charging of macroparticles in a pulsed vacuum arc discharge

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008 2147

Charging of Macroparticles in aPulsed Vacuum Arc Discharge

Filip Rysanek and Rodney L. Burton

Abstract—A pulsed vacuum arc discharge emits a plasma aswell as macroparticles (MPs) in the form of micrometer-sizedmolten droplets of cathode material. Due to their direction of flightand submicrometer to 100-μm diameter, these MPs often posea contamination threat for both spacecraft-based thrusters andthin-film deposition systems. The velocity, mass, and charge of cop-per MPs emitted by a 100-A arc was experimentally measured andcompared to a model based on thermionic electron emission. TheMP velocity was determined by using a time-of-flight velocity filter.The charge was calculated by measuring particle deflection in atransverse electric field. The model predicts, and the experimentalresults verify, that the charge on the MPs becomes positive oncethe plasma is extinguished, and the MP travels in a vacuum, aswould occur in a pulsed vacuum arc, versus a dc arc. Experimentalresults show a roughly quadratic dependence of particle chargeon the particle diameter (q ∼ D2), with a 1-μm particle havinga positive charge of ∼1000 electronic charges (1.6 × 10−16 C),and a 5-μm particle having a charge of ∼25 000 electronic charges.The model is particle temperature dependent, and gives q ∼ D2

at 1750 K and q ∼ D1.7 at 2200 K. Arguments are also made forlimitations on particle temperature due to radiative and evapora-tive cooling.

Index Terms—Particle charging, particle measurements,plasma properties, vacuum arcs, velocity measurement.

I. INTRODUCTION

R ECENT YEARS have seen a decrease in spacecraft size,along with a need for smaller propulsion systems. There

is a wide range of available propulsion systems for satelliteslarger than 1000 kg. Many of these scales down for use insmaller 100 kg, or even 10-kg satellites. However, spacecraftweighing on the order of 1 kg have few propulsion optionscapable of providing orbit transfer, active attitude control, oreven desaturation of momentum wheels.

A. VAT

Among the few options that do exist for satellites smallerthan 1 kg are vacuum arc thrusters (VATs) [1]–[3]. These

Manuscript received November 19, 2007; revised April 7, 2008. First pub-lished October 21, 2008; current version published November 14, 2008. Thiswork was supported in part by the Center for Microanalysis of Materials,University of Illinois and in part by the U.S. Department of Energy under GrantDEFG02-91-ER45439.

F. Rysanek was with the University of Illinois at Urbana–Champaign,Urbana, IL 61801 USA (e-mail: [email protected]).

R. L. Burton is with the Department of Aerospace Engineering, Universityof Illinois at Urbana–Champaign, Urbana, IL 61801 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPS.2008.2000880

thrusters provide thrust by utilizing the high-velocity ionsejected from the cathode of a vacuum arc. The reduced mass ofthese thrusters is achieved by using an inductive energy storage(IES) power processing unit (PPU). A semiconductor switchin parallel with the thruster is closed to draw current fromthe dc low-voltage power supply through an inductor. Oncethe switch is opened, a voltage peak of L dI/dt is produced,igniting a plasma by running current through a thin-metal-film coating between the two electrodes [4], [5]. Since thesethrusters operate in a pulsed mode, they can provide a widerange of thrust and Isp depending on cathode material, pulsefrequency, pulse shape, geometry, and other variables.

One of the factors that makes the VAT a useful and versa-tile thruster is the range of geometries available. Three maingeometries are commonly used in the thruster design. Thecoaxial geometry has a central cathode and an outer anode,separated by an insulator. In the sandwich geometry, the thrusterelectrodes and insulator material are layered sheets. Finally,the ring geometry has a cylindrical cathode with a ring-shapedanode separated by a ring-shaped insulator.

Along with the versatility of the geometry, the VAT has theadvantage of using a high-density solid (namely the cathodemetal) as the fuel. This allows the VAT to be more compact,and also allows the option of incorporating the thruster into thestructure of the spacecraft, possibly even using the spacecraftstructure as the fuel itself. A four-thruster version of the VATweighing a total of 200 g has been incorporated into a 2-kgUniversity of Illinois CubeSat [6]. Unfortunately, the launchof the CubeSat from Baikonur Cosmodrome in Kazakhstanon July 26, 2006 failed to reach orbit, and the satellite waslost [7].

The most recent version of the VAT is the magneticallyenhanced VAT (MVAT). The inductor used to store the energyduring operation is coiled around the thruster itself, providinga magnetic field which collimates the exhaust, reducing space-craft contamination and increasing thrust by 50%. In a recentstudy, the MVAT demonstrated an impulse bit of 2.7 μN · swhile firing at 50 Hz and 10 W [8]. Although this thrustersystem (including PPU) weighs 1 kg, future work will focuson mass reduction for use on even smaller satellites.

Along with the VAT, vacuum arcs are used in many appli-cations. The first published paper on the topic was written byArthur Wright in 1877. In the 1880s, Thomas Edison appliedfor a patent for the use of vacuum arcs for metal film depositionfor use in duplicating phonograms [9]. Vacuum arc depositionis a process still used today. The largest commercial applicationincludes a nitrogen background gas to form a TiN coating ondrill bits greatly increasing their lifetime. Vacuum arcs are also

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2148 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 5, OCTOBER 2008

used in high-current switching. The ability to quickly changestates from the insulating vacuum to the conducting metalvapor of a vacuum arc are desirable for such an application.Another application of vacuum arcs is vacuum arc degassingor remelting, where a vacuum arc is used to purify the cathodematerial. Degassing has the effect of removing impurities suchas sulfur, while remelting results in more uniform metal alloyswith a controllable grain size [10].

B. Cathode Spots

The seemingly simple operation of a VAT hides featuresthat have been studied for decades and continue to be studiedtoday. At moderate currents, the arc attaches to the cathodeat individual spots, on the order of 10 μm in diameter, whileattaching to the anode as a diffuse plasma [11]–[13]. Eachcathode spot can support a limited amount of current dependingon the cathode material [14]. When the current exceeds thisvalue, (approximately 100 A for copper cathode) multiplecathode spots are simultaneously formed. The cathode spotlifetime ranges from nanoseconds to microseconds [15], [16].Spots that have a lifetime on the order of microseconds aregenerally attributed to short lifespan spots that reattach to thesame location. Cathode spots generally attach to small-scaledeformations in the cathode material, due to the enhancedelectric field. The site of a previous cathode spot, has many ofthese deformations, often resulting in reattachment.

Since the current travels through a micrometer-sized area, thecurrent density at the cathode surface within the cathode spotranges from 109 to 1012 A/m2 [17], [18]. The extreme currentdensities result in a high magnetic pressure on the order of150 atm. The high current density results in heating and meltingof the cathode material, leaving small craters in the cathodesurface [19]. Larger crater diameters are often generated byarcing to oxide-free or, “clean” surfaces. Cleaning a surfaceis accomplished by prolonged arcing, or by using a differentelectrical setup to produce an intense glow discharge resultingin ion bombardment.

During the arc discharge, the cathode mass loss can beaccounted for by the emission of ions, neutrals, and macropar-ticles (MPs) in the form of molten droplets. The neutrals areevaporated from molten metal, both of the cathode and ofMPs. Neutrals account for less than 1% of the total emittedflux because the majority are ionized by electron collisions[20]. Once the neutrals are ionized, these ions are primarilyaccelerated toward the cathode by the sheath voltage, but aportion is accelerated away from the cathode. Daalder showedthat the number of ions emitted from the cathode is proportionalto the total charge transfer, accounting for 7%–10% of the totalarc current for a wide range of materials [21], [22]. Whilethe number of ions and neutrals is generally proportional tothe charge transfer, the number of MPs increases with thepulse duration [22]. The ions emitted from a cathode spot areaccelerated to high velocities ranging as high as 23 km/s, withcopper ion velocities at 13.2 km/s [23]. The mean ion chargestate is 2.0 for copper, and generally higher than 1 for mostmaterials [23]. The value of the electron temperature variesfrom 1 to 4 eV within the literature [11], [16].

The electrons necessary to carry the current are extractedfrom the cathode by a combination of thermionic heating of thecathode surface and field emission. When these two processesoccur simultaneously in what is called thermofield (TF) emis-sion, the electron yield is nonlinearly increased, allowing thevacuum arc to operate as it does. The cathode surface is heatedby ions accelerated toward the cathode in the sheath [13].The cathode surface temperature is also enhanced by resistiveheating of the arc current in the cathode. The temperature ofthe cathode spot liquid surface ranges from 2500 K–4000 K forcopper [13], [24], [25]. The field emission is enhanced by theelectric field at the surface, generated by the space charge of theions flowing toward the cathode. In this way, both conditionsfor TF emission are primarily caused by the ion flow towardthe cathode surface. The ions are generated by the ionization ofneutral vapor evaporated from the hot cathode spot surface, aswell as MP surfaces [25], [26].

The MPs emitted from the cathode are in the form ofmicrometer-sized molten metal droplets. These MPs are formedas a result of recoil from outward-directed ions acting on themolten surface of the cathode spot. Qualitatively, the highmagnetic and gas dynamic pressures at the cathode spot surfacesplashes out droplets of cathode material from the small puddleof molten metal in the cathode spot. McClure [24] estimatedthat this mechanism could eject MPs from the surface at ve-locities ranging from 20 to 200 m/s. The measured velocity ofthe MPs ranges up to 800 m/s with a peak around 200 m/sas measured by a laser Doppler anemometer [27]. It was alsoshown that the axial velocity of molybdenum MPs increaseswith axial location as well as instantaneous arc current. Radialvelocity increases only slightly with location within the arc[28]. Qualitatively, this appears to be consistent with [25],which states that the MPs are accelerated by the momentumimparted on them by collisions with high-velocity ions.

Daalder’s study of the exhaust mass of vacuum arcs [22] hasshown that the majority of MPs exit the cathode at a slightangle to the cathode plane. For copper, peak MP emission isapproximately 10◦ from the cathode plane, and 20◦–30◦ forcadmium. The study also showed that MP size decreases withincreasing angle from the cathode plane but increasing thetransfer charge increases the appearance of larger MPs at largeangles. As the MP travels through the plasma, it collides withboth electrons and ions. These collisions, along with electronemission from the surface, charge the MP during its flight [25],[29]–[31].

C. Motivation

One of the uses of vacuum arcs is the VAT described above.Due to their high scalability along with a small impulse bit,these thrusters have potential as an electric propulsion systemon a wide range of missions. However, one factor that haslimited the use of electric propulsion in general has been therisk of spacecraft contamination. The ions emitted from electricpropulsion systems usually have a very high directed velocity,limiting their contribution to spacecraft contamination. On theother hand, MPs are emitted from the cathode of a vacuum arcat shallow angles, often making their direction of flight toward

RYSANEK AND BURTON: CHARGING OF MACROPARTICLES IN A PULSED VACUUM ARC DISCHARGE 2149

Fig. 1. (Top view) Schematic of the relationship between the orifices and line of sight in the experimental setup.

the spacecraft. They have a large mass which can disrupt opticalinstruments onboard. They are also composed of a conductivematerial which can damage electronic systems.

Another common use for vacuum arcs is the deposition of athin metallic film coating [32]. The relatively high-velocity ionsprovide energetic depositing particles. The ion energy level canbe controlled using an electric field, allowing for flexibility inthe deposition energy. MPs from the vacuum arc act to degradethe uniformity of the deposited layer.

One way to reduce the number of MPs in the deposited filmis by turning the ions 90◦ with the magnetic field inside of aquarter torus [33]. This reduces the MP number density alongthe centerline by a factor of 50, but it is suspected that MPselectrically reflect from the walls of the chamber and continueto contaminate the deposition layer.

Experiments have shown that a negative bias on the substratealso reduces the number of MPs in the deposited film. However,not all the MPs are reflected by the electric field, possibly dueto MP charging within the substrate sheath [34]. Although boththese methods reduce the number of MPs in the deposited film,the existence of any MPs limits the usefulness of a vacuum arcdeposition film.

In order to reduce the MP contamination from a VAT or adeposition system, more needs to be known about the MPs. Thevelocity and size distribution of MPs, including the direction offlight, has already been studied. Although there are numerousmodels in the literature, there is little if any experimental dataon the charge of these MPs [16], [24], [29]. This paper is anexperimental study to determine the charge, mass, and velocityrelationship of MPs from a vacuum arc.

II. APPROACH AND APPARATUS

A. Approach

Simply measuring the charge of MPs emitted from a vacuumarc would not provide information such as the particle sizedistribution, necessary to help alleviate the problem of MP con-tamination. For that, the mass and velocity are also necessary.To this end, an experiment was designed to measure the chargeof MPs emitted by measuring the mass, velocity, and the effectthat a transverse electric field has on their trajectory.

1) MP Trajectory: Consider a particle traveling through auniform perpendicular electric field. The particle of mass Mp isassumed to have a constant charge q, and initial velocity vx. Theelectric field Ez is generated by charging two parallel plateseach � long, set d apart, to voltages of ±Vo/2. The particletravels in the electric field for a time �/vx, and experiences aforce (qVo/d) in the direction of the electric field. When theparticle exits, it has the same x-component of velocity as when

it entered, but also has a z-component vz parallel to Ez , wherevz is the particle acceleration times the time it spent in theelectric field

vz =q

Mp

Vo

d

�

vx. (1)

The total displacement so of the MP by the electric field is

so =qVo

2Mpd

(�

vx

)2

. (2)

The particles are collected on a polished silicon wafer wit-ness plate. In order to measure the displacement on the witnessplate, the MPs coming from the vacuum arc must first becollimated or filtered to allow only particles with a certaintrajectory to impact the witness plate. This is done by firingthe MPs through an orifice to produce a distribution area ofcollected MPs on the witness plate that is relatively smallcompared to the particle displacement. Assuming a straightline MP trajectory, the particles inside the distribution on thewitness plate correspond to the mirror image of the initiationpoint on the cathode surface. In this experiment, two orificesare used in order to reduce the chances that MPs generated bystray arcing away from the cathode are collected on the witnessplate. A top-view schematic of this setup is shown in Fig. 1,where h1 represents the width of the cathode and h2 representsthe image of the cathode or the MP distribution on the witnessplate. The diameters of the orifices are labeled d1 and d2, withd1 > d2. The distance between the cathode and the first orificeis l1, the distance between the second orifice and the witnessplate is l2, and the distance between the orifices is s.

By adjusting the location and size of the cathode, the sizeof the MP distribution can be kept to a few millimeters. Withthe addition of an electric field after the second orifice, the MPscan be sufficiently deflected to measure their deflection from theoriginal trajectory. Then, by measuring the velocity and mass ofthe MPs, the charge of each MP can be determined by solving(2) for charge as a function of particle mass Mp, velocity vx,and displacement so

q = 2soMp

�2Ezv2

x. (3)

2) MP Mass: From (3), in order to determine the chargeof the MP, both its trajectory and mass must be known. Thedisplacement so of the MP on the witness plate describes itstrajectory, while the size of the MP on the witness plate is anindication of the MP mass. In the literature, Daalder estimatedthe volume Vp of collected MPs from measurements taken ofindividual particles [22] and generated a curve fit to correlate


the measured outer diameter of the impacted particles to thevolume of an MP. In Daalder’s work, this relation took the form

Vp = aDbi = a

(4π

) b2

Ab2 (4)

where the impact diameter Di is in micrometers and the vol-ume Vp is in cubic micrometers, and the coefficients a andb for copper are 0.178 and 2.672, respectively. Because theMPs are circular on the witness plate surface, the right sideof (4) represents the volume Vp in terms of the area A ofthe impacted MP, where A = (π/4)D2

i . For this paper, anAsylum MFP-3D atomic force microscope (AFM) was used totake measurements of particles impacted on the witness plate.These measurements resulted in a detailed height profile ofthe impacted particles. A particle analysis routine was used tocalculate the volume of the particles [35], and a least squarescurve fit of the data reveals the values of the coefficient a and bof (4) to be 0.0628 and 2.828, respectively.

The software used during the analysis of the SEM imagesgives the number of pixels that each particle encompasses.This correlates to the area A of the impacted MP. Since theimpacted MPs are circular in the SEM images, the diameter Di

is calculated from the impact area A.Equation (4) along with the volume of a sphere, results in a

relation between the impacted surface area and the diameter ofthe MP during the flight. To get the actual flight diameter ofthe liquid copper, the volume is scaled by the ratio of densitiesof copper in solid to liquid form which introduces a diametercorrection of 4%. For this calculation, the density of copper inthe liquid form (at 1083 ◦C) is 8.00 × 10−15 kg/μm3 [36]. Theparticle diameter D in flight is then

D = 2(

3aρs

4πρl2bπ−b/2

)1/3

Ab/6. (5)

From [37], the density ρs of solid copper at 20 ◦C is 8.93 ×10−15 kg/μm3 making the final mass as a function of impactedsurface area

Mp = ρsVp = ρsaDbi = ρsa

(4A

π

)b/2

. (6)

3) MP Charge: Combining the knowledge of the MPmass in (6) with the equation relating the MP charge to itsdisplacement on the witness plate (3) above, we get a relationfor the charge (in coulombs) on the particle as a function ofits transverse displacement so from its original trajectory inmeters, impacted surface area A in square micrometers, andvelocity vx in meters per second

q = 2ρsd

�2Voa

(4π

)b/2

sov2xAb/2 (7)

where the values of the coefficients a and b are 0.0628 and2.828, respectively.

B. Facility Description

The experiment is conducted in the University of IllinoisElectric Propulsion Laboratory facility. The thruster operatesin a 1-m diameter 1.5-m-long chamber. The vacuum is main-tained by a 1500 L/s Balzers TPH1500 turbomolecular vacuumpump. The turbo pump is backed by a 1180 L/s Roots blower,614 L/s Roots blower, and two 71 L/s Kinney mechanicaldisplacement pumps. The thruster begins operation at a vacuumof approximately 40–50 μtorr. By the end of each experiment,the pressure has fallen to approximately 20 μtorr. The pres-sure is measured by a Granville–Phillips model 270 ionizationgauge, placed 15 cm above the turbo pump. The testing occursapproximately in the middle of the chamber, directly abovethe turbo pump, where the pressure is expected to be only afew microtorr above the measured pressure. At these pressures,the mean free path of a nitrogen molecule is larger than thediameter of the chamber.

C. Apparatus

1) Vacuum Arc Source: The design of the vacuum arc forthis experiment was based on the microvacuum arc thruster(μVAT) in the sandwich or bi-level thruster geometry [1]. Thisgeometry uses layers of flat sheets to comprise the differentcomponents of the thruster and was used on the University ofIllinois CubeSat named Illinois Observing Nanosatellite. Thefirst layer in this thruster is the cathode which is also the struc-ture of the satellite. The cathode is separated from the anodeby a ceramic insulator which is coated with a thin conductivefilm to help initiate the breakdown. Past the anode is anotherinsulator separating it from an aluminum layer used to hold thelayers together.

This thruster design is typically used with the small inductivepower supply described earlier, making it suitable for smallsatellites. However, the thruster performance is sensitive tothe thickness of the thin conductive film coating the ceramicbetween the anode and the cathode. For this experiment, the de-sign of the thruster was modified to include a trigger electrode.Fig. 2 is a schematic of the front view of the thruster, showingthe different layers listed.

The power-processing unit used in this laboratory vacuumarc source is different from the IES circuit used in the flightmodel thruster. Instead of storing the discharge energy in aninductor, it is stored in an eight-stage pulse-forming network(PFN) [38]. With 3-μF capacitors charged to −600 V, and30 μH inductors, the PFN is designed to deliver 100 A for150 μs. The designed current of 100 A is intended to limit thenumber of cathode spots formed during a single pulse [14].A resistance of 2 Ω is placed in series with the dischargeto match the impedance of the PFN. The triggering pulse isgenerated by discharging a 9.2-μF mica capacitor through a∼1 : 3 transformer. With the capacitor charged to −600 V, thetransformer secondary produces a 16.7-kV potential across anopen circuit. This voltage is sufficient to initiate the breakdownbetween the trigger electrode and the cathode, producing aplasma to initiate the main discharge between the cathode andthe grounded anode. The trigger pulse is initiated by a firing


Fig. 2. Front view of VAT used in this paper.

Fig. 3. Schematic showing exhaust direction and location of orifice withrespect to the thruster. Note: Only the insulated structure (part 1 in Fig. 2) andpart of the cathode are shown.

circuit which closes a silicon control rectifier to send the currentto the transformer. The trigger pulse is ∼35 μs long with a peakcurrent of 19 A.

The energy stored in the trigger circuit capacitor is approx-imately 35% that of the main discharge. It is uncertain whatfraction of that energy is deposited into the trigger pulse, dueto the presence of the transformer. It is possible that the triggerpulse also generates MPs. The design of this experiment did notdistinguish between MPs generated from the trigger pulse andthose generated from the main discharge.

According to Daalder [22], the angle at which the most MPsexit a copper cathode is between 5◦ and 15◦ from the cathodeplane. For this reason, the vacuum arc source was tilted sothe exhaust (cathode normal) is approximately 50◦ from thedirection of the witness plate, in order to increase the number ofMPs emitted in the direction of interest. A larger angle, whichmight further increase the number of MPs, would also increasethe chance of arcing to the ground plane instead of the groundedanode. Fig. 3 hows the orientation of the thruster with respectto the orifice and ground plane. For reference, only the anodeand part of the cathode are shown, to indicate the general shapeof the thruster.

2) Orifice and Deflection Plates: The double orifice assem-bly used in this experiment uses a pair of boron nitride plates.The primary setup, used in the majority of the experiments, usesan orifice diameter of 0.51 mm and cathode width of 0.8 mm.The secondary setup uses a smaller 0.37-mm diameter orificeand 0.4-mm-width cathode in a single test to reduce the particledistribution on the witness plate.

The witness plate is a 20-mm-tall by 30- mm-wide sectionof a diced silicon wafer. The wafer used is a P-type Si:Bwafer with a 5–25 Ω · cm resistivity. The wafer is cleanedand dried to aid in locating the MPs. With the assumptionthat the first orifice diameter d1 is greater than the second d2,using similar triangles, we can find the width of the particle

distribution on the witness plate h2 according to the followingequation:

h2 =(

h1 + d2

l1 + s

)l2 + d2. (8)

The width of the distribution on the witness plate (h2),calculated by using (8) for the primary and secondary setup are1.9 and 1.2 mm, respectively.

The electric field used to deflect charged particles after theytravel through the orifices is generated by charging two 98 ×25 mm parallel copper plates to opposite polarities. They areplaced in a Delrin holder, to keep the plates from arcing tothe ground plane above or below. The plates are separated by12.8 mm and charged to ±3500 (Vo = 7000 V), resulting in anominal electric field of 5.5 × 105 V/m.

3) Assembly: The thruster, velocity filter (described below),orifices, witness plate, and electric field plates are all placedonto a grounded aluminum plate. Once the electric field platesare aligned, another grounded aluminum plate is attached on topof the experiment downstream of the orifices. This is to ensurea uniform electric field, without a potential gradient dominatedby a single ground plane. This entire assembly, along with thetransformer is placed into the vacuum tank. Fig. 4 is an overalltop-view schematic of the thruster assembly.

4) Velocity Filter: The velocity of the MPs is determined byusing a time-of-flight velocity filter to allow particles within acertain velocity range to reach the witness plate. The velocityfilter operates by only allowing particles to pass through thefilter and orifices during a short “window” of time after the150-μs current pulse. The velocities that are transmitted areprimarily determined by the delay between the beginning ofthe arc current pulse and the opening window. This delaycorresponds to the time of flight of the particle, and rangesfrom 400 to 1100 μs. Particles traveling too fast will reachthe velocity filter before the window is open, while particlestraveling too slowly will arrive after the window has closed.

The velocity filter produces this window opening by blockingthe entrance to the orifice with a spinning slotted disk. Whenthe slot in the disk is in line with the entrance to the orifice,particles can proceed through the filter. By adjusting the spinrate, the width of the slot, and the time when the thruster isfired, the velocity of particles that will pass through the filtercan be adjusted. Fig. 5 shows a schematic view of the velocityfilter setup. A typical “window” duration is 220 μs.

If all the particles were generated at one known time, then thevelocity filter could be designed to allow all the particles trav-eling in a certain velocity range, and obstruct all those travelingfaster or slower. However, if we assume the MPs are generatedsome time during the 140-μs current pulse, particles traveling


Fig. 4. (Top view) Schematic of the overall experimental setup, along with a particle trajectory in the electric field region.

Fig. 5. Schematic of the velocity filter setup and operation.

Fig. 6. Fraction of particles allowed through the velocity filter, plotted for1100, 870, 640, and 430 μs flight times.

certain velocities will make it through the filter depending onwhen during the current pulse they were generated.

For any given velocity, the percentage of particles that willmake it through the filter is equal to the percentage probabilitythat the particle was generated at a time during the pulse, whenit will reach the filter during that opening window. If we assumethat the probability distribution of generating an MP throughoutthe pulse is constant, Fig. 6 shows the fraction of particlesthat will make it through the velocity filter for four differentdelay times Δtflight between the current pulse and the openingwindow. Table I shows a summary of the information describedin Fig. 6, and is used in later calculations.

The timing of the velocity filter is achieved by using a lightand sensor pair to sense the location of the slot as it passes apoint in its rotation.

TABLE IPERFORMANCE CHARACTERISTICS OF THE VELOCITY FILTER USED

Fig. 7. Moderate magnification of MPs on a silicon wafer witness plateshowing a wide range of MP sizes.

The motor and disk used in the velocity filter are recycledfrom a computer hard drive. The rotation rate of the disk is3600 ± 0.3 r/min. However, the electrical noise generatedduring the arc discharge reduces the precision of the motor to3600 ± 10 r/min.

D. Scanning Electron Microscope Results

A single test consists of firing the vacuum arc source atapproximately 8 Hz for 200 000 shots. After some preliminarytests were performed to verify the repeatability of the alignmentof the setup, four tests were performed to measure the charge onMPs of different velocities. Each of these tests corresponds tothe velocities listed in Table I. After these four tests, one finaltest using the secondary thruster geometry was performed toreduce the error bars of the results by reducing the undeflectedparticle distribution width.

1) MP Shape on Witness Plate: After the test, the witnessplate was removed from the experimental setup, and the MPswere observed using a JEOL model 6060 scanning electronmicroscope. Fig. 7 shows a high-resolution image of the MPscollected on the witness plate with a wide range of MPs sizes.


Particle “a” in Fig. 7 is approximately 16 μm in diameter (Di),while some of the smaller MPs such as “b” and “c” have adiameter less than 1 μm.

The shape of the MPs in the SEM images is consistent withthe premise that the MPs are in the form of molten metaldroplets when they impact the witness plate. The vast majorityof the impacted MPs and almost all of the particles with adiameter less than 5 μm have the shape of a flattened torus witha thin layer of material in the middle, such as “d,” “e,” and “f” ofFig. 7. However, the shape of the larger particles appears to varyslightly. For example, particle “e” in the bottom right of Fig. 7appears to have the typical shape. Particle “a,” the dominantparticle in the center of the image, appears to have a heightprofile where the peak is not at the outside diameter. Finally,particle “g” at the bottom of the image has the shape of a toroid,but the aspect ratio, or thickness of the toroid to the diame-ter, appears larger than the majority of the MPs. We hypothesizethat this variation is due to a combination of particle velocityand temperature at impact.

2) Data Reduction: After each test, the witness plates werescanned at 200× magnification. In order to aid in finding theMPs, the SEM was operated in backscattered electron mode,showing a high contrast between the low molecular weight ofthe background Si(28) and the Cu(63.5).

Approximately 220 images were taken for each test over anarea approximately 10 mm × 4 mm on the witness plate. Theseimages were stitched together using a software package calledPanorama Factory [39].

Once the image is converted to black and white, a softwarepackage called ImageJ [40] is used to determine the locationand pixel count of each particle. The position in the image isthen used to determine the particle displacement from its initialtrajectory, and the pixel count is used to determine the diameterof the impacted particle.

The pixel count corresponds to the surface area of the particleon the witness plate. By assuming that the MPs are circular onthe witness plate, the surface area is converted into a particleimpact diameter Di by using the equation for the area of acircle. The flight diameter, mass, and charge are then calculatedaccording to (5)–(7).

3) Atomic Force Microscopy Results: In order to correlatethe impact diameter of the MP to a flight diameter, particleheight profiles were taken using an Asylum MFP-3D AFM.Fig. 8 shows a 3-D representations of a particle after impactwith the witness plate along with cross sections of the particle.The diameter of the particles measured range from 0.3 to40 μm. An Asylum particle measurement package [35] wasused to calculate the volume of 36 particles to within anestimated accuracy of 1%–2%. The volume of the particlesmeasured range from 0.002 to 2700 μm3. Fig. 9 shows the mea-sured particle volume Vp plotted versus the impacted particlediameter Di, along with the least squares curve fit of the datapoints, used in the data reduction. The plot also includes thecurve fit of the work done by Daalder [22] in 1976.

The measured volume for the current work is lower by30% to 70% for a given particle diameter than the results ofDaalder’s work in 1976. The MPs measured in this paper have apeak height ranging from 0.6 μm for the largest particles to less

Fig. 8. (a) AFM 3-D image representation of an 11.5-μm-diameter MP, alongwith (b) two cross-sectional height profiles of a MP after impact.

Fig. 9. Particle volume measured using an AFM, plotted versus the particleimpact diameter.

than 0.1 μm. Daalder’s work determined the particle volumesby using an optical microscope designed to measure height ofa sample from a minimum of around 1 μm [22], [41]. Therange of particle impact diameters in [22] is similar to those ofthis paper, which means that particles in [22] must have had asignificantly different shape in order for optical measurementsto be taken. There are a number of possible reasons for thisdifference. First, the particles in the current system travel fartherand through a lower vacuum (higher pressure) than in Daalder’swork. Because the temperature of the MPs decreases during the


Fig. 10. Number density of particles normalized by the total number ofcollected particles versus the z-location, along with the calculated particledistribution width based on the 0.51-mm orifice geometry.

flight, this could have resulted in a lower temperature duringimpact.

Also, the witness plates used by Daalder were made ofstainless steel instead of the silicon wafer used in the currentwork. This could have resulted in a different particle shape duenot only to the interaction between the copper MP and witnessplate material but also due to the different values of thermalconductivity. The thermal conductivity of silicon and stainlesssteel are 150 and 16 W/mK, respectively, significantly less than385 W/mK for copper.

Finally, the resolution of the optical instrument in [22] whichis limited by optics to be no better than 0.5 μm, is far surpassedby the more modern AFM technology used in this paper. WhereDaalder measured the height of two points on the MP and cal-culated a volume based on that measurement, the AFM gives onthe order of 1 × 106 height measurements with subnanometerheight resolution. Daalder’s work may simply have resulted inan overestimation of the volume due to the limited resolution ofdata available.

III. EXPERIMENTAL RESULTS

A. Witness Plate Alignment

To verify the repeatability of the setup alignment, as well asdetermine the location and size of the undeflected particle dis-tribution, some preliminary tests were run. Two tests collectedparticles onto the same witness plate without the use of thevelocity filter or deflecting electric field, using the 0.51-mm-diameter orifice and 0.8-mm cathode width configuration.Fig. 10 shows a histogram of the particle locations on thewitness plate, using 0.05-mm “bins.” The width of the distri-bution is slightly less than the 1.9-mm width expected fromthe geometry. The two particle distributions are also locatedat the same z-location, indicating that the method used to alignthe witness plates is repeatable.

Recall that in the absence of a deflecting electric field, thelocation of the MPs on the witness plate corresponds to theimage of the formation point on the cathode. The minimumvalue at z = 0 in Fig. 10 indicates that more particles wereformed near the edge of the cathode than in the center, or morespecifically, more of the particles that were formed near theedge were directed toward the orifice and were collected on the

Fig. 11. Particle impact diameter versus displacement from original trajectoryfor particles traveling 110 m/s.

witness plate. This phenomenon was not studied in depth, butthe eroded shape of the cathode could have contributed to theshape of this distribution.

B. Results

Considerable data were taken at 88, 110, 145, and 214 m/sparticle velocity [42]. Fig. 11 shows the size distribution ofthe particles plotted versus the z-displacement on the witnessplate so for the 110 m/s, primary case tested. The vertical linesindicate the size and location of the particle distribution if noelectric field was used. Note that the electric field is positive inthe direction of the arrow.

The plot clearly shows that the particles collected on thewitness plates are deflected by the electric field and have a pos-itive charge. The plot also shows that the larger particles weredeflected less than the smaller particles. For small particles,each pixel used in the calculation of the diameter Di representsa significant fraction of the particle area, resulting in largeerror bars.

Using (7), the charge on each of the collected MPs is calcu-lated and plotted in Fig. 12. The displacement so is the distancebetween the location of the particle on the witness plate andthe midway point of the unperturbed particle distribution. Theelectric field used during the tests is 5.5 × 105 V/m for theprimary setup, and 5.7 × 105 V/m for secondary setup. Thelength of the electric field region � is 0.098 m. A quadratic curvefit of the form q = C2D

2 + C1D + C0 has been used to showthe trends of the data. Along with the calculated charge, thefigures show a line on the log–log plot with a slope of 2.0 orq ∼ D2 for comparison.

By comparing the quadratic curve fits of all the data taken,except for the 214 m/s test case, the particle velocity doesnot appear to have an impact on the collected charge of theparticles. The particles in the 214-m/s test case consistentlycollect more charge than the other velocities.

C. Error Analysis

Due to a number of uncertainties, the error bars associatedwith the calculated charge data are relatively large, particularlyfor smaller particles.


Fig. 12. Accumulated MP charge, plotted versus the particle diameter in flightfor particles traveling 110 m/s, along with curve fit of the form q = C2D2 +C1D + C0. Test performed using 0.51-mm orifice configuration.

There are three major sources of experimental uncertainty inthe calculated charge: the measured surface area A, the particlevelocity vx, and the displacement so. Other errors such as thevalue of the electric field and the variation in copper densityas a function of temperature are negligible for most particles.For the calculated diameter during flight, the primary source oferror is in the correlation between the particle volume and theimpact diameter.

The uncertainty in the particle impact area stems from thefact that before the software can be used to locate and measurethe size of the particles, the SEM images have to be converted toblack and white. This involves setting a threshold value where apixel brighter than the threshold is considered part of the parti-cle, and pixels darker are not. The threshold is set in such a waythat none of the background noise in the SEM images appearsas particles and is different for each test, based on the contrastand brightness settings used in the SEM. Because pixels on theedge of a particle may have a brightness near this threshold, thisprocess has the effect of slightly changing the perceived size ofMPs. The number of pixels actually changed by this processper MP is relatively small, but for small particles, it has a largeeffect on the calculated charge. At 200×, a 1-μm diametercorresponds to 4 pixels, resulting in large errors for smallparticles.

The uncertainty in the velocity is based on the finite veloci-ties that the filter allows through. Notice that as the velocitiesincrease, the transmitted velocity distribution become wider.This is due to the short flight time of the particle (∼350 μs)compared to the pulse duration (∼150 μs). This is one ofthe reasons why there are many more particles in the 214-m/svelocity case, compared to the 88 m/s. There are also uncer-tainties in the electronics of the velocity filter, based on theprecision of the motor speed, and the delay pulse duration;however, these are outweighed by the uncertainty associatedwith the design of the velocity filter.

The largest source of uncertainty is the error in the displace-ment so, particularly for the larger particles which were notdisplaced as much by the electric field as the smaller particles.Some of the largest particles were displaced as little as 2–3 mm.Since the error in that displacement is ±0.95 mm due to the sizeof the particle distribution as a result of the geometry of the

setup, the error bars on the large particles become large. Thisuncertainty assumes that the undeflected particle distribution isuniform. That is, the probability of an MP forming anywhereon the cathode surface is the same. Fig. 10 shows that thisis not the case. The actual particle distribution is weightedtoward the middle, resulting in a smaller error. In this instance,the error used to calculate the error bars is a worst casevalue.

The uncertainty in the correlation between the particle vol-ume and the impact diameter is based on the standard deviationof the measured AFM data. Although the AFM results havea high precision, the actual measurements deviate from thecurve fit enough to result in a significant uncertainty of the finaldiameter calculation.

The calculation of the diameter in flight D also dependson the density of the liquid copper. That density varies withthe temperature. The difference in copper density between themelting point (1356 K) and 2500 K is approximately 12%of the value resulting in an underestimation of the particleflight diameter by 4%. Even with such a large variation, theuncertainty in the impact area A, and the correlation betweenthe volume and impact diameter (a and b), greatly outweigh theuncertainty in the density of the liquid.

There is an error associated with the fact that the elec-tric field used to deflect the particles may not be perfectlyperpendicular to the flight of the particle. This could havethe effect of slightly increasing or decreasing the MP veloc-ity. Such an error is greatly outweighed by the uncertaintyin the particle velocity due to the design of the velocityfilter.

The electric field is generated by finite length parallel platesresulting in fringe fields near the ends of the deflecting region.This will have the effect of increasing the length of the electricfield. Although the magnitude of the electric field in the fringearea will be reduced, there will be a transverse electric fieldpresent. Because the length of the electric field region is muchlonger than the plate separation, this error is assumed to benegligible.

The analysis used to calculate the charge on the MP is basedon the assumption that the MP charge is constant throughoutits flight in the electric field. Due to the MP’s thermionicemission of electrons, the charge varies throughout its flightto the witness plate. Modeling will show that the charge onthe MP due to thermionic emission sharply increases after theplasma has extinguished, and then again when the particleenters the deflecting electric field. The time that the particletakes to reach an equilibrium charge is expected to be smallcompared to the time of flight. This means that particle chargethroughout the electric field region will approximately beconstant.

The number of particles that collide with the witness plate isvery small compared to the total number of particles generatedby the vacuum arc. It is also possible that not all the particlesthat collide with the witness plate remain attached after thecollision. Although there is no evidence of particles that did notstick, it should be noted that the results of this paper reflect onlythe properties of particles that remained attached to the witnessplate after collision.


IV. MP CHARGING MODEL

A. Background

As the MP travels from the cathode spot to the witness plate,its flight can be separated into three stages. The first stage iswhen the vacuum arc is still present, and the MP is travelingwithin the arc plasma. The second stage occurs after the archas extinguished, and the MP has not yet reached the orificeor deflecting electric field. In this stage, the MP is traveling ina vacuum with little external influence. In the final stage, theparticle has traveled through the two orifices and entered thedeflecting electric field. Each of these three stages is separatelytreated because the method of MP charging is significantlydifferent during each stage.

During the first stage, the charge on the MP is a balance be-tween three factors. When plasma particles, namely electrons,ions, and neutrals collide with the MP, they are captured. Whenthe MP collides with electrons or positive ions, the charge of theMP decreases or increases, respectively. Each MP in the plasmaacts as a floating Langmuir probe, i.e., it will assume a potentialnecessary to assure zero net current to the MP. Due to their high-directed velocity compared to random velocity, the ions can bedescribed as beamlike, while the electrons are gaslike becausetheir random velocity is much higher than their drift velocity.

MP charging and transport in vacuum arcs were also studiedby Keidar et al. [29], [43], [45]. Those studies found that dueto the higher mobility of the electrons, more electrons arecollected than ions, resulting in a net negative MP charge in theplasma. An experimental test where MPs were deflected from awitness plate by placing the witness plate at a negative potentiallater confirmed this result [34]. Before the present experiment,it was therefore predicted that the pulsed vacuum arc MP wouldalso have a negative charge.

Theoretical studies by Delzanno et al. [45] showed that forhigh temperatures, the thermionic emission of the MP must betaken into consideration when modeling MP charge in a plasma.If the MP has a sufficiently high temperature, this electronemission can alter the equilibrium charge, even reversing itand resulting in a net positive charge. The orbit motion limited(OML) theory describes the charging of particles in a plasma,taking into consideration the thermionic emission of the particle[46]. However, using a numerical simulation, it was shown thatthe quantitative results of the OML theory are only accurate forsmall particles [45]. For particles whose diameter is larger thanthe Debye length near the particle, the OML theory becomesinaccurate.

During the second stage of flight, the MP is flying in vacuumwithout the presence of a plasma, or other external influences.The MP charge is solely affected by the thermionic emissiondue to the high temperature of the particle. In this stage, asthe MP charge increases, the floating potential of the particlebecomes high enough to inhibit emitted electrons from escapingthe potential well. Once the MP floating potential becomeshigh enough, the particle reaches a potential where very fewelectrons have sufficient energy to escape, and consequently,the MP charge remains constant.

At this point, most of the electrons emitted from the particlesurface return to the particle due to its attractive potential. This

results in an electron cloud around the particle. An analysisof the thermionic emission showed that the mean free path inthis electron cloud is many orders of magnitude larger thanthe particle diameter [42]. This means that electrons emittedfrom the MP do not interact with each other, and their motionis governed purely by the local electric field.

Once the particle enters the strong deflecting electric field,however, the strength of the electric field is such that forlarger particles, the potential well around the particle is signif-icantly affected. On one side of the MP, the electric field fromthe particle surface is increased, making it more difficult forelectrons to escape. On the other side, the deflecting electricfield decreases the strength of the particle local electric field,resulting in increased electron emission. For example, for a10-μm-diameter particle charged to 10 000e the electric fieldat the surface of the particle is 5.7 × 105 V/m. This is approx-imately the same magnitude as the deflecting electric field of5.5 × 105 V/m.

When the particle charge is small, the electric field on onehalf of the particle surface is reversed, resulting in increasedelectron emission due to the negative electric field. For largerparticles, this effect results in a jet of electrons emitted fromone side of the particle. This jet further increases the chargeon the particle, until the electric field due to the particle chargecounteracts the effect of the deflecting electric field. This resultsin reduced electron emission, until the electric field at thesurface is such that very few electrons have sufficient energyto escape the particle, and thermionic emission ceases.

It will be shown later that the charge on the particle im-mediately after the arc is extinguished does not significantlyaffect the final MP charge, and that the thermionic emissionof the particle in vacuum, and in the deflecting electric field,dominates the final charge on the MP. Therefore, in this paper,primary consideration will be given to the second and thirdstages of the particle flight.

B. MP Thermionic Emission

When the MP leaves the cathode spot, it is estimated thatthe particle temperature is greater than 1500 ◦C, dependingon where in the cathode spot it was formed. The thermionicemission current density Jthe for a particle at temperature Tp

is described by Richardson’s law or the Richardson–Dushmannequation

Jthe = AT 2p exp

[− e

kTp(φ)

](9)

where φ is the material work function in electron volts and A isRichardson’s constant

A =4πmek

2e

h3= 1.2017 × 106 A

m2 · K2 (10)

where me and e are electron mass and charge, respectively, k isBoltzmann’s Constant, and h is Planck’s constant [30], [47].

1) Negatively Charged Particle: If the emitting particlebecomes negatively charged, an electric field is formedaround the MP, accelerating electrons away. In this case,


the Richardson–Dushmann equation must be adjusted for theSchottky effect. The thermionic emission is dependent on thework function of the material. This work function is reduced bythe presence of an electric field at the particle surface accordingto the following equation [48]:

Jthe = AT 2p exp

⎡⎣− e

kTp

⎛⎝φ −

√e(−Es)4πεo

⎞⎠

⎤⎦ (11)

where εo is the permittivity of free space and Es is the electricfield at the particle surface.

2) Positively Charged Particle Without External E-Field:After the plasma has extinguished, and the MP is traveling inthe open vacuum, there is no longer a mechanism to negativelycharge the particle. Thus, thermionic emission will dominatethe charge of the MP, resulting in a positive charge. A positivelycharged particle has a spherically symmetric potential humparound the particle and radial electric field lines from theparticle surface.

In order for an electron to escape the particle, not only doesit have to overcome the energy barrier associated with leavingthe particle surface, it then has to have enough kinetic energy toescape the potential hump formed around the particle.

The same analysis used to determine the Richardson–Dushmann equation is used with this added requirement, re-sulting in the following equation for the thermionic emissionof a positively charged particle without an external electricfield [31]:

Jthe = AT 2p

(1 +

eΦR

kTp

)exp

[− e

kTp(φ + ΦR)

]. (12)

In this equation, the work function φ in the exponent isadjusted by the particle floating potential ΦR.

The total current emitted from the MP is simply the currentdensity times the surface area.

3) Particle in Transverse Electric Field: Once the particletravels past the orifice and enters the electric field, (12) is nolonger valid because the equation assumes that the potentialhump that the electrons have to overcome in order to escape theparticle is spherically symmetric. Once a high external electricfield Ez is applied, the potential around the particle becomesstrongly modified, and the method of images as discussed byJackson [49] is used to calculate the potential Φ around theparticle

Φ = −Ez

(r − R3

r2

)cos(θ) +

q

4πεor(13)

where R is the radius of the MP, and r and θ are the radiusand the azimuthal angle, respectively, in spherical coordinates.Differentiating this equation in spherical coordinates gives theradial and azimuthal electric field terms

Er =Ez

(1 +

2R3

r3

)cos(θ) +

q

4πεor2

Eθ = − Ez

r

(r − R3

r2

)sin(θ). (14)

Fig. 13. (Top) Plot of the potential along the z-axis and the (dashed) potentialand (solid arrows) electric field lines near a 10-μm-diameter MP with q =3000e and Ez = 5.5 × 105 V/m.

Once the particle has passed the orifices and has enteredthe deflecting electric field, the potential contours due to theelectric field will dominate the potential in the vicinity of theparticle. The electric field at the surface of the MP on the sidenearest the positive electric field plate (upfield side) will sig-nificantly be altered by the electric field, possibly opposite insign to the electric field on the downfield side. This effect ismore pronounced for larger particles. The field lines near a10-μm particle with a charge of 3000e, entering a region ofEz = 5.5 × 105 V/m are calculated using equations (13) and(14), and shown in Fig. 13. The top plot in the figure shows thepotential along the z-axis (θ = 0 and θ = π) and assumes thatthe particle is precisely half way between the plates producingthe electric field.

As the charge of the particle increases to a point where itovercomes the Ez field, the electric field on the entire surfacewill become positive. The potential in the immediate vicinity ofthe MP on the up-field side (left side in Fig. 14) begins to forma potential hump near the particle, similar to the sphericallysymmetric potential hump in the case of no external electricfield. Farther away from this particle, the deflecting electricfield again dominates. Fig. 14 shows an example of such aconfiguration where the charge is 30 000e, and the Ez fieldremains 5.5 × 105 V/m.

In order to calculate the thermionic emission from a particleinside an external electric field, the current density is inte-grated over the surface of the particle. The equation for thecurrent density is determined by the potential experienced by anemitted electron. By assuming a radial electron trajectory (θ =constant), that potential can be calculated from (13). The trajec-tory is not typically radial; however, calculating the thermionicemission by calculating the trajectory of each electron emittedis left for future work.

If the electron sees a negative electric field, the currentdensity from the emitted location will be that of a negativelycharged particle (11). If the electric field is positive, and thepotential has a minimum value as in the left side potential inFig. 14, then the current density takes the form of a positively


Fig. 14. (Top) Plot of the potential along the z-axis and the (dashed) potentialand (solid arrows) electric field lines near a 10-μm-diameter MP with q =30 000e and Ez = 5.5 × 105 V/m.

charged particle (12). In this case, in order to escape the MP,the electron kinetic energy must be greater than the depth of thepotential well through which it travels (ΔΦ) as opposed to thefloating potential of the particle. For this reason, ΦR in (12) isreplaced with well depth (ΔΦ), which is the difference betweenthe potential at the particle surface and the potential at the localminimum. Finally, if the electric field is positive, and there isno local minimum, then it is assumed that the electron will beattracted back to the MP. This is the case on the side of theparticle nearest the negative electric field plate (0 < θ < π/2).The total current emitted from the particle is then the integralof the current density across the particle surface (15), and thecurrent density is summarized in (16).

Ithe = 2πR2

π∫0

Jthe(R,φ, Tp, q, θ, Ez) sin(θ)dθ (15)

Jthe =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(Es ≤ 0)AT 2p exp

[− e

kTp

(φ−

√e(−Es)4πεo

)]

(Es >0)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

(Ez =0)AT 2p

(1+ eΦa

kTp

)× exp

[− e

kTp(φ+Φa)

]

(Ez �=0)

⎧⎪⎪⎨⎪⎪⎩

(θ> π

2

)AT 2

p

(1+ e(ΔΦ)

kTp

)× exp

[− e

kTp(φ+ΔΦ)

](θ≤ π

2

)0

(16)

where ΔΦ is the depth of the potential well through which theelectron travels and Es is the radial electric field at the surfaceof the particle.

Fig. 15 shows the current emitted from a 10-μm-diameterparticle at 2200 K, both with and without an external electricfield of 5.5 × 105 V/m. When the particle has a low positivecharge, the electric field has the effect of reducing the totalthermionic current Ithe from 3.1 × 10−8 to 1.9 × 10−8 A.However, at high particle charge, the electric field significantly

Fig. 15. Thermionic current from a 10-μm-diameter particle at Tp = 2200 K,plotted versus the MP charge, both with and without and external electric fieldEz = 5.5 × 105 V/m.

increases the thermionic current, which increases the finalparticle charge by a factor of five for a 10-μm particle.

C. MP Temperature

The above equations for the thermionic current density areheavily dependent on the particle temperature. After the arc hasextinguished and the particle is in open vacuum, two sources ofheat loss dominate the temperature calculations for the particle.The primary source of heat loss is due to radiation which isproportional to T 4.

The second source of heat loss is the energy removed by eachelectron as it escapes the particle through thermionic emission.Each electron removes an energy equal to the work function φas it leaves the MP, resulting in a power loss due to thermionicemission Pthe = φIthe.

Another source of heat loss is the energy removed due to theMP evaporation. As copper atoms evaporate from the surface ofthe MP, they remove energy equal to the heat of vaporization.The heat of vaporization for copper is 300 kJ/mol or 4.98 ×10−19 J/particle. Using calculations for thermal evaporationfrom particle vapor deposition [50], the molecular flux F fromthe MP surface follows the following equation:

F =peq√

2πmkTp

(17)

where peq and m are the vapor pressure and molecular weightof copper, respectively. The vapor pressure of copper is

peq = 10A10−BTp Pa (18)

where A and B for copper are 10.588 and 15 821, respec-tively [51].

For all particle sizes considered, at Tp = 2200 K, the heatloss due to evaporation is equal to the heat loss due to radiation.Because the evaporation heat loss is much more sensitive to theMP temperature than the radiation term which is proportionalto T 4

p , the evaporation term will dominate the MP heat lossat temperatures above 2200 K. Above 2200 K, the high sen-sitivity of the evaporation heatloss term will quickly reduce theparticle temperature to approximately 2200 K. This means thatalthough the MP temperature is not well known, the peak MP


Fig. 16. MP charge and temperature during flight for a 1-μm-diameter parti-cle, with initial conditions: To = 2200 K, qo = 0, φ = 4.7 eV, and ε = 0.14.At t = 900 μs, the MP enters the deflecting electric field, and the chargeincreases sharply.

temperature outside of the plasma is not expected to be largerthan 2200 K.

D. Model Results

In order to calculate the MP temperature and charge duringflight, the following differential equations were solved usingMathematica’s numerical differential equation solver [52]:

T ′p[t] = − Prad[t] + Pthe[t]

ρ[Tp]CpVpK/s

q′[t] =Pthe

φeC/s (19)

where Cp is the specific heat of liquid copper 494 J/(kg · K)[37], Vp is the volume of the particle, and ρ[Tp] is the densityof the copper particle as a function of the temperature [37]

ρ[Tp] = 8002 − 0.801(Tp − 1083) kg/m3. (20)

The work function [53] and the emissivity [54] used inthese calculations are φ = 4.7 eV and ε = 0.14, respectively.Equation (19) assumes that the temperature distribution insidethe MP is constant. Namely, the heat conduction from thesurface into the center of the sphere is faster than the heat lossdue to radiation. The heat conducted away from the surface intothe particle Pcond is approximated by the equation

Pcond =κTp

aπD2 (21)

where the thermal conductivity of copper κ = 380 W/m · K.For Tp = 2500 K, the ratio Pcond/Prad is 6 × 105, indicatingthat the assumption of a constant temperature distribution insidethe particle is valid.

Fig. 16 shows the charge and temperature during flight fora 1-μm-diameter particle with initial conditions: To = 2200 Kand qo = 0. An initial charge qo = 0 is chosen because the highthermionic emission rate of negatively charged particles makesthe final charge independent of initial charge. As describedabove, the charge sharply increases when the particle entersthe electric field (∼ 900 μs). This increase is more pronouncedfor larger particles. For a 10-μm particle, the particle charge

Fig. 17. Power loss due to radiation and thermionic emission during flight fora 1-μm-diameter particle, with initial conditions: To = 2200 K and qo = 0.ΔTp = 564 K. At t = 900 μs, the MP enters the deflecting electric field, andthe thermionic loss increases sharply (shown as a discontinuity).

Fig. 18. Final MP charge and change in MP temperature ΔTp plotted versusthe starting temperature for a 1-μm-diameter particle, with initial conditions:qo = 0, φ = 4.7 eV, and ε = 0.14.

increases by a factor of 4 within 1 μs as the particle enters theelectric field. Fig. 17 shows the magnitudes of the power lostto radiation and thermionic emission during the flight. Due tothe sharp increase in electron emission as the MP enters theelectric field, the thermionic loss is shown as discontinuous att = 900 μs.

Fig. 18 shows the final charge and temperature drop afterthe particle flight versus initial temperature. Throughout theflight, for all initial conditions, the radiation term dominates thetotal power loss compared to thermionic emission. This makesthe rate of change of temperature proportional to the particlesurface area divided by the volume, which results in a greatertemperature change for smaller particles. By compiling the finalcharge data for particles of different size, a relationship betweenthe particle diameter and final particle charge is calculatedand shown in Fig. 19 along with the experimental data fromFig. 12. The charge in Fig. 19 is plotted for 5 different initialtemperatures ranging up to 3000 K.

E. Discussion

This model is primarily focused on the flight of the MP afterthe vacuum arc has extinguished. The interaction between theMP and the plasma provide the initial conditions for the abovecalculations. A model to determine the effect that the vacuumarc plasma has on the MP temperature and charge can be found


Fig. 19. Final MP charge plotted versus diameter for various initial tempera-tures, along with an approximate curve fit to the experimental data in Fig. 12.

in the literature [25], [29]. However, one of the input parametersinto that model is the poorly known temperature of the MP as itejects from the cathode spot.

The temperature in the center of the cathode spot can beas high as 4000 K [10]. However, that temperature falls offwith radial distance from the center, until it reaches the meltingpoint of copper. Thus, the MP temperature is dependent onwhere within the cathode spot it was formed, as well as theMP size. Because MPs are formed when magnetic and gasdynamic pressure splash out liquid cathode material [24], theinitial temperature is expected to be lower than the temperatureof the center of the cathode spot. The time that a particle spendsin the plasma is also not well known because of the uncertaintyin the time of formation with respect to the duration of thevacuum arc. For these reasons, the initial temperature for themodel described above has been left as a variable.

From Fig. 16, the charge of a particle with qo = 0 increases to80% of its final charge outside the deflecting electric field (t ≈800 μs) within the first 10 μs of its flight. Also, the thermionicemission exponentially increases when the particle is negativelycharged (11). Thus, although the charge of the MP in the plasmais expected to be negative due to the higher mobility of theelectrons, the time for the particle to become positively chargedis insignificant compared to the time of flight. This has theeffect of making the final charge independent of the initialcharge qo for qo < the final charge.

On the other hand, if the ion collisions or thermionic emis-sion of the particle during the arc overpowers the electroncollision rate, and the particle charge were positive when the arcextinguished, this would have the same effect as increasing theflight time. However, because the final charge is not limited bythe flight time, but instead by the final floating potential of theMP, the charge of the MP would not be affected by variationsin the initial charge.

As previously mentioned, in the beginning of the MP flight,the charge on the MP quickly increases until it reaches anequilibrium value, after which point it increases only slightly.Recall that the method used to calculate the charge on a particlefrom the experimental results assumes that the charge on theMP is constant. In order to estimate the error associated withthis assumption, the actual displacement using the charge pro-file during flight was calculated. This calculated displacement

TABLE IIPERCENTAGE DIFFERENCE IN THE CALCULATED FINAL MP CHARGE

FOR A 43% CHANGE IN THE ORIGINAL EMISSIVITY E = 0.14

was then plugged into (3) to calculate the charge based on aconstant charge assumption. For particle temperatures above2500, this error is never greater than approximately 5%. Thecharge calculated by (3) is an average charge on the MP duringits flight, which in the case of an increasing MP charge, willunderestimate the actual final charge.

The actual value of the emissivity of copper varies from0.112 to 0.20 in the literature [55]–[57]. One study showed thatthe emissivity increases with temperature to a value of 0.20 at1800 K [57]. The sensitivity of the calculated final charge tothe emissivity is not severe. Table II shows the percentage dif-ference that a 43% change in the emissivity has on a particle ofvarious size for an initial temperature of 2200 K. A smalleremissivity results in a greater final charge because the tempera-ture drop throughout the flight is reduced. The largest effectis on a 1-μm particle with a reduced emissivity of 0.08,resulting in a charge increase of 18%. As the particle diameterincreases, this effect quickly falls resulting in a 6% change in a3-μm-diameter particle and a 1% change in a 10-μm-diameterparticle.

There is also some uncertainty in the literature as to the workfunction of liquid copper. Some measurements indicate that thework function can be as low as 4.4 eV [53], [58]. The greatesteffect of lowering the work function occurs when the startingtemperature is below 2000 K. Above To = 2000 K the effectof reducing the work function to 4.4 is small compared to theuncertainty of the temperature [42].

V. SUMMARY AND CONCLUSION

A. Summary

This paper described the design and implementation ofan experiment to measure the charge on MPs leaving theexhaust plume of a pulsed VAT. The MPs exiting the VATare in the form of molten copper cathode droplets. Theexperiment accomplished this by first limiting the velocity ofMPs examined to a small range with a time-of-flight velocityfilter. Once a particle traveled through the velocity filter, it wasexposed to a transverse electric field generated by chargingtwo parallel plates to a positive and negative high voltage. Bymeasuring the change in trajectory of the MPs after travelingthrough the electric field, the charge was calculated.

The velocity filter was designed to pass particles during ashort time window using a spinning slotted disk. Only particlesthat arrive at the velocity filter when the slot is in the correctposition will make it through. By adjusting the time whenthe vacuum arc fires relative to the position of the slot, onlyparticles that are traveling in a certain velocity range will make


it through the filter. Due to the duration of the arc, this methodis more accurate with longer flight times, i.e., lower velocities.

The primary mechanism that determines the MP charge afterthe vacuum arc has extinguished is thermionic emission. Amodel of the thermionic emission was developed to calculatethe charge on the ejected MPs. From the model, the electricfield has a significant effect on the MP charge. However, afterentering the electric field region, the MP reaches a charge80% of its final value within 1% of its flight time. This fastresponse of the MP charge to the electric field, allows the ap-proximation of constant MP charge used during the experimen-tal calculations. Although the electric field affects the charge,an electric field could possibly be employed in an attemptto reduce MP contamination on a spacecraft. The knowledgegained by employing an electric field in this experiment wasimportant to help develop a method of deflecting MPs fromtheir original trajectory.

The model results indicate that the MP charge after the archas extinguished is almost independent of the charge duringthe arc. When the arc extinguishes, and there is no plasmato charge the MP negatively, thermionic emission dominatesthe charging of the MP, resulting in a positive charge. As theMP charge increases, the thermionic emission continues, butemitted electrons are attracted back to the particle due to itslocal potential well resulting in an asymptotic limit to charge,an effect amplified by particle cooling. As the particles enter thedeflecting electric field, the potential well around the particle isaltered to the point where more electrons are able to escape.This causes the charge on the MP to increase, until the localelectric field around the MP is strong enough to dominate thepotential in the vicinity of the MP and reduce or eliminate theeffect of the external electric field.

An early model of the thermionic emission of the MPsby Rysanek et al. [59] determined that the final accumulatedcharge approximately follows:

q = C2Dγ (22)

where C2 is a constant and γ is approximately 1.0 for particleslarger than D = 2 μm [59]. A curve fit of the experimental data(see Fig. 12) indicates that γ ≈ 2 and C2 ≈ 1000. By includingthe effect of the electric field in the model of the MP thermionicemission, the value of gamma increases from 1.0 to 2.0 for astarting temperature To = 1750 K, and 1.6 for To = 3500 K(see Fig. 19), which more closely matched the experimentalresults. For the To = 1750 K case, the magnitude of the chargeis lower than the experimental date. Although the temperatureof the MP is not well known, models of the cathode spot, aswell as the effect that the plasma has on the MP temp indicatethat the MP temp after the arc will be greater than 2200 K.

The difference between the model described above andthe experimental data is likely to be accounted for by a moreprecise model of the electron motion around the MP. Theassumption of radial electron trajectory is an approximationof the actual electron motion, and a more in-depth analysis issuggested as future work.

Due to their interaction with the plasma, MPs ejected fromthe cathode spot of a vacuum arc are initially charged negatively

due to the higher electron mobility. In a pulsed arc, oncethe vacuum arc extinguishes thermionic emission from theparticle will begin to dominate, resulting in a positive charge.This will also be the case for a dc arc, because the plasma den-sity will decrease as the particle travels away from the vacuumarc source. As the particle travels away from the spacecraft,both the positively charged particle and the emitted electronsmay collide with the spacecraft, affecting the charge on thespacecraft. If the particle does not collide with the spacecraft, itwill solidify into a solid copper sphere in less than 100 ms for a10-μm particle due to heat loss due to radiation and evaporation.For a typical velocity of 100 m/s this will occur about 10 m fromthe spacecraft.

During the experiment, the trajectory of MPs larger than1 μm in diameter was changed by no more than approximately5◦. This was done using a relatively strong electric field. Largerparticles on the order of 10 μm in diameter were deflected lessthan 1◦. A system of electric fields could be used to reduce MPcontamination on a spacecraft, but care would have to be takenin the design of such a system because of the limited effect thatthe electric field has on the larger MPs.

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[59] F. Rysanek, R. L. Burton, and M. Keidar, “Macroparticle charging in apulsed vacuum arc thruster discharge,” presented at the Joint PropulsionConf., Sacramento, CA, Jul. 9–12, 2006, Paper AIAA-2006-4499.

Filip Rysanek received the M.S. and Ph.D. degreesin aerospace engineering from the University ofIllinois at Urbana–Champaign, Urbana, in 2002 and2007, respectively.

He has worked for CU Aerospace, Champaign, IL,as well as Alameda Applied Sciences Corporation,San Leandro, CA. He has worked on a numberof topics, including pulsed plasma thruster perfor-mance, chemical oxygen and iodine laser system de-sign, lunar regolith beneficiation, along with vacuumarc thruster design and analysis.

Dr. Rysanek is a member of the American Institute of Aeronautics andAstronautics.

Rodney L. Burton received the B.S.E. and Ph.D.degrees in mechanical and aerospace engineeringfrom Princeton University, Princeton, NJ, in 1962and 1966, respectively.

He is a Professor of aerospace engineering withthe University of Illinois at Urbana–Champaign,Urbana. His areas of research include electromag-netic and electrothermal space thrusters and di-agnostics, high-pressure metal particle combustion,electromagnetic railguns, and vehicular Rankine cy-cle engine systems.

Dr. Burton is an Associate Fellow of the American Institute of Aeronauticsand Astronautics.

charging of macroparticles in a pulsed vacuum arc discharge

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