Interactions Between Charged Particles in a Magnetic Field (eBook)

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

Preface 6
Contents 8
1 Introduction 11
2 Previous Work, Status and Overview 14
2.1 Energy Loss in an Unmagnetized One–Component–Plasma ( OCP) 14
2.2 Challenges Imposed by the Magnetic Field 20
2.3 Classical-Trajectory-Monte-Carlo (CTMC) Simulations 23
2.4 Dielectric Treatment (DT), Vlasov–Poisson Equation, Linear Response ( LR) 25
2.5 Particle-In-Cell (PIC) Simulations 31
3 Binary Collision Model 34
3.1 Introductory Remarks 34
3.2 Equations of Motion 35
3.3 Energy Loss and Velocity Transfer 37
3.4 General Interactions, no Magnetic Field 38
3.5 Binary Collisions (BC) in a Magnetic Field 42
3.6 Parallel Ion Motion 48
3.7 Chaotic Scattering and Validity of the Perturbation Treatment 51
3.8 Binary Collision Model for Arbitrary Ion Motion in a Strong Field 60
3.9 Binary Collisions in aWeak Field 66
3.10 Impact Parameter Integration and Velocity Averaging 70
3.11 Velocity Diffusion (Straggling) of Charged Particles in a Magnetic Field 77
4 Dielectric Theory 82
4.1 Stopping Power (SP) in PlasmasWithout Magnetic field 82
4.2 Stopping in PlasmasWithWeak Magnetic field 85
4.3 Stopping in PlasmasWith Strong Magnetic Field 88
4.4 Stopping in the Low-Velocity Limit at Arbitrary Field Strengths 92
4.5 High-Velocity SP in a Magnetized Plasma 94
4.6 Reduced LR (RLR) Treatment 105
4.7 Conformity Between Reduced LR and BC approaches 115
5 Quantum Theory of SP in Magnetized Plasmas 118
5.1 Dielectric Theory 118
5.2 Equation of State for Quantum Magnetized Plasmas 124
5.3 Dielectric Function, Fully Degenerate Plasma 127
5.4 Dielectric Function, Semiclassical Limit 130
5.5 Stopping Power in a Magnetized Quantum Plasma 133
5.6 Binary Collision Treatment, Conformity Between BC and RLR 139
5.7 Correspondence Between Quantum and Classical BC Treatments 143
5.8 Averaged Classical Second–Order Energy Transfer 149
6 Applications and Illustrating Examples 151
6.1 Electron Cooling in Storage Rings 151
6.2 Electron Cooling in Penning Traps 158
7 Summary and Conclusion 172
A Dielectric Function of the Magnetized Electron-Ion Plasma 175
B Anomalous Term 177
C Dielectric Function of the Magnetized Quantum Plasma 179
D Some Properties of the Function Fnn(.) 181
References 183
List of Symbols and Abbreviations 188