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ANDERSON Michael Gordon
FORMATION AND PROPAGATION OF PULSED HIGH CURRENT PLASMA AND ION BEAMS IN TRANSVERSE MAGNETIC FIELD AND MAGNETIZED PLASMA
01.04.20 - Physics of Charged Particle Beams and Accelerating Technique
DISSERTATION
Submitted for the Scientific Degree: CANDIDATE of Physics and Mathematical Sciences
Supervising Professor,
Doctor of Physics and Mathematical Science:
Vitaly Mikhailovich Bystritskii
TOMSK-2006
CONTENTS
Page
Introduction Rationale and justification of the research topic.....................5
Chapter 1 Review of relevant, existing experimental and theoretical data
on pulsed high current PB/IB formation and propagation.............10
1.1 Ion beam formation............................................10
1.2 Plasma beam formation.........................................11
1.3 Plasma and ion beam propagation...............................12
1.4 Planned tasks of research..................................... 16
Chapter 2 Description of experiment, hardware and diagnostics..........17
Chapter 3 Results and analysis of the formation and transport of pulsed
high current IT PB across B-field in vacuum and magnetized plasma............................................................51
3.1 Plasma beam formation..........................................51
3.2 PB propagation in vacuum without magnetic field................54
3.3 PB propagation in plasma without magnetic field................56
3.4 PB propagation in vacuum transverse magnetic field 57
3.5 Plasma beam propagation in magnetized plasma...................58
3.6 Main results and analysis......................................59
3.7 Main tasks completed...........................................61
Chapter 4
Results and analysis of the formation and transport of pulsed
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high current FT IB across B-field in vacuum and magnetized plasma.............................................................62
4.1 Ion beam formation.............................................62
4.1.1 Marx generator...............................................63
4.1.2 Magnetically insulated diode.................................64
4.1.3 Anode........................................................65
4.1.4 Cathode......................................................65
4.1.5 Puff valve...................................................66
4.1.6 AC gap magnetic field........................................67
4.1.7 Plasma ion source............................................69
4.1.8 Magnetic lens................................................70
4.1.9 Solenoid.....................................................71
4.1.10 Plasma guns.................................................72
4.2 IB propagation in vacuum transverse magnetic field 72
4.3 Ion beam propagation in magnetized plasma......................74
4.4 Main results and analysis......................................76
4.5 Main tasks completed...........................................77
Chapter 5 Results and analysis of FRC formation and injection of pulsed
high current PB/IB into FRC........................................ 79
5.1 FRC formation with background plasma...........................79
5.2 FRC formation by PB injection into vacuum B-field 82
5.3 Injection of plasma beam into preformed FRC....................83
5.4 Injection of ion beam into preformed FRC.......................85
5.5 Main results of PB/IB injection into an FRC....................86
Conclusion Executive summary of main novel results of thesis......................89
Acknowledgements.............................................................92
List of Publications.........................................................93
Cited References.............................................................96
Appendix................................................................... 108
Al. Derivation of ExB conditions............................108
A2. List of calculated plasma beam parameters................115
A3. List of calculated ion beam parameters...................124
A4. Scaling study of IB propagation experiments..............133
A5. Calculation of IB space-charge expansion in free space... .137
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INTRODUCTION
Rationale and Justification of the Research Topic
Low energy, intense, - jis duration, neutralized ion beams (IBs) [Et - 105 to 106 eV, j - 1 to a few 10s of A/cm2], and plasma beams (PBs) [E ~ 100 eV, j ~ 10 to 100 A/cm ] are promising candidates for various applications requiring charged particle propagation across magnetic field to stand-off targets and/or capture in magnetized plasmas such as: the field reversed configuration (FRC), tokamak, magnetic mirror, etc [1-6]. The most pertinent of these plasma confinement systems to this thesis is the field reversed configuration which has attracted a variety of research for its potential as an alternative approach for thermonuclear magnetic confinement fusion [7-14]. However, the generation and transport of high current ion and plasma beams still present nontrivial problems. Some of the well known difficulties encountered in this area of research are: initial beam divergence due to incomplete space charge neutralization, non-uniformity of the beam density' during its formation, beam-plasma instabilities during transport and/or the problem of producing “long” pulse duration beams with high current densities due to plasma shorting of the anode-cathode (A-C) gap [15-18].
Pertinent to these problems, this thesis was focused on the production and transport of intense low energy pulsed plasma and ion beams across B-field in vacuum, magnetized plasma and their subsequent injection into a field reversed configuration.
An innovative approach using a combination of ballistic focusing magnetically insulated diode (MID) with a “concave” toroidal magnetic lens (TML) and a straight transport solenoid (TS) was implemented in order to
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substantially increase the density and propagation length of the IB across B-field.
As for the PB, a plasma accelerator based on a modified Marshal gun [19], was constructed and tested which utilized a tapered squirrel-cage electrode assembly and an auxiliary plasma source to increase beam duration and its current density.
The goal of the study
Study the formation and transport of high current PB and IB in vacuum and magnetized plasma across B-field pertinent to their future application for heating and confinement of stand-off plasma configurations. Fulfill experiments using injection of PB/IB for enhancing FRC lifetime and B-field.
Scientific value and novelty of results
Collected new experimental data in a wider parameter range (E - 100 eV, J ~ 10 to 100 A/cm2) on PB propagation across B-field (0.1 - 1.5 kG) compared to previous experiments in vacuum and magnetized plasma, such as: decrease in density of PB’s peripheral layers, strong PB braking with pronounced bunching of the central core with more than one order density increase (> 200 A/cm2). Demonstrated diamagnetic and collective modes of PB propagation in vacuum B-field and magnetized plasma.
Collected new experimental data for IB enhanced transport efficiency along the novel guide channel, and for beam propagation across B-field (0.1 - 1.5 kG) in vacuum and magnetized plasma in a wider parameter range (E ~ 60 to 120 keV, J ~ 1 to 25 A/cm2) compared to previous experiments. Demonstrated collective and single particle modes of IB propagation in vacuum and plasma
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respectively.
Fulfilled systematic experiments on the formation of FRC using axial injection of annular plasma flows in a coaxial solenoid reactor.
Designed, fulfilled and analyzed the first experiments on tangential injection of PB and IB into an FRC.
Scientific and practical significance of the work
Tested new scheme for IB formation and transport which is valuable for many applied and fundamental studies related to the use of particle beams for the magnetic fusion, plasma laser pumping by IB, transport of IB to stand-off targets.
Verified existing data on PB and IB transport across B-field in vacuum and magnetized plasma and added new data for a wider range of experimental conditions.
The results of the first experiments on cross B-field injection of PB/IB into an FRC are valuable for a variety of studies related to the heating and sustaining of magnetically confined plasma systems which use the particle beams.
Presently, these results are being used, in the collaborative effort of the University of California Irvine and Tri Alpha Energy Inc., as a guide to determine the required beam parameters for effective heating and sustainment of a large FRC with pulsed high current particle beams.
Publications of results
There are 13 published works on the theme of this thesis in scientific journals and conferences (see List of Publications, P1-P13, at the end of the thesis), including 6 papers published in refereed scientific journals. The results of this
thesis work were reported at: the 14th IEEE International Pulsed Power Conference, (Piscatavvay, NJ, USA, 2003); the 31st IEEE International Conference on Plasma Science, (Piscataway, NJ, USA, 2004); the 13th International Symposium on High Current Electronics, (Tomsk, Russia, 2004); the 15th International Conference on High Power Particle Beams, (St. Petersburg, Russia, 2004); the 6th Symposium on Current Trends in International Fusion Research, (Washington D.C., USA, 2005); the 32nd IEEE International Conference on Plasma Science, (Monterey, California, USA, 2005) and the 14°’ International Symposium on High Current Electronics, (Tomsk, Russia, 2006).
Structure and volume of dissertation
The thesis consists of an introduction, five chapters and a conclusion. The total volume of the dissertation is composed of 137 pages, 47 figures and 5 tables. The list of references includes 116 sources.
Digest of content
A brief review of relevant, existing, experimental and theoretical data on high current PB/IB formation and propagation is given in chapter 1. Chapter 2 is dedicated to the description of experiment, hardware and diagnostics. In Chapter 3, the results and analysis of the formation and propagation of the PB in vacuum transverse B-field and magnetized plasma are discussed. Chapter 4 is devoted to the results and analysis on the generation and transport of the IB in vacuum across B-field and magnetized plasma. In Chapter 5, results and analysis of FRC formation and PB/IB injection into the FRC are presented. Chapter 6 summarizes the main novel results followed by Acknowledgements, Publications, Cited References and Appendix.
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Claims submitted for defense
1. It was shown, for a wide range of beam parameters compared to previous experiments, that the propagation of pulsed high current plasma beams (PB) (E ^ 100 eV, J - 10 to 100 A/cm2) and ion beams (IB) (E ~ 60 to 120 keV, J - 1 to 25 A/cm2) across B-field (0.1 - 1.5 kG) in vacuum is controlled by the collective mechanism of ExB drift accompanied by a decrease in density of beam peripheral layers along B-field lines and, in the case of PB propagation, a pronounced bunching of the beam’s central core (> 200 A/cm2).
2. It was suggested and proved that the new method of forming long-lived Field Reversed Configuration (FRC) via axial injection of annular plasma flows is critically sensitive to the value of the residual B-field (< 10 G) in the coaxial region during the FRC startup stage, which defines the pressure balance on the plasma configuration.
3. It was demonstrated that tangential injection of a pulsed high current PB into the preformed FRC results in beam trapping in the configuration and a respective enhancement of FRC lifetime (10%) and B-field amplitude (50%).
4. It was shown the possibility of trapping a pulsed high current IB, injected across B-field, in the preformed FRC.
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CHAPTER 1
Review of relevant, existing, experimental and theoretical data on pulsed high current IB/PB formation and propagation
1.1 Ion Beam Formation
Due to a three order difference in mass between electrons and ions, the electrons will make up more than 98% of the conventional diode current if left unrestrained. For a non-relativistic mono-polar flow across a one-dimensional AC gap (without magnetic insulation) the maximum current density is given by
the Child-Langmuir Law (CLL) [20, 21]: j~iCL = 2 3*10'* \~ where
d
Vo is the applied AC gap voltage [Volts], d is the AC gap width, me, is the electron orion mass, Z is the ionization state, and A is the atomic number of the ions. This limit takes into account the zero E-field at the cathode set up by self space charge effects and therefore provides a self-consistent flow analysis. Furthermore, when there is bi-polar flow in the diode (both electron and ion flux), the non-relativistic approximation for electron or ion current density gives:;,, *186Wi.
To overcome this limitation, several different types of anode systems have been developed which operate in a flow regime where the CLL no longer applies: (i) Reflex systems: multiple electron oscillations through a transparent anode, (ii) MID systems: applied magnetic insulation of AC gap and (iii) Pinch Diode systems: self magnetic insulation of AC gap by converging electron flow. All of these methods attempt to increase the electron crossing time of the AC gap and therefore increase the ion portion of the total diode current [15-18].
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