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A Theoretical Analysis of Vacuum Arc Thruster Performance

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A Theoretical Analysis of Vacuum Arc Thruster Performance ATheoretical Analysis of Vacuum Arc Thruster Performance ∗ James E. Polk, Mike Sekerak and John K. Ziemer Jet Propulsion Laboratory, M/S 125-109, 4800 Oak Grove Drive, Pasadena, CA 91109 (818) 354-9275, [email protected] Jochen Schein, Niansheng Qi and Robert Binder Alameda Applied Sciences Corp, 2235 Polvorosa Ave, San Leandro, CA 94577 (510) 483-4156, [email protected] AndreA´ nders Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (510) 486-6745, [email protected] IEPC-01-211† In vacuum arc discharges the current is conducted through vapor evaporated from the cathode surface. In these devices very dense, highly ionized plasmas can be created from any metallic or conducting solid used as the cathode. This paper describes theoretical models of performance for several thruster configurations which use vacuum arc plasma sources. This analysis suggests that thrusters using vacuum arc sources can be operated efficiently with a range of propellant options that gives great flexibility in specificimpulse. In addition, the efficiency of plasma production in these devices appears to be largely in- dependent of scale because the metal vapor is ionized within a few microns of the cathode electron emission sites, so this approach is well-suited for micropropulsion. Introduction are initiated at locations where there are local micro- protrusions or dielectric inclusions which cause lo- Vacuum arcs, or discharges burning in metal vapor cal enhancement of the applied electric field. Field liberated from the cathode into an interelectrode gap emission in these regions causes explosive vaporiza- initially at vacuum, produce high velocity, highly tion of the microprotrusion or inclusion due to very ionized plasma flows which can be exploited for rapid Joule heating. A combination of Joule heating propulsion applications. On cathode surfaces which and ion bombardment heating sustains the tempera- are too cold to support bulk thermionic emission, tures required to emit electrons and vaporize cathode current continuity across the metal-vacuum interface material. The loss of cathode material causes the for- is maintained through one or more highly mobile, lu- mation of a tiny crater on the surface. As the crater minous spots. Although the bulk cathode tempera- diameter grows, the power deposition by ohmic heat- ture is relatively low, the local temperature in these ing and ion bombardment decreases. Eventually the spots is well over the boiling point of the cathode temperature drops to the point where it is no longer material and electrons are emitted by a combination possible to sustain electron and vapor emission and of thermal and field emission. These emission sites the site extinguishes. The characteristic site lifetime ∗ Copyright c 2001 by the California Institute of Technol- appears to be on the order of a few tens of nanosec- ogy. Published by the Electric Rocket Propulsion Society with onds [1, 2, 3, 4, 5]. The resulting craters have a permission. † diameter that is typically only 1-10 microns [6, 7], Presented at the 27th International Electric Propulsion Con- although gross melting may result in larger struc- ference, Pasadena, CA, 15-19 October, 2001. 1 POLK: VACUUM ARC THRUSTER PERFORMANCE 2 tures [8, 9, 10, 11, 12]. The extinction of an emis- vided by the consumable cathode, no gas feed system sion site is generally followed by the ignition of a is necessary. This not only reduces mass and volume, new site at a nearby microprotrusion, often appar- buteliminates the need for low leak-rate valves. It is ently self-generated by the molten metal flows from very difficult to achieve low leak rates in microfab- the previous site. The luminous spot therefore ap- ricated valves, so this is a significant advantage over pears to move over the cathode surface. conventional ion engines for microspacecraft appli- Extraordinary conditions are achieved in the cations. cathode spots. Current densities on the order of 108 Vacuum arc discharges exhibit certain regular- A/cm2 [13, 14] in the emission site and heat fluxes ities in their behavior which allow simple, semi- of 108–109 W/cm2 [15] produce rapid vaporization empirical models of thruster performance. The pur- and ionization of the cathode material. Plasma den- pose of the models developed in this paper is to pro- sities in the near-cathode region reach 1020–1021 vide guidance in choosing cathode materials and ex- cm−3 [5, 2], nearly the density of the solid metal. plore the performance potential of several implemen- The plasma is generally almost 100 percent ionized, tations of vacuum arc thrusters. We will first describe often with multiple charge states [16]. What is truly the performance models and then discuss the perfor- remarkable is how easy it is to generate these condi- mance characteristics of a number of candidate pro- tions in cold cathode arc discharges. These extreme pellants. environments lead to vigorous acceleration of the metal vapor plasma away from the cathode spot, and ASemi-Empirical Performance Model velocities achieved in the expanding plasma plume are typically on the order of 104 m/s [17, 18]. Vacuum Arc Plasma Sources Vacuum arc-generated plasmas can be used in several different types of propulsion devices. The Mass is eroded from cathode spots in the form of plasma plumes produced in cathode spots are highly metal vapor ions, droplets or “macroparticles,” and directional, and can be used to produce thrust di- neutral vapor [19, 20, 21], although the majority of rectly. Vacuum arcs may also be used as plasma the neutral vapor appears to be evaporated from the sources in ion accelerators such as ion or Hall macroparticles in flight [20, 22]. For sufficiently low thrusters. The focus of this paper is on application values of energy deposited in the cathode, the total of vacuum arc discharges in thermal Vacuum Arc erosion rate m˙ t scales with the arc discharge current Thrusters (VAT’s) and in electrostatic Vacuum Arc Jd [23, 24, 25], Ion Thrusters (VAIT’s). The unique physical condi- m˙ = E J , (1) tions achieved in vacuum arcs offer several potential t r d advantages in these devices. A highly ionized plasma The erosion rate Er is constant in this regime be- is generated very efficiently in cathode spot opera- cause the mass loss occurs primarily within single, tion. Because the ionization process occurs within isolated emission sites. Higher current levels are ac- tens of microns of the emission site, the plasma commodated by more emission sites. Above a cer- source is inherently scalable to very small sizes for tain threshold current or during long pulses the tem- micropropulsion applications. No magnetic field is perature fields of individual emission sites may over- required for an efficient discharge, unlike electron lap and cause gross melting. Under these condi- bombardment ion engines. Vacuum arc discharges tions the droplet erosion rate may increase dramat- can be operated in pulses with no sacrifice in plasma ically [26, 27, 28, 29, 30, 31, 32, 33, 34]. production efficiency, so the duty cycle can be varied The ion component of the mass flux can be de- to match the engine power to that available from the scribed as a current Ji,whichisthe sum of the cur- spacecraft. This can enable the use of high specific rents JZ associated with the fluxes of ions in vari- impulse electric thrusters for power-constrained mi- ous charge states Z.Experiments over a wide range crospacecraft. Finally, because the propellant is pro- of conditions show that the ion current in the spot POLK: VACUUM ARC THRUSTER PERFORMANCE 3 plasma plume can be expressed as a nearly constant fraction fi of the discharge current ranging from 0.07 to 0.1 [23, 26, 31]. We can therefore write the ion flow in the cathode spot plasma as φ Ji = JZ = fiJd (2) l Z and the ion mass flow rate as dA1 θ JZ Mi fiJdMi − m˙ = = Z 1, (3) i Ze e Z where e is the charge on an electron, Mi is the mass − Figure 1: Geometry used to define ion current distri- of the ion, Z 1 represents the mean inverse charge bution. state, −1 fZ 0.4 Z = . (4) Cosine Distribution Z Z Exponential Distribution, k=4.5 0.3 and fZ is the ratio of the current due to a single charge state to the total ion current, 0.2 JZ f = . (5) Z J i 0.1 This charge state distribution (CSD) is assumed to Current Density Distribution be constant for a given cathode material. An equi- 0.0 librium composition of multiply charged ions is cre- -150 -100 -50 0 50 100 150 ated in the hot, high density metal vapor plasma near Angle from Surface Normal (deg) the emission zone and “freezes” at some point in Figure 2: Normalized angular ion current distribu- the plume from the cathode spot as the recombina- tion for cosine and exponential functions. tion rate drops due to plasma expansion and cool- ing [35]. Measurements in pulsed discharges show that the CSD for a certain material changes over the the emission site [40]. Experimental measurements first 100 µsofthedischarge and then becomes rela- of the ion current density in the plume expanding tively constant [36]. The CSD does not vary signifi- from the cathode region in vacuum arcs suggest that cantly with discharge current over a range of 50-1200 it follows a cosine [20, 41, 42] or exponential dis- A [4, 37], but may be influenced by applied magnetic tribution [40]. The geometry used in defining these fields and higher discharge currents [38, 39]. The distributions is shown in Fig. (1). For a cosine dis- fraction of the total mass loss that occurs in the form tribution in polar coordinates the current density at a l φ of ions is given by the expression radius and angle defined from the surface normal due to mass generated in area dA1 on the cathode −1 fiMiZ surface is Fi = .
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