Binary collisions of charged particles in a magnetic field

Binary collisions between charged particles in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and non-singular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail. (i) The collision of two identical (e.g., electron-electron) particles; (ii) and the collision between a magnetized electron and an uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte--Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the non-perturbative numerical classical trajectory Monte--Carlo results agree excellently with the predictions of the perturbative treatment.Comment: submitted to Phys. Rev.

Cooling force on ions in a magnetized electron plasma

Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. In the common rest frame of the ion and the electron beam the ion is subjected to a drag force and it experiences a loss or a gain of energy which eventually reduces the energy spread of the ion beam. A calculation of this process is complicated as the electron velocity distribution is anisotropic and the cooling process takes place in a magnetic field which guides the electrons. In this paper the cooling force is calculated in a model of binary collisions (BC) between ions and magnetized electrons, in which the Coulomb interaction is treated up to second-order as a perturbation to the helical motion of the electrons. The calculations are done with the help of an improved BC theory which is uniformly valid for any strength of the magnetic field and where the second-order two-body forces are treated in the interaction in Fourier space without specifying the interaction potential. The cooling force is explicitly calculated for a regularized and screened potential which is both of finite range and less singular than the Coulomb interaction at the origin. Closed expressions are derived for monochromatic electron beams, which are folded with the velocity distributions of the electrons and ions. The resulting cooling force is evaluated for anisotropic Maxwell velocity distributions of the electrons and ions.Comment: 22 pages, 10 figure

On some generalized stopping power sum rules

The Lindhard-Winther (LW) equipartition sum rule shows that within the linear response theory, the stopping power of an energetic point-charge projectile in a degenerate electron gas medium, receives equal contributions from single-particle and collective excitations in the medium. In this paper we show that the LW sum rule does not necessarily hold for an extended projectile ion and for ion-clusters moving in a fully degenerate electron gas. We have derived a generalized equipartition sum rule and some related sum rules for this type of projectiles. We also present numerical plots for He$^{+}$ ion and He$^{+}$ ion-clusters.Comment: 2 figures, LaTe

Stopping Power of Ions in a Magnetized Plasma: Binary Collision Formulatio

In this chapter, we investigate the stopping power of an ion in a magnetized electron plasma in a model of binary collisions (BCs) between ions and magnetized electrons, in which the two-body interaction is treated up to the second order as a perturbation to the helical motion of the electrons. This improved BC theory is uniformly valid for any strength of the magnetic field and is derived for two-body forces which are treated in Fourier space without specifying the interaction potential. The stopping power is explicitly calculated for a regularized and screened potential which is both of finite range and less singular than the Coulomb interaction at the origin. Closed expressions for the stopping power are derived for monoenergetic electrons, which are then folded with an isotropic Maxwell velocity distribution of the electrons. The accuracy and validity of the present model have been studied by comparisons with the classical trajectory Monte Carlo numerical simulations

Energy transfer in binary collisions of two gyrating charged particles in a magnetic field

Binary collisions of the gyrating charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions which are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of a binary collisions treatment which is valid for any strength of the magnetic field and involves all harmonics of the particles cyclotron motion. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and nonsingular at the origin. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo (CTMC) calculations which also allow to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the nonperturbative numerical CTMC results agree excellently with the predictions of the perturbative treatment.Comment: 12 pages, 4 figure

Formation of correlations in strongly coupled plasmas

The formation of binary correlations in plasma is studied from the quantum kinetic equation. It is shown that this formation is much faster than dissipation due to collisions. In a hot (dense) plasma the correlations are formed on the scale of inverse plasma frequency (Fermi energy). We derive analytical formulae for the time dependency of the potential energy which measures the extent of correlations. We discuss the dynamical formation of screening and compare with the statical screened result. Comparisons are made with molecular dynamic simulations.Comment: Proceedings of the 8th International Workshop on Atomic Physics for Ion-Driven Fusion, Heidelberg 1997, appear in Laser and Particle Beam