generally descending, due to which the electron temperature cannot be increased. One more factor is that there is no magnetic field behind the edge of the hollow cathode that would prevent fast electrons from escaping toward the electrodes and provide nonmono tonic potential distribution. The PEES is capable of operating in both regimes with a high electron temper ature, which is created by the PEES itself, and regimes with a low Te, for which it is sufficient, e.g., to increase the mass flow rate through the hollow cathode to a level typical of the conventional cathode compensator. The conventional cathode compensator can operate only in regimes with a low Te, because the high density of neutrals leads to an increase in electron energy losses. Attempts to increase Te by decreasing the mass flow rate lead to an increase in the electron mean free path length; as a result, in the absence of a magnetic field, the fastest electrons fall onto the wall, thereby making impossible the very existence of the discharge. na =
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Thus, the consequences of an increase in the elec tron temperature behind the edges of the PEES and the SPT acceleration channel are as follows: the ion flux onto the wall of the acceleration channel decreases (accordingly, the thruster lifetime increases appreciably); the range of admissible operating regimes of the thruster, as well as the ranges within which the discharge parameters can be varied, extends; and the thrust for the same parameters of the main discharge increases. The replacement of the conventional cathode compensator with the PEES in the SPT has resulted in an increase in the maximum thrust of the SPT50 by 10−25% and that of the SPT 100 by 10% (according to data presented by the employees of the Fakel Experimental and Design Bureau). The possibility of increasing the electron tempera ture to a level at which the prevailing ionization mech anism behind the edge of the acceleration channel changes, as well as the low mass flow rate and low energy consumption, allows us to conclude that the PEES [10, 11] has obvious advantages over the con ventional cathode compensator (cathode neutralizer). The data obtained in experiments on the focusing of a negative ion beam by a plasma lens [4] are similar in the physical sense to those obtained in experiments with the “SPT50 anode unit−PEES” assembly. Using easily ionized heavy gases (such as argon, krypton, and xenon), a plasma lens with a focal length of f ≤ 20 cm was created. The gas in the lens was ionized not only by the ion beam, but also by an ~100eV electron beam produced by an additional ionizer. The use of such an ionizer made it possible to reduce the pressure in the lens channel by almost one order of magnitude as compared to the typical pressure of p ~ 10−3 Torr and decrease chargeexchange ion beam losses. From the physical standpoint, there is a deep analogy between the consequences of the introduction of an additional ionizer into a lowpressure discharge and the replace ment of the conventional cathode compensator with the PEES in the SPT. In both cases, the ionization fre quency increases considerably due to the simulta neous use of two ionization mechanisms: resonance charge exchange and direct ionization by fast elec trons. The results of these experiments also agree: the neutral particle density in the ion beam drift space, the processes in which substantially affect the characteris tics of the device, decreased by a factor of 3−10. Thus, the results of experiments with the PEES [10, 11] and the plasma lens [4] allow us to conclude that, as the plasma electron temperature in the drift space of a xenon ion beam increases from 3 to above 7 eV, the minimum admissible density of neutrals in a lowpres sure BPD decreases severalfold. 6. CONCLUSIONS The generation of an intense neutralized ion beam in a lowpressure steadystate arc discharge is always
accompanied by the formation of a peripheral plasma, which is a single whole with the ion beam plasma. The problem of efficient transformation of the neutral particle flow supplied to the thruster into a fast ion beam was previously solved by increasing the elec tron temperature in the main ionization region to Te ~ 10 eV. For all types of EST, the electron temperature is increased at the expense of the discharge energy released in the magnetic field of this region. The increase in the electron temperature is accompanied by an increase in the generation rate of fast ions and their density in the ion beam core. Simultaneously, the neutral particle density behind the edge of the thruster decreases. Nevertheless, these certainly favorable changes give rise to a problem that hampers the improvement of the thruster characteristics, specifi cally, the problem of preserving the required ratio between the densities of fast and slow ions in the criti cal region. The density of slow ions behind the accel erator edge should be comparable with or higher than the density of fast ions; otherwise, conditions for the plasma existence are violated. In this case, the mini mum mass flow rate in the form of slow ions that is necessary for the existence of a steadystate peripheral plasma and selfconsistent electric field does not exceed 2−5% of the total xenon flow rate through the thruster. For an SPT equipped with a conventional cathode compensator, the electron temperature behind the edge of the thruster is on the order of 3 eV; therefore, the probability of generating primary slow ions is low. As a result, the fact that an appreciable fraction of the total xenon flux leaves the thruster in the form of neutral particles that are necessary for gen erating slow ions has to be paid for by the high density of the ion flux onto the wall of the acceleration chan nel (in this case, a substantial fraction of neutral parti cles leave the accelerating channel without being ion ized). The PEES experiments have demonstrated the necessity of creating conditions in the lowpotential region behind the edge of the thruster similar to those created in the main ionization region of an EST in order to produce a peripheral plasma with the mini mum mass and energy consumption. Unlike the con ventional cathode compensator, the PEES allows one to simultaneously increase the mean energy of emitted electrons above 7 eV and substantially decrease the mass flow rate. The neutral particle density behind the edge of the acceleration channel and, accordingly, the fraction of the working medium that leaves the thruster in the form of neutral atoms decrease at least twofold due to an increase in both the ionization frequency and the volume of the region in which primary slow ions are generated. The decrease in the xenon flow rate through the cathode unit by a factor of 2−3, as well as the appearance of the PEES selfthrust, almost com pletely solves the problem of reducing the mass flow rate. PLASMA PHYSICS REPORTS
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The lifetime of the “SPT50 anode unit−PEES” assembly has been increased considerably, and the threshold for the development of crisis phenomena has been shifted toward higher discharge powers. This allows one to additionally increase the specific power and, accordingly, the thrust efficiency by simulta neously reducing the total mass flow rate and increas ing the discharge voltage by a factor of 1.5−2. The tests of an SPT equipped with the PEES [10, 11] have demonstrated that the thrust can be increases by 10−25% and the thrust efficiency, by a factor of 1.2− 1.6 for the same parameters of the main discharge. The region of admissible operation regimes has been extended. This allows one to improve the thruster characteristics and extend the range in which the dis charge parameters can be varied. Our experiments have partially removed the previous constraints on the thruster characteristics, thereby predetermining a new direction for improving ESTs. The concept proposed in this paper supplements the onedimensional hydrodynamic and hybrid SPT models developed in [7, 8] to describe the processes occurring in the accelerator channel with a description of the formation of the peripheral plasma behind the edge of the thruster. This concept allows one to con sider the lowpressure beam−plasma discharge and the gasdischarge positive column from a unified stand point.
I thank V.A. Muravlev (Keldysh Center Federal State Enterprise) for his assistance in preparing and carrying out PEES experiments and I.P. Nazarenko and V.M. Gavryushin (Moscow State Institute of Avi ation) for helpful discussions of the results obtained. REFERENCES 1. S. D. Grishin, Fundamentals of the Theory of Electric Propulsion Thrusters (MGTU im. N.E. Baumana, Moscow, 1999) [in Russian]. 2. A. I. Morozov, Physical Principles of Space Electric Pro pulsion Thrusters (Atomizdat, Moscow, 1978) [in Rus sian]. 3. The Physics and Technology of Ion Sources, Ed. by I. G. Brown (Wiley, New York, 1989; Mir, Moscow, 1998). 4. V. P. Goretskii, A. M. Zavalov, and I. A. Soloshenko, Fiz. Plazmy 31, 923 (2005) [Plasma Phys. Rep. 31, 855 (2005)]. 5. A. I. Bugrova and V. P. Kim, in Plasma Accelerators and Ion Injectors, Ed. by N. P. Kozlov and A. I. Morozov (Nauka, Moscow, 1984) [in Russian]. Vol. 35
6. A. I. Bugrova, V. K. Kharchevnikov, and S. A. Yakunin, Teplofiz. Vys. Temp. 19, 1045 (1981). 7. A. I. Morozov and V. V. Savel’ev, Fiz. Plazmy 26, 238 (2000) [Plasma Phys. Rep. 26, 219 (2000)]. 8. A. I. Morozov and V. V. Savel’ev, Fiz. Plazmy 26, 934 (2000) [Plasma Phys. Rep. 26, 875 (2000)]. 9. A. I. Morozov, Fiz. Plazmy 29, 261 (2003) [Plasma Phys. Rep. 29, 235 (2003)]. 10. V. I. Minakov, Patent RF No. 2 208 871; Byull. Izobr., No. 20, 765 (2003). 11. V. I. Minakov, Patent US No. 7 009 342 B2, March 7, 2006. 12. V. I. Minakov, in Proceedings of the International Con ference “Aviation and Cosmonautics2004,” Moscow, 2004, Paper 18.3. 13. A. A. Temeev and V. I. Minakov, in Proceedings of the XII International Conference on Gas Discharges and Their Application, Greifswald, 1997, V. 2, p. 711. 14. S. N. Askhabov, M. P. Burgasov, V. V. Fishgoit, et al., Fiz. Plazmy 7, 225 (1981) [Sov. J. Plasma Phys. 7, 125 (1981)]. 15. I. V. Melikov and A. I. Morozov, Fiz. Plazmy 3, 388 (1977) [Sov. J. Plasma Phys. 3, 221 (1977)]. 16. J. R. Brophy and P. J. Wilbur, AIAA J., No. 9, 1516 (1986). 17. T. B. Antonova, G. E. Bugrov, E. A. Kral’kina, et al., Preprint No. 7414288 (MAI, Moscow, 1988). 18. A. T. Forrester, Large Ion Beams (Wiley, New York, 1988; Mir, Moscow, 1992).
ACKNOWLEDGMENTS
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19. A. S. Roberts, Jr., J. L. Cox, Jr., and W. N. Bennet, J. Appl. Phys. 37, 3231 (1966). 20. Yu. E. Kreindel’, Plasma Sources of Electrons (Atomiz dat, Moscow, 1977) [in Russian]. 21. A. V. Bishaev, V. K. Kalashnikov, V. Kim, and A. V. Sha vykina, Fiz. Plazmy 24, 989 (1998) [Plasma Phys. Rep. 24, 923 (1998)]. 22. Handbook of Physical Quantities, Ed. by I. S. Grigoriev and E. Z. Meilikhov (Énergoatomizdat, Moscow, 1991; CRC, Boca Raton, 1997). 23. D. H. Manzella and J. M. Sankovic, in Proceedings of the 31st AIAA/ASME/SAE/ASEE Joint Propulsion Con ference, San Diego, CA, 2005, Paper AIAA952927. 24. S. K. Absalamov, V. B. Andreev, T. Colder, et al., in Pro ceedings of the 28th AIAA/SAE/ASME/ASEE Joint Pro pulsion Conference, Nashville, TN, 1992, Paper AIAA 923156. 25. V. P. Mikhailov, Partial Differential Equations (Nauka, Moscow, 1976; Mir, Moscow, 1978). 26. B. M. Smirnov, Physics of Weakly Ionized Gases: Prob lems and Solutions (Nauka, Moscow, 1985) [in Rus sian].
Translated by É.G. Baldina
