Plasma and Spot Phenomena in Electrical Arcs

<div><div>Preface</div><div>Introduction</div><div>Part 1. General plasma and solid-plasma interface phenomena</div><div>Chapter 1. Base particle-surface and plasma particle effects</div><div>1.1 Plasma, particle collisions at the surface and in plasma volume</div><div>1.2 Plasma</div><div>1.2.1 Quasi-neutrality</div><div>1.2.2 Oscillations.</div><div>1.2.3 Electron beam-plasma interaction.</div><div>1.2.4 Plasma State.</div><div>1.3 Surface-particle collisions</div><div>1.4 Plasma particle collisions</div><div>1.4.1 Charge particle collisions</div><div>1.4.2 Electron scattering on atoms</div><div>1.4.3 Charge-exchange collisions</div><div>1.4.4 Excitation and ionization collisions</div><div>1.4.4.1 Classical approach</div><div>1.4.4.2 Quantum mechanical approach</div><div>1.4.4.3 Experimental data</div><div>1.4.5 Electron-ion recombination</div><div>1.4.6 Ionization-recombination equilibrium</div><div>Chapter 2. Atom and electron emission from the metal surface</div><div>2.1 Kinetics of metal vaporization</div><div>2.1.1 Non-equilibrium (kinetic) region</div><div>2.1.2 Kinetic approaches. Atom evaporations</div><div>2.1.3 Kinetic approaches. Evaporations into plasma</div><div>2.2 Electron emission</div><div>2.2.1 Work function. Electron function distribution</div><div>2.2.2 Thermionic or T-emission</div><div>2.2.3 Schottky effect. Field or F-emission</div><div>2.2.4 Thermionic and Field or TF-emission</div><div>2.2.5 Threshold approximation</div><div>2.2.6 Individual electron emission</div><div>2.2.7 Fowler-Northeim-type equations and their correcting for measured plot analysis</div><div>2.2.8 Explosive electron emission</div><div>Chapter 3. Arc spot as a local heat source. Heat conduction of a solid body.</div><div>3.1 Brief state of the art analysis</div><div>3.2 Thermal regime of a semi-finite body. Methods in linearly approximation</div><div>3.2.1 Point source. Continuous heating</div><div>3.2.2 Normal circular heat source on a body surface.</div><div>3.2.3 Instantaneous normal circular heat source on semi-infinity body</div><div>3.2.4 Moving normal circular heat source on a semi-infinity body</div><div>3.3 Heating of a thin plate</div><div>3.3.1 Instantaneous normal circular heat source on a plate</div><div>3.3.2 Moving normal circular heat source on a plate</div><div>3.4 A normal distributed heat source moving on lateral side of a thin semi-infinite plate</div><div>3.4.1 Instantaneous normally distributed heat source on side of a thin semi-infinite plate</div><div>3.4.2 Moving continuous normally distributed heat source on thin plate of thickness .</div><div>3.4.3 Fixed normal-strip heat source with thickness x0 on semi-infinite body.</div><div>3.4.4 Fixed normal-strip heat source with thickness x0 on semi-infinite body limited by plane x=-/2</div><div>3.4.5 Fixed normal-strip heat source with thickness x0 on lateral side of finite plate (x0&lt;)</div><div>3.4.6 Moving normal-strip heat source on a later plate side of limited thickness (x0&lt;)</div><div>3.5 Temperature field calculations. Normal circular heat source on a semi-infinite body</div><div>3.5.1 Temperature field in a tungsten</div><div>3.5.2 Temperature field in a copper.</div><div>3.5.3 Temperature field calculations. Normal heat source on a later side of thin plate and plate with limited thickness</div><div>3.5.4 Summary</div><div>3.6 Nonlinear heat conduction&nbsp;</div><div>3.6.1 Heat conduction problems related to the cathode thermal regime in vacuum arcs</div><div>3.6.2 Normal circular heat source action on a semi-infinity body with nonlinear boundary condition</div><div>3.6.3 Numerical solution of 3D heat conduction equation with nonlinear boundary condition</div><div>References</div><div>Chapter 4. The transport equations and diffusion phenomena in multicomponent plasma</div><div>4.1 The problem</div><div>4.2 Transport phenomena in a plasma. General equations</div><div>4.2.1 Equations of particle fluxes for three-components cathode plasma</div><div>4.2.2 Transport equations for three-component cathode plasma</div><div>4.2.3 Transport equations for five-component cathode plasma</div><div>References</div><div>Chapter 5. Plasma surface transition at the cathode of a vacuum arc</div><div>5.1 Cathode sheath</div><div>5.2 Space charge zone at the sheath boundary and the sheath stability</div><div>5.3 Two regions. Boundary conditions&nbsp;</div><div>5.4 Kinetic approach</div><div>5.5 Electrical field.</div><div>5.5.1 Collisionless approach</div><div>5.5.2 Electric field. Plasma electrons. Particle temperatures</div><div>5.5.3 Refractory cathode. Virtual cathode</div><div>5.5.3.1 Single charged ions</div><div>5.5.3.2 Multi charged ions. Quasineutrality.</div><div>5.6 Electrical double layer</div><div>References</div><div>Chapter 6. Vacuum arc ignition. Electrical breakdown</div><div>6.1 Contact triggering of the arc</div><div>6.1.1 Triggering of the arc using additional trigger electrode</div><div>6.1.2 Initiation of the arc by contact breaking of the main electrodes</div><div>6.1.3 Contact phenomena</div><div>6.2 Electrical breakdown</div><div>6.2.1 Electrical breakdown conditions</div><div>6.2.2 General mechanisms of electrical breakdown in a vacuum</div><div>6.2.3 Mechanisms of breakdown based on explosive cathode protrusions</div><div>6.2.4 Mechanism of anode thermal instability</div><div>6.2.5 Electrical breakdown at an insulator surface</div><div>6.3 Conclusions</div><div>References</div><div>Part 2. Electrode spots. Mass and heat losses. Experiment</div><div>Chapter 7. Arc and Cathode spot. Current density</div><div>7.1 Arc electrical characteristics.</div><div>7.1.1 Arc definition.</div><div>7.1.2 Arc instability</div><div>7.1.3 Arc voltage.</div><div>7.1.4 Cathode potential drop</div><div>7.1.5 Threshold arc current</div><div>7.2 Cathode spots dynamics. Spot velocity</div><div>7.2.1 Spot definition</div><div>7.2.2 Study of the spots. General experimental approaches</div><div>7.2.3 Spot study by high speed images.</div><div>7.2.3.1 Early observations of spots on different cathodes</div><div>7.2.3.2 Spot types on fresh and cleaned cathode surfaces</div><div>7.2.3.3 High temporal and spatial resolution of spots on arc-cleaned cathodes&nbsp;</div><div>7.2.4 Autograph observation. Crater sizes</div><div>7.2.5 Summary of the spot types studies.</div><div>7.2.5.1 Spot image dynamics.</div><div>7.2.5.2 Summary of the autographs study</div><div>7.2.5.3 Comparison of the results of both approaches</div><div>7.2.6 Classification of the spot types by their characteristics</div><div>7.3 Cathode spot current density</div><div>7.3.1 Spot current density determination.&nbsp;</div><div>7.3.2 Image sizes with optical observation</div><div>7.3.3 Crater sizes observation</div><div>7.3.4 Influence of the conditions. Uncertainty</div><div>7.3.5 Interpretation of the observed subjects</div><div>7.3.6 Effects of small cathode and low current density. Heating estimations.</div><div>7.3.7 Summary</div><div>References</div><div>Chapter 8. Electrode erosion. Total mass losses</div><div>8.1 Electroerosion phenomena.</div><div>8.1.1 General overview</div><div>8.1.2 Electroerosion phenomena in air</div><div>8.1.3 Electroerosion phenomena in liquid dielectric media</div><div>8.2 Erosion phenomena in vacuum arcs</div><div>8.2.1 Moderate current of the vacuum arcs</div><div>8.2.2 Electrode erosion in high current arcs</div><div>8.2.3 Erosion phenomena in vacuum of metallic tip as high field emitter</div><div>8.3 Summary and discussion of the erosion measurements</div><div>References</div><div>Chapter 9. Electrode erosion. Macroparticle generation</div><div>9.1 Macroparticle generation. Conventional arc</div><div>9.2 Macroparticle charging</div><div>9.3 Macroparticle interaction</div><div>9.3.1 Interaction with plasma</div><div>9.3.2 Interaction with a wall and substrate</div><div>9.4 Macroparticle generation in an arc with hot anodes.</div><div>9.4.1 Macroparticles in a Hot Refractory Anode Vacuum Arc (HRAVA).</div><div>9.4.2 Macroparticles in a Vacuum Arc with Black Body Assembly (VABBA).</div><div>9.5 Concluding remarks</div><div>References</div><div>Chapter 10. Electrode energy losses. Effective voltage.</div><div>10.1 Measurements of the effective voltage in a vacuum arc</div><div>10.2 Effective electrode voltage in an arc in presence of a gas pressure</div><div>10.3 Effective electrode voltage in a vacuum arc with hot refractory anode</div><div>10.4 Energy flux from the plasma of a vacuum arc with hot refractory anode</div><div>10.5 Summary</div><div>References</div><div>Chapter 11. Repulsive effect. Force phenomena due to plasma jet reaction.</div><div>11.1 General view</div><div>11.2 Repulsive effect upon the electrodes of electrical arc. Early measurements of hydrostatic pressure and plasma expansion</div><div>11.3 Measurements of the force at electrodes in an electrical arc</div><div>11.4 Preliminary discussion of the force mechanism at the electrodes in arcs</div><div>11.5 Resume</div><div>References</div><div>Chapter 12. Cathode spot jets. Velocity and ion current</div><div>12.1 Plasma jet velocity</div><div>12.2 Ion energy</div><div>12.3 Ion velocity and energy in an arc with large rate of current rise dI/dt</div><div>12.4 Ion current fraction</div><div>12.5 Ion charge state</div><div>12.6 Influence of the magnetic field</div><div>12.7 Vacuum arc with refractory anode. Ion current</div><div>12.8 Summary</div><div>References</div><div>Chapter 13. Spot motion in a transverse and in oblique magnetic fields</div><div>13.1 The general problem.</div><div>13.2 Effect of spot motion in a magnetic field</div><div>13.3 Retrograde spot motion.</div><div>13.3.1 Magnetic field parallel to the cathode surface. Direct cathode spot motion</div><div>13.3.1.1 Cathode spot velocity moved in transverse magnetic field.</div><div>13.3.1.2 Cathode heating and retrograde cathode spot motion</div><div>13.3.1.3 Gas pressure and gap distance influence on the spot motion under TMF</div><div>13.3.1.4 Magnetic field and group spot dynamics</div><div>13.3.2 Phenomena in an oblique magnetic fields</div><div>13.3.2.1 Cathode spot motion in oblique magnetic fields</div><div>13.3.2.2 Cathode spot motion with a long roof-shaped cathode under magnetic field</div><div>13.3.2.3 Cathode spot splitting in an oblique magnetic field</div><div>13.4 Summary</div><div>References</div><div>Chapter 14. Anode phenomena in electrical arcs</div><div>13.1 General functions of the anode</div><div>13.2 Anode modes in vacuum arcs</div><div>13.2.1 Anode spotless mode. Low current arcs</div><div>13.2.2 Anode spot mode for large arc current.</div><div>13.2.3 Anode spot mode for small anode diameter</div><div>13.3 Anode modes in presence a gas pressure</div><div>13.3.1 Low pressure gas</div><div>13.3.2 Moving normal circular heat source on a plate</div><div>13.4 Anode parameters measurements</div><div>13.4.1 Anode temperature measurements</div><div>13.4.2 Plasma parameters&nbsp;</div><div>13.5 Summary&nbsp;</div><div>References</div><div>Part 3. Electrode phenomena. Theory&nbsp;</div><div>Chapter 15. Cathode Spot. Previous theoretical models</div><div>15.1 Early Ideas&nbsp;</div><div>15.2 First quasi-consistent description.&nbsp;</div><div>15.3 Explosive models.&nbsp;</div><div>15.4 Analysis of the state, and the cathode spot problem formulation ()</div><div>15.5 Summary</div><div>References</div><div>Chapter 16. Cathode Spot. Diffusion model. Mathematically closed theory</div><div>16.1 Cathode plasma and role charge-exchange collisions.</div><div>16.2 Idea of continuum cathodic plasma description. First basis of hydrodynamic approach and its applicability for the cathode plasma spot description., 1969-1971.</div><div>16.3 Electrical sheath. Diffuse model of spot plasma.</div><div>16.3.1 Low ionized plasma approach.</div><div>16.3.2 High ionized plasma approach.</div><div>16.3.3 Spot physical model and mathematically closed system of equation.</div><div>16.3.4 Numerical investigation of cathode spot parameters.</div><div>16.4 Summary</div><div>References</div><div>17. Cathode spot. Kinetic model. Physically closed theory</div><div>17.2 Kinetic model.</div><div>17.3 Kinetic of cathode vaporization. Knudsen layer.</div><div>17.3.1 New approach of kinetic of atom vaporization into the plasma.</div><div>17.3.2 Function distribution of near cathode vaporized and plasma particles.</div><div>17.3.3 Conservation laws and the equations of conservation.</div><div>17.3.4 Integration. The multi system of equations derivation.</div><div>17.4 Physically closed system of equation of cathode spot.</div><div>17.5 Numerical investigation of cathode spot parameters by physically closed approach.</div><div>17.6 Summary</div><div>References</div><div>Chapter 18. Spot-plasma and plasma jet.</div><div>18.1 State of the mechanism of plasma jet generation and expansion.</div><div>18.2 Plasma jet. Model of plasma expansion.</div><div>18.3 Mathematical description and system of equations.</div><div>18.4 Plasma jet and boundary condition.</div><div>18.5 Self-consistent spot-jet plasma expansion.</div><div>18.6 Summary</div><div>References</div><div>Chapter 19. Cathode spot motion in magnetic fields</div><div>19.1 Cathode spot motion in a transverse magnetic field.&nbsp;</div><div>19.1.1 Retrograde motion. Literature hypothesis</div><div>19.1.2 Cathode spot grouping</div><div>19.1.3 Physical and mathematical model of spot current-magnetic field action</div><div>19.1.4 Calculation of spot grouping in a magnetic field.</div><div>19.1.5 Calculation of retrograde spot motion</div><div>19.2 Cathode spot motion in oblique magnetic field. Acute angle effect.</div><div>19.2.1 Literature hypothesis</div><div>19.2.2 Physical and mathematical model of spot drift due to the acute angle effect</div><div>19.2.3 Model of spot splitting in oblique field</div><div>19.2.4 Calculation of spot splitting</div><div>19.2.5 Calculation of spot motion in oblique field</div><div>19.3 Summary</div><div>References</div><div>Part 4. Applications</div><div>Chapter 20. Short arc. Vacuum arc spot thruster&nbsp;</div><div>20.1 Phenomena in arcs with small electrode gaps</div><div>20.2 Microplasma generation in a microscale short vacuum arc</div><div>20.3 Modeling of a microscale short vacuum arc for a space propulsion thruster</div><div>20.4 Summary</div><div>References</div><div>Chapter 21. Vacuum arcs with refractory anode</div><div>21.1 New arc mode. Physical phenomena. Two anode configuration</div><div>21.2 Theory. Mathematical description</div><div>21.3 Time dependent anode temperature</div><div>21.4 Application for coatings. Advances and comparison with other methods.</div><div>21.5 Time dependent thin film deposition.</div><div>21.6 Dependencies on arc current, cathode-anode configuration and materials.</div><div>21.7 Summary</div><div>References&nbsp;</div><div>Chapter 22. Laser spot. Laser plasma generation</div><div>22.1 Physics of laser plasma generation&nbsp;</div><div>22.2 Laser plasma interaction with ablative target</div><div>22.3 Theory. Self-consistent system of equations</div><div>22.4 Results of calculations of plasma and target parameters. Effect of reduction of plasma-target shielding. Effect of conversion of the laser power radiation.</div><div>22.5 Summary</div><div>References</div><div>Chapter 23. Effects of current carrying wall in a plasma flow in a magnetohydrodynamic duct. Arcing mode.</div><div>23.1 MHD energy conversion, Electrode problem</div><div>23.2 Hot electrodes. Overheating instability.</div><div>23.3 Volt-current characteristics. Conditions for arcing with spot mode.</div><div>23.4 Cold cathode. Spot presence in plasma flow with potashium doping.</div><div>23.5 Spot model in MHD ducts. Specifics of system of equations. Calculations</div><div>23.6 Summary</div><div>References</div><div>Conclusions</div><div><br></div></div>