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

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

An exact solution of the moving boundary problem for the relativistic plasma expansion in a dipole magnetic field

An exact analytic solution is obtained for a uniformly expanding, neutral, highly conducting plasma sphere in an ambient dipole magnetic field with an arbitrary orientation of the dipole moment in the space. Based on this solution the electrodynamical aspects related to the emission and transformation of energy have been considered. In order to highlight the effect of the orientation of the dipole moment in the space we compare our results obtained for parallel orientation with those for transversal orientation. The results obtained can be used to treat qualitatively experimental and simulation data, and several phenomena of astrophysical and laboratory significance.Comment: 7 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:physics/060323

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.

The moving boundary problem in the presence of a dipole magnetic field

An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were considered as well. The results obtained can be used in analyzing the recent experimental and simulation data.Comment: 17 pages, 1 figure, Submitted to J. Phys. A, Math. and Genera

A number-conserving linear response study of low-velocity ion stopping in a collisional magnetized classical plasma

The results of a theoretical investigation on the low-velocity stopping power of the ions moving in a magnetized collisional plasma are presented. The stopping power for an ion is calculated employing linear response theory using the dielectric function approach. The collisions, which leads to a damping of the excitations in the plasma, is taken into account through a number-conserving relaxation time approximation in the linear response function. In order to highlight the effects of collisions and magnetic field we present a comparison of our analytical and numerical results obtained for a nonzero damping or magnetic field with those for a vanishing damping or magnetic field. It is shown that the collisions remove the anomalous friction obtained previously [Nersisyan et al., Phys. Rev. E 61, 7022 (2000)] for the collisionless magnetized plasmas at low ion velocities. One of major objectives of this study is to compare and contrast our theoretical results with those obtained through a novel diffusion formulation based on Dufty-Berkovsky relation evaluated in magnetized one-component plasma models framed on target ions and electrons.Comment: Submitted to Phys. Rev. E, 17 pages, 4 figure