Tel Aviv University

 

RESEARCH PROJECTS

Deposition of Hard, Transparent, and Electrically Conducting Coatings on Transparent Polymer Panel

Transparent polymer sheets are used as window material in numerous applications, including: helmet visors, control room windows, clean room windows and cabinets, shatter-proof windows for various applications, and in particular for aircraft windows and canopies. Polymers such as polycarbonate (PC) and acrylic (PMMA) are desirable in these applications because of their strength and impact resistance, and their low weight. However, they are very soft and hence prone to scratching and pitting. In addition, they are electrically insulating. Scratching and pitting often limit the lifetime of these devices. In several of them, electrical conductivity is desired for invisible window defrosters, invisible antennae, and reduction of electromagnetic wave penetration. The objective of this project is to develop a coating, and means of applying it, for protecting the surface of polymer sheets from scratching while making the surface electrically conductive.

The initial strategy was to develop a two layer coating, to be placed on the outer surface of the polymer sheet: a first layer of tin oxide for electrical conductivity, and an outer layer of “diamond-like-carbon” (DLC) – a very hard amorphous carbon film. In the first stage, these films were deposited using filtered vacuum arc deposition system, on small glass and polymer substrates. Tin oxide was deposited at a rate of about 10 nm/s using a 160 A arc in an oxygen gas background at a pressure of approximately 4 mTorr. As deposited coatings with a surface resistivity of less than 100 W¤Œ and with a relative optical transmission exceeding 85% were achieved. The coatings on the plastic substrates had a tendency to crack, especially on PMMA. However, under appropriate conditions, in particular by limiting the heat flux to PC substrates, undamaged coatings could be deposited. The tin oxide coated PC had a scratch resistance 50 times greater than the uncoated substrates, for light scratch loads. On the other hand, attempts to deposit DLC on tin oxide coated substrates were not successful. However, thin DLC coatings could be applied directly to the polymer substrates. Preliminary calculations using a theoretical model indicated that there was little to gain in indentation resistance from the increased hardness of DLC in comparison to tin oxide. Therefore it was decided to utilize a single tin oxide layer in future tests.

Fig. 1. Filtered vacuum arc plasma jet impinging on a glass slide substrate.

Fig. 2. Optical interference rings on a SnO2 coated glass substrate

 

The second stage of the project is to coat large PC panels with tin oxide. A 60 cm wide rectangular filtered vacuum arc deposition system was designed and constructed, which includes a substrate carriage which transports a 40x40 cm substrate past a rectangular plasma filter. Currently, a Sn plasma source for this system is being tested. The source has a nominal current rating of 1 kA, and uses a 44 cm long rectangular Sn cathode.

system 4 picture

Fig. 3. Rectangular filtered vacuum arc deposition system.

Sponsor:

Ministry of Science – Technological Infrastructure Program

Participants:

EDPL: (R.L. Boxman, S. Goldsmith, V. Zhitomirsky, E. Gidalevich, E. Shuryan, T. David, Y. Daniel)

Israel Aircraft Industries

Holon Academic Institute of Technology

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Carbon Nanotube Production by Short Arc Pulses in Air

Carbon nanotubes (CNTs) are rolled-up sheets of graphite graphite is the primary ingredient in pencil leads. A sheet of graphite is composed of carbon atoms arranged in a flat hexagonal pattern like chicken wire mesh. The CNT is thus a hollow tube, with an inside diameter of typically 7 nm. CNTs have exciting potential applications as electron emitters for flat display panels and probe tips for scanning microscopes. This project explores a new method to produce CNTs in the open air on room temperature substrates.

Pulsed arcs were sustained in air between a thin counter-electrode and the sample. The arcs were ignited either by (a) mounting the counter-electrode on a vibrator, which periodically (at 100 Hz) contacted the sample while a voltage was applied between them (contact mode), or (b) applying sufficiently high voltage pulses to break-down the gap between the thin electrode and the sample (break-down mode). The samples were mounted on an x-y table connected to step motors, which scanned the substrate position relative to the counter-electrode. Pulse ignition and sample scanning were controlled by a personal computer. Arc pulses with peak currents of 7-100 A, and pulse lengths of 0.2-20 ms, were applied. The substrates were: a) 10X10 mm graphite plates (in the both modes), and b) copper grids coated with a carbon film (TEM grids, mesh 200) in the break-down mode. Graphite counter-electrodes (1X4 mm) were used in both modes and 0.1 mm diam steel rods in the break-down mode. In the contact mode, the samples were connected as the arc cathode and counter-electrodes were connected as the anode. Both polarities were tested in the break-down mode. The surface morphology of the treated samples was studied with scanning electron microscopy (SEM). The CNT structures were investigated by high-resolution transmission electron microscopy (HRTEM).

On the graphite sample surfaces processed in the contact mode, there were multiple affected regions, each consisting of concentric zones: (1) a central zone with a smooth-walled crater of ~5 mm diameter, (2) an annular zone with an outer diameter of ~200 mm having a fine-grain structure (0.3-0.5 mm), and (3) an outer annular zone (outer diameter ~400 mm) with grain diameters of 1-3 mm. Randomly orientated fiber-like structures with characteristic diameters of ~10 nm and lengths of ~1000 nm were observed in zones 1 and 3.

Grid samples were exposed to 0.2 ms, 7-10 A arc pulses of both polarities in the break-down mode. No zone structure was observed. CNTs were observed on the grid samples with both polarities and types of counter-electrodes. HRTEM investigation showed that CNTs were produced in the form of closed multi-wall nanotubes (MWNTs) with diameters of 10-30 nm and lengths of 0.5-1 mm. There were typically 5-15 walls, and the separation between the walls was ~0.35 nm, close to the spacing between the graphite planes.

TEM photograph of a CNT produced on sample 26. Note bill-like cap on left end, and asymmetrical hemispherical cap on right end.

HRTEM photograph of a MWNT produced on sample 22.

Participants: Dr. N. Parkansky, Prof. R.L. Boxman, Prof. B. Alterkop, Mr. Y. Zontag

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Effect of an electric field perpendicular to copper oxide films on their growth and structure

Two copper disks were connected as d.c. capacitor electrodes while heated in air. The capacitor was placed in a furnace with controlled temperatures of 500°C and 600°C for 1 h with an imposed electrical field of 2.5´103 V/cm. The surface structure of the electrodes was examined by X-ray diffraction (XRD), scanning electron microscopy and energy dispersive X-ray analysis before and after the treatment.  After annealing, XRD showed the presence of Cu, Cu2O and a small quantity of CuO. The O/Cu atomic concentration ratio after annealing at 500°C was 2/3 on the anode and 1/2 on the cathode. The CuO phase was not observed after annealing at 500°C, whereas annealing at 600°C increased the intensity of the CuO XRD lines associated with the anode relative to the CuO XRD lines associated with the cathode. Areas with approximately equal concentrations of Cu and O were observed at 600°C only on the anode. After annealing at 600°C, the grain size on the anode was approximately 2.2 mm, whereas on the cathode the observed grain size was approximately 4 mm. The joint effects of a higher annealing temperatures and electric fields were also studied.  Electric fields in the range of 0-5 kV/cm were applied between the copper electrodes placed in the setup described above during one hour of oxidation at temperatures from 100 to 500°C. A dense and homogeneous layer of CuO with a characteristic grain size of 2-4 mm was formed on the anode. The oxide on the cathode and on a sample annealed without applied voltage consisted of disconnected CuO grains distributed over a background of smaller Cu2O grains. The grain sizes were 6-10 mm and 1.5 mm, respectively, on the cathode at 5000 V/cm, and 5-7 mm and 1 mm, respectively, on the sample heated without applied voltage. Oxide thickness and mass were greater on the anode than on the cathode. For applied fields greater than 1000 V/cm, a decrease of the electrode mass were observed, resulting from spallation of the oxide layers. The cathode mass decreased less than that of the anode, whose decrease was smaller by a factor of 13 at 5000 V/cm in comparison to its decrease at 1000 V/cm. A leakage current between the electrodes was observed for T³400°C.

A physical model was proposed to explain the observed formation of different oxides on the cathode and anode, based on the influence of the applied electric field on oxygen adsorption.

Sponsor: Israel Science Foundation. Project completed 9/2001.

Participants: Dr. N. Parkansky, Prof. B. Alterkop, Prof. S. Goldsmith, Prof. R.L. Boxman

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ZnO Thin Films in the EDP lab 

ZnO is considered one of the “hottest” materials in the solid state “world”, and there are specific conferences and workshops dedicated to this material alone.

The objective of the present project is to produce ZnO thin films by filtered vacuum arc deposition, and characterize their properties. 

 

In the first stage of this study, a series of samples were deposited with different O2 pressure, and film properties were determined as a function of the O2 pressure. In the second stage, samples are being studied in a narrow range of pressures and arc currents, based on the first stage.

Refraction index, extinction coefficient and film thickness are being determined from measurements of the relative spectral transmission.

Electrical measurements are likewise being used to determine electrical resistivity, hall mobility and charge carrier concentration.

Structural examinations (such as XRD and XPS) are used to study the film composition and microstructure.

In the near future we plan to study effects of the substrate temperature, bias, injected transverse current and doping (with Al, Sb, Mg and more) on film properties.

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Hot Refractory Anode Vacuum Arc. Experiment.

A new vacuum arc mode was discovered and named the hot refractory anode vacuum arc (HRAVA). In the HRAVA, cathodic material is emitted by cathode spots, and transported toward the anode by plasma jets. This material is re-evaporated at the hot anode surface, or is deflected by high-pressure stagnant plasma adjacent to the anode surface.

The HRAVA is sustained between a thermally isolated refractory anode and a water-cooled copper cathode. The arc starts as a multi-cathode-spot (MCS) vacuum arc and then transforms to the HRAVA mode. In the MCS mode, the cathodic plasma jet deposits a film of the cathode material on the anode. Simultaneously, the temperature of the thermally isolated anode begins to rise, reaching eventually a sufficiently high temperature to re-evaporate the deposited material, which is subsequently ionized in the interelectrode gap. The transition to the HRAVA mode is completed when the density of the inter-electrode plasma consists mostly of ionized re-evaporated atoms – the anode plasma. The evolution of the HRAVA mode is characterized by the propagation of a luminous plasma plume from the anode to the cathode and in the radial direction (see Fig.1). The HRAVA can potentially be utilized as plasma source (e.g. for coatings) with substantially reduced macroparticle (MP) contamination, in comparison to MCS vacuum arc plasma sources.

HRAVA thin film deposition experiments and plasma diagnostics were conducted with an arc contained in a cylindrical stainless steel chamber, 500 mm long and 160 mm in diameter, inside of which the electrodes were mounted. Arc currents of 175, 250 and 340 A and a chamber pressure of 3ª10-5 Torr before arc initiation were used. A water-cooled 30 mm diameter copper cylindrical cathode and graphite anode of 32 mm diameter and 30 mm height were used. Two cylindrical Mo radiation shields with 60 and 70 mm diam surrounded the anode to reduce radiative heat loss. The inter-electrode gap was about 1 cm. A substrate chamber was attached to the arc chamber, connected through a shutter, which was opened during deposition.

Interelectrode gap. The HRAVA was studied experimentally using a Langmuir probe and two types of thermal probes. The plasma density, electron temperature, plasma energy flux, cathode erosion, mass deposition rate on a substrate, and MP contamination in the deposited films were measured. The plasma parameters were measured when the arc initially operated as an MCS arc and at a later stage when the anode heated up and metal vapor originating at the cathode was re-evaporated from the hot anode. The electron temperature initially was about 1.6 eV and decreased with time to a steady state value of about 1.1 eV after 20 s. The plasma density increased with time from about (3-4)ª´1014 cm-3 reaching about 2ª1015 cm-3 after 60 s in a 340 A arc. The radial plasma energy flux generated by 175 and 340 A arcs was about 1 and 2 MW/m2, respectively, at 1.6 cm from the electrode axis.

Participants:   EDPL: (I.I Beilis, R.L. Boxman and S. Goldsmith)

                                    University of Michigan: (M. Keidar)

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Radially expanding plasma. The electron temperature, plasma density, and plasma potential were measured with a Langmuir probe in the radially expanding plasma streaming from the interelectrode gap of the HRAVA. Plasma parameters were measured when the anodic plume was formed, during the first 20 s after arc ignition, at points located 3 to 18 cm from the electrode edge. In addition, the ion energy distribution was determined using a retarding field analyzer. As a function of radial distance at 20 s, the electron temperature decreased from 1.2 eV to 0.6 eV, the plasma potential decreased from 3.5 V to 1.5 V, and the plasma density decreased from 2.1013 cm-3 to 1.8.1011 cm-3. The measured mean ion energy per unit charge state increased from 8 eV at an axial distance of 3 cm to 20 eV at 18 cm. The electron temperature and plasma potential decreased with time by about 0.4 eV and 2 V, respectively, near the electrode region. The relatively small magnitude of the ion energy observed near the gap may be caused by non-elastic resonance charge exchange scattering of the cathode jet ions with atoms that are re-evaporated from the anode. The observed ion acceleration at larger distances from the gap is caused by the gradient in the electron pressure caused by the plasma expansion from the interelectrode gap into the ambient vacuum.

Participants:  EDPL: (I.I Beilis, R.L. Boxman and S. Goldsmith)

                                   Irkutsk State University: (V. Paperny)

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Metallic thin film deposition. The HRAVA was investigated as a plasma source for depositing coatings. Arc currents of 155-250 A were sustained for periods of up to 120 s between a water-cooled Cu source cathode, and a non-consumable refractory anode, which was heated by the arc. Cu coatings were deposited on ground stainless steel and glass substrates. A shutter controlled when and how long the substrate was exposed to the plasma. The coating rates were measured by weighing the substrates, and the MP's presence on the coating surface was examined by optical microscopy.

                  

Text Box: Figure 2. Coating from conventional cathodic vacuum arc.

Text Box: Figure 3. Coating from HRAVA.

 

Films formed in a 30 s exposure at the beginning of a 175 A arc, when it operated in the cathode spot mode, were heavily contaminated with MP’s (Fig.2). The density of MP’s with diameters of 3-50 mm was ~ 103 mm-2. However, with a 30 s exposure, which began 30 s after arc initiation, by which time the arc was in the HRAVA mode, the MP density was reduced to about 1 mm-2 (Fig.3). The HRAVA deposition rate was about 0.6 mm/min in the anode region and 1-2mm/min in the cathode region onto substrates placed at distance of about 110-120 mm from the arc axis. The HRAVA deposition rate is comparable (exceed by factor 2) to filtered cathode spot vacuum arc deposition, but over a much larger deposition area in radial direction.

Participants: EDPL: (I.I Beilis, S. Goldsmith and R.L. Boxman)

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Hot Refractory Anode Vacuum Arc. Theory.

Interelectrode gap. Two approaches, steady state and time dependent, were considered. In the steady state, the calculated plasma and anode parameters (temperature, effective voltage) were compared with that measured. In the time-dependent case, the transition time and the evolution of arc parameters in time were investigated. The model of the various physical processes taking place during the transition to the HRAVA mode was represented by a system of equations describing atom re-evaporation, atom ionization through the interaction of the cathode jet and the inter-electrode plasma with the anode vapor (Fig. 4). The plasma plume propagation, plasma radial expansion, plasma energy and heavy particle density balance was also described by the system of equations. The time dependence of the anode heat flux and the effective anode voltage were obtained by solving these equations. In addition, the time dependent plasma electron temperature, plasma density, anode potential drop, arc voltage and anode temperature distribution were calculated and compared with previous measurements. It was shown that the observed decrease of the effective anode voltage with time during the mode transition is due to a decrease of the heat flux incident on the anode surface from the cathode spot jets.

Participants: EDPL: (I.I Beilis, S. Goldsmith and R.L. Boxman)

 

 

 

Text Box:  
Text Box: Cathode
Text Box: Anode
Text Box: Cathode jets
 

 

 

 

 

 

 

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Radially expanding plasma. The free, steady state, two-dimensional radial plasma flow initiated between a pair of disc-shaped electrodes of a hot anode vacuum arc was analyzed in the hydrodynamic approximation. Studies include the influence of the self magnetic field on the plasma density, velocity, and radial spreading of the arc current and potential distribution. The free plasma boundary was calculated by solving the equations for the normal and tangential velocity components at the free boundary. It was found that the plasma significantly expands over a radial distance of about half of the interelectrode gap, starting from the electrode edge -- the plasma density in the center plane decreases by factor of 2, whereas the density of the fringe current decreases by a factor of 10. The self magnetic field does not influence the plasma flow and current spreading at radial distances larger than the interelectrode gap. The potential distribution is strongly non-symmetric with respect to the central plane due to the influence of the plasma density gradients on the current spreading.

Participants: EDPL: (I.I Beilis, R.L. Boxman and S. Goldsmith)

           University of Michigan: (M. Keidar)

                               University of Minnesota: (J. Heberlein and E. Pfender)

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Future HRAVA investigation. In order to minimize MP contamination in the plasma flux, future experiments will be conducted with different electrode geometries. In particular in the present time the HRAVA electrode assembly is constructed with inclined anode surface. A vacuum chamber with water-cooled walls will be used. The time dependent anode temperature, effective anode voltage and plasma parameters will be measured. The characteristics of metallic film deposited by HRAVA plasma will be analyzed (e.g. film thickness, the rate of deposition, MP size and number distribution). A two-dimensional, non-linear thermal model of the anode will be considered and the anode temperature distribution will be calculated and compared with experimental measurements.

Participants: EDPL: (I. I. Beilis, A. Shashurin, A. Nemirovsky, D. Arbilly, S. Goldsmith and R. L. Boxman)

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Vacuum Arcs.

The present understanding of vacuum arc cathode phenomena including the experimental data, the current continuity mechanism, the nature of the cathode mass loss, cathode spot motion, cathode plasma jet generation, and the cathode potential drop, were reviewed recently (see I.I. Beilis, “State of the Theory of Vacuum Arcs, IEEE Trans. Plasma Sci. Vol. 29, N5, 657-670, 2001). The explosive model and gas-dynamical model of cathode spot processes were described. The problems of anode spot, interelectrode plasma in magnetic fields and vacuum arcs with hot electrodes were discussed.

Participant: EDPL: (I. I. Beilis)

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Near-electrode phenomena in vacuum arcs.

Cathode spot theory.

Application to the graphite cathode. A physical model based on a kinetic treatment of cathode evaporation, electron emission from the cathode, and plasma production to describe spot behavior on a graphite cathode in a vacuum arc was developed. Spot parameters, such as, cathode erosion rate, cathode potential drop, cathode surface temperature, current density, electric field, and plasma density, temperature and velocity as dependencies on spot current and spot life time were calculated numerically. The calculation showed that the spot parameter variations are stronger at times shorter than 10 ms and that Joule heating in the cathode body can be significant in comparison to the ion energy flux and energy flux due to the cathode mass loss.

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Non-stationary operation. A model for nanosecond cathode spot operation in vacuum arcs including a description of the cathode processes and a calculation of the parameters at the electrode surface and in the near-cathode plasma was developed. The present model takes in account increasing spot current during the spot life time and relatively high rates of rise of the spot current (dI/dt). Calculations for a copper cathode indicate that the spot current density increases when dI/dt increases and can exceed 108 A/cm2 for dI/dt of about 1011 A/s. The plasma electron temperature Te is about 3-4 eV when the cathode potential drop is Uc = 15-20 V and Te reaches 7-8 eV when the Uc increases up to 40-50 V. The calculated spot parameters are in the range measured in recent experiments with nanosecond time resolution.

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Spot behavior in a transverse magnetic field. Two of the important vacuum arc phenomena observed when the arc runs in a transverse magnetic field are cathode spot grouping and the cathode spot retrograde motion, i.e. in the anti-Amperian direction. A physical model for spot grouping and spot retrograde motion was proposed. The proposed spot motion model take in account the cathode thermal regime and the peculiarities of plasma flow near the cathode. The current per group spot is calculated assuming that the plasma kinetic pressure is comparable to the self-magnetic pressure in the acceleration region of cathode plasma jet. The model includes equations for the current per spot group, spot velocity dependence on the magnetic field and on the arc current in vacuum as well as in gas filled arc gaps. The calculated currents per spot group and spot velocity increase linearly with the magnetic field and arc current, and these dependencies agree well with previous observations. The cathode spot retrograde motion in short electrode gaps and in atmospheric pressure arcs, and the reversal motion in strong magnetic fields (>1T) observed by Robson and Engel are discussed.

Participant:   EDPL: (I. I. Beilis)

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Anode spot theory

 A physical model and a system of equations was formulated, based on a kinetic treatment of anode evaporation and a description of plasma flow in the plasma acceleration region in a self-consistent manner. The plasma energy balance was described considering the Joule energy in the anode plasma, the energy dissipation caused by ionization of atoms, energy convection by the electric current and the energy required for anode plasma acceleration. The anode surface temperature, current density, plasma density, plasma temperature and velocity were calculated. Calculations for graphite anodes indicate that Joule energy in the anode body is significant, and in some cases may exceed the anode surface energy source (i.e., the difference between the electron energy flux and energy flux related to the anode mass loss). The anode erosion rate in vacuum arcs can differ significantly from the anode evaporation rate in vacuum. The degree of plasma ionization increases from a= 10—3 to 5.10-2, when the spot current increases from 10 to 400 A and a can exceed 0.1 when the current is about 1kA.

Participant: EDPL: (I. I. Beilis)

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Vacuum arc plasma jet.

Plasma and MP flow in biased ducts. The influence of positive bias on plasma and MP flow in curved magnetized plasma ducts was considered. The plasma bulk and sheath regions were analyzed. In the plasma bulk the current density and electrical field component normal to the wall were obtained. In the sheath a non-stationary model for MP charging and motion was developed. It was shown that the electric field in the plasma and a field in the sheath confine the ions in the positively biased toroidal duct. The MP's traveling in the sheath accumulate a charge which depends on the potential distribution, in contrast to MP charging in the quasi-neutral plasma where the charge depends on plasma density and electron temperature. MP trapping in the near wall sheath was found. MP's may move in the sheath region along the wall by a repetitive process of electrostatic attraction to the wall, mechanical reflection and neutralization, followed by MP charging and attraction, etc. For example, titanium MP's with a radius less than 0.4 mm and with a velocity component normal to the wall of about 20 m/s are trapped if the sheath potential drop exceeds 20 V. It was obtained that the MP transmission fraction through filter decreases by more than few order of magnitude due to the trapping effect when a bias potential of +100 V is applied between the wall and the plasma.

Participants: EDPL: (I.I Beilis, R.L. Boxman and S. Goldsmith)

                               University of Michigan: (M. Keidar)

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Multiply-charged ion transport. The free boundary plasma arc jet expansion was analyzed based on a previously developed two-dimensional hydrodynamic model. Due to the existence of an electric field in the quasi-neutral plasma, the different charged ion species can be spatially separated. It was found that the mean charge state distribution is strongly non-uniform with a tendency for the highly charged species to appear near the plasma jet boundary region. Along the centerline, the density of singly charged ions falls off by about 4 times while the density of quadruple charged ions drops by more than 100 times with distance. The radial charge state distribution becomes more non-uniform with increasing magnetic field. Good qualitative agreement between calculated and experimental radial distributions of different charged species was obtained.

Participants: EDPL: (I. I. Beilis)

                              University of Michigan: (M. Keidar)

                              Lawrence Berkeley National Laboratory, University of California: (J. Brown)

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Plasma jet expansion in curved magnetic ducts. A hydrodynamic model of free-boundary vacuum arc plasma jet flow through a curved magnetic field was developed. The plasma flow was modeled by sourceless steady state equations. It was found that the maximum of plasma density shifts with respect to the centerline. The shift is maximal at the guide exit plane (_=90°) and in the case of smaller magnetic field (beo=0.1). The maximal increasing of the longitudinal plasma velocity was obtained to be by factor of 3. Plasma distribution within the duct was analyzed using deposition probe technique. The plasma jet expansion predicted by the model was compared with experiment and good qualitative agreement was found.

Participants: EDPL: (I. I. Beilis)

                               University of Michigan: (M. Keidar)

                               Lawrence Berkeley National Laboratory, University of California: (A. Anders and J. Brown)

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Thrusters.

Pulsed plasma thruster (PPT). The physical processes of a discharge in a dielectric (Teflon) cavity producing a high-pressure cloud of ablation products in a co-axial PPT were analyzed. The mathematical model included the Teflon thermal conduction, the plasma energy balance, mass and momentum conservation in the quasi-neutral plasma region and the relation for plasma parameters in non-equilibrium layer near the ablated Teflon surface. Predicted plasma parameters, such as temperature, ablation rate and gasdymanic thrust are found to be in agreement with available experimental data.

Participants: EDPL: (I. I. Beilis)

        University of Michigan: (M. Keidar and I. Boyd)

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Hall thruster. A model of the quasi-neutral plasma and the transition between the plasma and the dielectric wall in a Hall thruster channel was developed. The plasma flow was considered using a 2D hydrodynamic approximation. The secondary electron emission (SEE) from the dielectric wall is taken into account. In order to obtain a self-consistent solution, the boundary parameters for the sheath edge (ion velocity and electric field) were analyzed. It was found that the radial ion velocity component at the plasma-sheath interface varies along the thruster channel from about 0.5Cs (where Cs is the Bohm velocity) near the anode up to Cs near the exit plane, dependent on the SEE coefficient. The SEE significantly affects the electron temperature distribution along the channel. The predicted electron temperature is close to that measured experimentally. The model predictions of the dependence of the current-voltage characteristic of the ExB discharge on the SEE coefficient were found to agree with experiments.

Participants:  EDPL: (I. I. Beilis)

                    University of Michigan: (M. Keidar and I. Boyd)

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