| Introduction | p. 1 |
| Previous Work, Status and Overview | p. 5 |
| Energy Loss in an Unmagnetized One-Component-Plasma (OCP) | p. 5 |
| Challenges Imposed by the Magnetic Field | p. 11 |
| Classical-Trajectory-Monte-Carlo (CTMC) Simulations | p. 14 |
| Dielectric Treatment (DT), Vlasov-Poisson Equation, Linear Response (ER) | p. 16 |
| Particle-In-Cell (PIC) Simulations | p. 22 |
| Binary Collision Model | p. 25 |
| Introductory Remarks | p. 25 |
| Equations of Motion | p. 26 |
| Energy Loss and Velocity Transfer | p. 28 |
| General Interactions, no Magnetic Field | p. 29 |
| Binary Collisions (BC) in a Magnetic Field | p. 33 |
| Parallel Ion Motion | p. 39 |
| Chaotic Scattering and Validity of the Perturbation Treatment | p. 42 |
| Binary Collision Model for Arbitrary Ion Motion in a Strong Field | p. 51 |
| Binary Collisions in a Weak Field | p. 57 |
| Impact Parameter Integration and Velocity Averaging | p. 61 |
| Velocity Diffusion (Straggling) of Charged Particles in a Magnetic Field | p. 68 |
| Dielectric Theory | p. 73 |
| Stopping Power (SP) in Plasmas Without Magnetic field | p. 73 |
| Stopping in Plasmas With Weak Magnetic field | p. 76 |
| Small Projectile Velocities | p. 77 |
| High Projectile Velocities | p. 78 |
| Stopping in Plasmas With Strong Magnetic Field | p. 79 |
| Small Projectile Velocities | p. 81 |
| High Projectile Velocities | p. 81 |
| Stopping in the Low-Velocity Limit at Arbitrary Field Strengths | p. 83 |
| High-Velocity SP in a Magnetized Plasma | p. 85 |
| Heavy Ions with Rectilinear Trajectories | p. 87 |
| Weakly Coupled Plasma with Strong Magnetic Fields | p. 91 |
| Light Ions, The Effect of the Cyclotron Rotation | p. 93 |
| Reduced LR (RLR) Treatment | p. 96 |
| RLR, LR and BC Treatments Without Magnetic Field | p. 98 |
| RLR, LR and BC Treatments With Strong Magnetic Fields | p. 100 |
| Conformity Between Reduced LR and BC approaches | p. 106 |
| Quantum Theory of SP in Magnetized Plasmas | p. 109 |
| Dielectric Theory | p. 109 |
| Equation of State for Quantum Magnetized Plasmas | p. 115 |
| Critical Temperature | p. 115 |
| Fully Degenerate Electron Plasma | p. 116 |
| Semiclassical and Classical Limits | p. 118 |
| Dielectric Function, Fully Degenerate Plasma | p. 118 |
| Fully Degenerate Plasma in a Strong Magnetic Field | p. 120 |
| Acoustic Plasma Resonance | p. 121 |
| Dielectric Function, Semiclassical Limit | p. 121 |
| Stopping Power in a Magnetized Quantum Plasma | p. 124 |
| Low-Velocity Stopping Power in a Semiclassical Regime | p. 124 |
| Stopping power in an Infinitely Strong Magnetic Field, Low-Velocity Limit | p. 126 |
| Stopping power in a Strong Magnetic Field in the Nearly Degenerate Regime | p. 129 |
| Binary Collision Treatment, Conformity Between BC and RLR | p. 130 |
| Correspondence Between Quantum and Classical BC Treatments | p. 134 |
| Cartesian Basis | p. 134 |
| Cylindrical Basis | p. 137 |
| Averaged Classical Second-Order Energy Transfer | p. 140 |
| Applications and Illustrating Examples | p. 143 |
| Electron Cooling in Storage Rings | p. 143 |
| Energy Loss and Drag Force | p. 144 |
| Cooling Forces | p. 145 |
| Emittance and momentum spread | p. 148 |
| Electron Cooling in Penning Traps | p. 150 |
| Modeling of the Cooling Process in a Trap | p. 151 |
| Cooling of Protons and Highly Charged Ions | p. 153 |
| Cooling of Antiprotons and Protons by Electrons and Positrons | p. 159 |
| Summary and Conclusion | p. 165 |
| Dielectric Function of the Magnetized Electron-Ion Plasma | p. 169 |
| Anomalous Term | p. 171 |
| Dielectric Function of the Magnetized Quantum Plasma | p. 173 |
| Some Properties of the Function Fnn′(¿) | p. 175 |
| References | p. 177 |
| List of Symbols and Abbreviations | p. 183 |
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