Plasma and Spot Phenomena in Electrical Arcs

ISBN-13: 9783030447496 / Angielski / Miękka / 2021

Isak Beilis

Opis

This book is devoted to a thorough investigation of the physics and applications of the vacuum arc – a highly-ionized metallic plasma source used in a number of applications – with emphasis on cathode spot phenomena and plasma formation. The goal is to understand the origins and behavior of the various complex and sometimes mysterious phenomena involved in arc formation, such as cathode spots, electrode vaporization, and near-electrode plasma formation. The book takes the reader from a model of dense cathode plasma based on charge-exchange ion-atom collisions through a kinetic approach to cathode vaporization and on to metal thermophysical properties of cathodes. This picture is further enhanced by an in-depth study of cathode jets and plasma acceleration, the effects of magnetic fields on cathode spot behavior, and electrical characteristics of arcs and cathode spot dynamics. The book also describes applications to space propulsion, thin film deposition, laser plasma generation, and magnetohydrodynamics, making this comprehensive and up-to-date volume a valuable resource for researchers in academia and industry. 

Spis treści

Preface

Introduction

Part 1. General plasma and solid-plasma interface phenomena

Chapter 1. Base particle-surface and plasma particle effects

1.1 Plasma, particle collisions at the surface and in plasma volume

1.2 Plasma

1.2.1 Quasi-neutrality

1.2.2 Oscillations.

1.2.3 Electron beam-plasma interaction.

1.2.4 Plasma State.

1.3 Surface-particle collisions

1.4 Plasma particle collisions

1.4.1 Charge particle collisions

1.4.2 Electron scattering on atoms

1.4.3 Charge-exchange collisions

1.4.4 Excitation and ionization collisions

1.4.4.1 Classical approach

1.4.4.2 Quantum mechanical approach

1.4.4.3 Experimental data

1.4.5 Electron-ion recombination

1.4.6 Ionization-recombination equilibrium

Chapter 2. Atom and electron emission from the metal surface

2.1 Kinetics of metal vaporization

2.1.1 Non-equilibrium (kinetic) region

2.1.2 Kinetic approaches. Atom evaporations

2.1.3 Kinetic approaches. Evaporations into plasma

2.2 Electron emission

2.2.1 Work function. Electron function distribution

2.2.2 Thermionic or T-emission

2.2.3 Schottky effect. Field or F-emission

2.2.4 Thermionic and Field or TF-emission

2.2.5 Threshold approximation

2.2.6 Individual electron emission

2.2.7 Fowler-Northeim-type equations and their correcting for measured plot analysis

2.2.8 Explosive electron emission

Chapter 3. Arc spot as a local heat source. Heat conduction of a solid body.

3.1 Brief state of the art analysis

3.2 Thermal regime of a semi-finite body. Methods in linearly approximation

3.2.1 Point source. Continuous heating

3.2.2 Normal circular heat source on a body surface.

3.2.3 Instantaneous normal circular heat source on semi-infinity body

3.2.4 Moving normal circular heat source on a semi-infinity body

3.3 Heating of a thin plate

3.3.1 Instantaneous normal circular heat source on a plate

3.3.2 Moving normal circular heat source on a plate

3.4 A normal distributed heat source moving on lateral side of a thin semi-infinite plate

3.4.1 Instantaneous normally distributed heat source on side of a thin semi-infinite plate

3.4.2 Moving continuous normally distributed heat source on thin plate of thickness .

3.4.3 Fixed normal-strip heat source with thickness x0 on semi-infinite body.

3.4.4 Fixed normal-strip heat source with thickness x0 on semi-infinite body limited by plane x=-/2

3.4.5 Fixed normal-strip heat source with thickness x0 on lateral side of finite plate (x0<)

3.4.6 Moving normal-strip heat source on a later plate side of limited thickness (x0<)

3.5 Temperature field calculations. Normal circular heat source on a semi-infinite body

3.5.1 Temperature field in a tungsten

3.5.2 Temperature field in a copper.

3.5.3 Temperature field calculations. Normal heat source on a later side of thin plate and plate with limited thickness

3.5.4 Summary

3.6 Nonlinear heat conduction 

3.6.1 Heat conduction problems related to the cathode thermal regime in vacuum arcs

3.6.2 Normal circular heat source action on a semi-infinity body with nonlinear boundary condition

3.6.3 Numerical solution of 3D heat conduction equation with nonlinear boundary condition

References

Chapter 4. The transport equations and diffusion phenomena in multicomponent plasma

4.1 The problem

4.2 Transport phenomena in a plasma. General equations

4.2.1 Equations of particle fluxes for three-components cathode plasma

4.2.2 Transport equations for three-component cathode plasma

4.2.3 Transport equations for five-component cathode plasma

References

Chapter 5. Plasma surface transition at the cathode of a vacuum arc

5.1 Cathode sheath

5.2 Space charge zone at the sheath boundary and the sheath stability

5.3 Two regions. Boundary conditions 

5.4 Kinetic approach

5.5 Electrical field.

5.5.1 Collisionless approach

5.5.2 Electric field. Plasma electrons. Particle temperatures

5.5.3 Refractory cathode. Virtual cathode

5.5.3.1 Single charged ions

5.5.3.2 Multi charged ions. Quasineutrality.

5.6 Electrical double layer

References

Chapter 6. Vacuum arc ignition. Electrical breakdown

6.1 Contact triggering of the arc

6.1.1 Triggering of the arc using additional trigger electrode

6.1.2 Initiation of the arc by contact breaking of the main electrodes

6.1.3 Contact phenomena

6.2 Electrical breakdown

6.2.1 Electrical breakdown conditions

6.2.2 General mechanisms of electrical breakdown in a vacuum

6.2.3 Mechanisms of breakdown based on explosive cathode protrusions

6.2.4 Mechanism of anode thermal instability

6.2.5 Electrical breakdown at an insulator surface

6.3 Conclusions

References

Part 2. Electrode spots. Mass and heat losses. Experiment

Chapter 7. Arc and Cathode spot. Current density

7.1 Arc electrical characteristics.

7.1.1 Arc definition.

7.1.2 Arc instability

7.1.3 Arc voltage.

7.1.4 Cathode potential drop

7.1.5 Threshold arc current

7.2 Cathode spots dynamics. Spot velocity

7.2.1 Spot definition

7.2.2 Study of the spots. General experimental approaches

7.2.3 Spot study by high speed images.

7.2.3.1 Early observations of spots on different cathodes

7.2.3.2 Spot types on fresh and cleaned cathode surfaces

7.2.3.3 High temporal and spatial resolution of spots on arc-cleaned cathodes 

7.2.4 Autograph observation. Crater sizes

7.2.5 Summary of the spot types studies.

7.2.5.1 Spot image dynamics.

7.2.5.2 Summary of the autographs study

7.2.5.3 Comparison of the results of both approaches

7.2.6 Classification of the spot types by their characteristics

7.3 Cathode spot current density

7.3.1 Spot current density determination. 

7.3.2 Image sizes with optical observation

7.3.3 Crater sizes observation

7.3.4 Influence of the conditions. Uncertainty

7.3.5 Interpretation of the observed subjects

7.3.6 Effects of small cathode and low current density. Heating estimations.

7.3.7 Summary

References

Chapter 8. Electrode erosion. Total mass losses

8.1 Electroerosion phenomena.

8.1.1 General overview

8.1.2 Electroerosion phenomena in air

8.1.3 Electroerosion phenomena in liquid dielectric media

8.2 Erosion phenomena in vacuum arcs

8.2.1 Moderate current of the vacuum arcs

8.2.2 Electrode erosion in high current arcs

8.2.3 Erosion phenomena in vacuum of metallic tip as high field emitter

8.3 Summary and discussion of the erosion measurements

References

Chapter 9. Electrode erosion. Macroparticle generation

9.1 Macroparticle generation. Conventional arc

9.2 Macroparticle charging

9.3 Macroparticle interaction

9.3.1 Interaction with plasma

9.3.2 Interaction with a wall and substrate

9.4 Macroparticle generation in an arc with hot anodes.

9.4.1 Macroparticles in a Hot Refractory Anode Vacuum Arc (HRAVA).

9.4.2 Macroparticles in a Vacuum Arc with Black Body Assembly (VABBA).

9.5 Concluding remarks

References

Chapter 10. Electrode energy losses. Effective voltage.

10.1 Measurements of the effective voltage in a vacuum arc

10.2 Effective electrode voltage in an arc in presence of a gas pressure

10.3 Effective electrode voltage in a vacuum arc with hot refractory anode

10.4 Energy flux from the plasma of a vacuum arc with hot refractory anode

10.5 Summary

References

Chapter 11. Repulsive effect. Force phenomena due to plasma jet reaction.

11.1 General view

11.2 Repulsive effect upon the electrodes of electrical arc. Early measurements of hydrostatic pressure and plasma expansion

11.3 Measurements of the force at electrodes in an electrical arc

11.4 Preliminary discussion of the force mechanism at the electrodes in arcs

11.5 Resume

References

Chapter 12. Cathode spot jets. Velocity and ion current

12.1 Plasma jet velocity

12.2 Ion energy

12.3 Ion velocity and energy in an arc with large rate of current rise dI/dt

12.4 Ion current fraction

12.5 Ion charge state

12.6 Influence of the magnetic field

12.7 Vacuum arc with refractory anode. Ion current

12.8 Summary

References

Chapter 13. Spot motion in a transverse and in oblique magnetic fields

13.1 The general problem.

13.2 Effect of spot motion in a magnetic field

13.3 Retrograde spot motion.

13.3.1 Magnetic field parallel to the cathode surface. Direct cathode spot motion

13.3.1.1 Cathode spot velocity moved in transverse magnetic field.

13.3.1.2 Cathode heating and retrograde cathode spot motion

13.3.1.3 Gas pressure and gap distance influence on the spot motion under TMF

13.3.1.4 Magnetic field and group spot dynamics

13.3.2 Phenomena in an oblique magnetic fields

13.3.2.1 Cathode spot motion in oblique magnetic fields

13.3.2.2 Cathode spot motion with a long roof-shaped cathode under magnetic field

13.3.2.3 Cathode spot splitting in an oblique magnetic field

13.4 Summary

References

Chapter 14. Anode phenomena in electrical arcs

13.1 General functions of the anode

13.2 Anode modes in vacuum arcs

13.2.1 Anode spotless mode. Low current arcs

13.2.2 Anode spot mode for large arc current.

13.2.3 Anode spot mode for small anode diameter

13.3 Anode modes in presence a gas pressure

13.3.1 Low pressure gas

13.3.2 Moving normal circular heat source on a plate

13.4 Anode parameters measurements

13.4.1 Anode temperature measurements

13.4.2 Plasma parameters 

13.5 Summary 

References

Part 3. Electrode phenomena. Theory 

Chapter 15. Cathode Spot. Previous theoretical models

15.1 Early Ideas 

15.2 First quasi-consistent description. 

15.3 Explosive models. 

15.4 Analysis of the state, and the cathode spot problem formulation ()

15.5 Summary

References

Chapter 16. Cathode Spot. Diffusion model. Mathematically closed theory

16.1 Cathode plasma and role charge-exchange collisions.

16.2 Idea of continuum cathodic plasma description. First basis of hydrodynamic approach and its applicability for the cathode plasma spot description., 1969-1971.

16.3 Electrical sheath. Diffuse model of spot plasma.

16.3.1 Low ionized plasma approach.

16.3.2 High ionized plasma approach.

16.3.3 Spot physical model and mathematically closed system of equation.

16.3.4 Numerical investigation of cathode spot parameters.

16.4 Summary

References

17. Cathode spot. Kinetic model. Physically closed theory

17.2 Kinetic model.

17.3 Kinetic of cathode vaporization. Knudsen layer.

17.3.1 New approach of kinetic of atom vaporization into the plasma.

17.3.2 Function distribution of near cathode vaporized and plasma particles.

17.3.3 Conservation laws and the equations of conservation.

17.3.4 Integration. The multi system of equations derivation.

17.4 Physically closed system of equation of cathode spot.

17.5 Numerical investigation of cathode spot parameters by physically closed approach.

17.6 Summary

References

Chapter 18. Spot-plasma and plasma jet.

18.1 State of the mechanism of plasma jet generation and expansion.

18.2 Plasma jet. Model of plasma expansion.

18.3 Mathematical description and system of equations.

18.4 Plasma jet and boundary condition.

18.5 Self-consistent spot-jet plasma expansion.

18.6 Summary

References

Chapter 19. Cathode spot motion in magnetic fields

19.1 Cathode spot motion in a transverse magnetic field. 

19.1.1 Retrograde motion. Literature hypothesis

19.1.2 Cathode spot grouping

19.1.3 Physical and mathematical model of spot current-magnetic field action

19.1.4 Calculation of spot grouping in a magnetic field.

19.1.5 Calculation of retrograde spot motion

19.2 Cathode spot motion in oblique magnetic field. Acute angle effect.

19.2.1 Literature hypothesis

19.2.2 Physical and mathematical model of spot drift due to the acute angle effect

19.2.3 Model of spot splitting in oblique field

19.2.4 Calculation of spot splitting

19.2.5 Calculation of spot motion in oblique field

19.3 Summary

References

Part 4. Applications

Chapter 20. Short arc. Vacuum arc spot thruster 

20.1 Phenomena in arcs with small electrode gaps

20.2 Microplasma generation in a microscale short vacuum arc

20.3 Modeling of a microscale short vacuum arc for a space propulsion thruster

20.4 Summary

References

Chapter 21. Vacuum arcs with refractory anode

21.1 New arc mode. Physical phenomena. Two anode configuration

21.2 Theory. Mathematical description

21.3 Time dependent anode temperature

21.4 Application for coatings. Advances and comparison with other methods.

21.5 Time dependent thin film deposition.

21.6 Dependencies on arc current, cathode-anode configuration and materials.

21.7 Summary

References 

Chapter 22. Laser spot. Laser plasma generation

22.1 Physics of laser plasma generation 

22.2 Laser plasma interaction with ablative target

22.3 Theory. Self-consistent system of equations

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.

22.5 Summary

References

Chapter 23. Effects of current carrying wall in a plasma flow in a magnetohydrodynamic duct. Arcing mode.

23.1 MHD energy conversion, Electrode problem

23.2 Hot electrodes. Overheating instability.

23.3 Volt-current characteristics. Conditions for arcing with spot mode.

23.4 Cold cathode. Spot presence in plasma flow with potashium doping.

23.5 Spot model in MHD ducts. Specifics of system of equations. Calculations

23.6 Summary

References

Conclusions

O autorze

Isak Beilis is a Professor in the Faculty of Engineering at Tel Aviv University. He received his PhD and Doctor of Science in Physics and mathematics from the Academy of Sciences, Moscow, and subsequently held positions at  Lomonosov University, Moscow, the Weizmann Institute for Science, joining Tel Aviv University in 1992. He has held visiting positions at the University of Minnesota, Minneapolis, USA in 1996 and 1997, at the Max Planck Institute, Berlin, and the Istituto Nazionale di Fisica Nucleare, Italy. His research centers around physical phenomena in high-current electrical discharges, at the electrode surface and in near-electrode plasma. In 2018 he was awarded the Walter P. Dyke Award for his many important contributions to discharge physics.

Blurb

This book is devoted to a thorough investigation of the physics and applications of the vacuum arc – a highly-ionized metallic plasma source used in a number of applications – with emphasis on cathode spot phenomena and plasma formation. The goal is to understand the origins and behavior of various complex and sometimes mysterious phenomena involved in arc formation, such as cathode spots, electrode vaporization, and near-electrode plasma formation. The book takes the reader from a model of dense cathode plasma based on charge-exchange ion-atom collisions through a kinetic approach to cathode vaporization and on to metal thermophysical properties of cathodes. The picture is further enhanced by an in-depth study of cathode jets and plasma acceleration, the effects of magnetic fields on cathode spot behavior, and electrical characteristics of arcs and cathode spot dynamics. The book also describes applications to space propulsion, thin film deposition, laser plasma generation, and magnetohydrodynamics, making this comprehensive and up-to-date volume a valuable resource for researchers in academia and industry.