Interactions between charged particles in a magnetic field : a theoretical approach to ion stopping in magnetized plasmas

This monograph focuses on the influence of a strong magnetic field on the interactions between charged particles in a many-body system. Two complementary approaches, the binary collision model and the dielectric theory are investigated in both analytical and numerical frameworks. In the binary collision model, the Coulomb interaction between the test and the target particles is screened because of the polarization of the target.

Author Notes

Dr. Hrachya Nersisyan

1986-1987 Junior Scientific Researcher, Laboratory of Radiation Physics, Yerevan

Physics Institute, Yerevan, Armenia

1987-1989 Pre-doctoral position, Department of Plasma Theory, P.N. Lebedev Physical

Institute, Moscow, Russia

1993 Dr. of Physical and mathematical sciences, P.N. Lebedev Physical Institute,

Moscow, Russia

1993-1994 Scientific Researcher, Institute of Radiophysics & Electronics, Ashtarak,

Armenia

1997 Guest Researcher, Laboratoire de Physique des Gaz et des Plasmas,

Université Paris-XI, Orsay, France

1999 DAAD (German Academic Exchange Service) Fellowship, Institut für

Theoretische Physik II, Universität Erlangen-Nürnberg, Erlangen, Germany

2001-2002 Alexander von Humboldt Fellowship, Institut für Theoretische Physik II,

Universität Erlangen-Nürnberg, Erlangen, Germany

2004-2005 Guest Researcher, Institut für Theoretische Physik II, Universität Erlangen-

Nürnberg, Erlangen, Germany

1994- Senior Scientific Researcher, Institute of Radiophysics & Electronics,

Ashtarak, Armenia

Prof. Dr. Christian Toepffer

1967 Dr. phil. nat.

1973-1974 Associate Professor, University Frankfurt/Main

1974-1980 Professor of Theoretical Physics, University of Witwatersrand,

Johannesburg, South Africa

1980- Professor of Theoretical Physics, University of Erlangen

Dr. Günter Zwicknagel

1994 Dr. rer. nat. in Physics at the University of Erlangen

1995-1997 Research scholar at the Laboratoire de Physique des Gaz et des Plasmas,

Orsay, France

1997-2000 Research assistant at the Institute of Theoretical Physics II, University of

Erlangen

2000- Researcher and lecturer at the University of Erlangen

1 Introduction	p. 1
2 Previous Work, Status and Overview	p. 5
2.1 Energy Loss in an Unmagnetized One-Component-Plasma (OCP)	p. 5
2.2 Challenges Imposed by the Magnetic Field	p. 11
2.3 Classical-Trajectory-Monte-Carlo (CTMC) Simulations	p. 14
2.4 Dielectric Treatment (DT), Vlasov-Poisson Equation, Linear Response (ER)	p. 16
2.5 Particle-In-Cell (PIC) Simulations	p. 22
3 Binary Collision Model	p. 25
3.1 Introductory Remarks	p. 25
3.2 Equations of Motion	p. 26
3.3 Energy Loss and Velocity Transfer	p. 28
3.4 General Interactions, no Magnetic Field	p. 29
3.5 Binary Collisions (BC) in a Magnetic Field	p. 33
3.6 Parallel Ion Motion	p. 39
3.7 Chaotic Scattering and Validity of the Perturbation Treatment	p. 42
3.8 Binary Collision Model for Arbitrary Ion Motion in a Strong Field	p. 51
3.9 Binary Collisions in a Weak Field	p. 57
3.10 Impact Parameter Integration and Velocity Averaging	p. 61
3.11 Velocity Diffusion (Straggling) of Charged Particles in a Magnetic Field	p. 68
4 Dielectric Theory	p. 73
4.1 Stopping Power (SP) in Plasmas Without Magnetic field	p. 73
4.2 Stopping in Plasmas With Weak Magnetic field	p. 76
4.2.1 Small Projectile Velocities	p. 77
4.2.2 High Projectile Velocities	p. 78
4.3 Stopping in Plasmas With Strong Magnetic Field	p. 79
4.3.1 Small Projectile Velocities	p. 81
4.3.2 High Projectile Velocities	p. 81
4.4 Stopping in the Low-Velocity Limit at Arbitrary Field Strengths	p. 83
4.5 High-Velocity SP in a Magnetized Plasma	p. 85
4.5.1 Heavy Ions with Rectilinear Trajectories	p. 87
4.5.2 Weakly Coupled Plasma with Strong Magnetic Fields	p. 91
4.5.3 Light Ions, The Effect of the Cyclotron Rotation	p. 93
4.6 Reduced LR (RLR) Treatment	p. 96
4.6.1 RLR, LR and BC Treatments Without Magnetic Field	p. 98
4.6.2 RLR, LR and BC Treatments With Strong Magnetic Fields	p. 100
4.7 Conformity Between Reduced LR and BC approaches	p. 106
5 Quantum Theory of SP in Magnetized Plasmas	p. 109
5.1 Dielectric Theory	p. 109
5.2 Equation of State for Quantum Magnetized Plasmas	p. 115
5.2.1 Critical Temperature	p. 115
5.2.2 Fully Degenerate Electron Plasma	p. 116
5.2.3 Semiclassical and Classical Limits	p. 118
5.3 Dielectric Function, Fully Degenerate Plasma	p. 118
5.3.1 Fully Degenerate Plasma in a Strong Magnetic Field	p. 120
5.3.2 Acoustic Plasma Resonance	p. 121
5.4 Dielectric Function, Semiclassical Limit	p. 121
5.5 Stopping Power in a Magnetized Quantum Plasma	p. 124
5.5.1 Low-Velocity Stopping Power in a Semiclassical Regime	p. 124
5.5.2 Stopping power in an Infinitely Strong Magnetic Field, Low-Velocity Limit	p. 126
5.5.3 Stopping power in a Strong Magnetic Field in the Nearly Degenerate Regime	p. 129
5.6 Binary Collision Treatment, Conformity Between BC and RLR	p. 130
5.7 Correspondence Between Quantum and Classical BC Treatments	p. 134
5.7.1 Cartesian Basis	p. 134
5.7.2 Cylindrical Basis	p. 137
5.8 Averaged Classical Second-Order Energy Transfer	p. 140
6 Applications and Illustrating Examples	p. 143
6.1 Electron Cooling in Storage Rings	p. 143
6.1.1 Energy Loss and Drag Force	p. 144
6.1.2 Cooling Forces	p. 145
6.1.3 Emittance and momentum spread	p. 148
6.2 Electron Cooling in Penning Traps	p. 150
6.2.1 Modeling of the Cooling Process in a Trap	p. 151
6.2.2 Cooling of Protons and Highly Charged Ions	p. 153
6.2.3 Cooling of Antiprotons and Protons by Electrons and Positrons	p. 159
7 Summary and Conclusion	p. 165
A Dielectric Function of the Magnetized Electron-Ion Plasma	p. 169
B Anomalous Term	p. 171
C Dielectric Function of the Magnetized Quantum Plasma	p. 173
D Some Properties of the Function F nn′ (¿)	p. 175
References	p. 177
List of Symbols and Abbreviations	p. 183

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Table of Contents