Energy loss of ions in a magnetized plasma: conformity between linear response and binary collision treatments

Time evolution and energy deposition for ion clusters injected into magnetized two-component plasmas

A two-dimensional particle-in-cell simulation model is proposed to study the time evolution and energy deposition for ion clusters injected into magnetized two-component plasmas. The injection of an isolated ion cluster is studied in the case of weak and strong magnetic fields. For strong magnetic fields, the ions tend to deposit their energy smoothly along the trajectory of the cluster, due to the confinement by the strong magnetic fields. However, in the case of weak magnetic fields, a large amount of energy is deposited by the ions near the initial cluster injection position, where the cluster density is expected to be largest. We attribute these to the influences of interference effects between the cluster ions, which have close relations to the distances between the ions. Furthermore, the influences of various magnetic fields, injection angles, and injection velocities on the time evolution and energy deposition of a beam pulse, which contains several similar ion clusters, are investigated in detail. The influences of different magnetic fields on the beam pulse show similar to that of a single ion cluster. For increasing injection angles, the beam velocity perpendicular to the magnetic field increases, leading to increasing oscillations in the beam trajectory and energy deposition profile. Besides, the amount of energy that transferred from the beam pulse to the plasma increases as the beam injection velocity approaches the electron thermal velocity.

Diffusion in a strongly coupled magnetized plasma

A first-principles study of diffusion in a strongly coupled one-component plasma in a magnetic field B is presented. As in a weakly coupled plasma, the diffusion coefficient perpendicular to the field exhibits a Bohm-like 1/B behavior in the strong-field limit but its overall scaling is substantially different. The diffusion coefficient parallel to the field is strongly affected by the field as well and also approaches a 1/B scaling, in striking contrast to earlier predictions.

Energy loss of ions by electric-field fluctuations in a magnetized plasma

The results of a theoretical investigation of the energy loss of charged particles in a magnetized classical plasma due to the electric-field fluctuations are reported. The energy loss for a test particle is calculated through the linear-response theory. At vanishing magnetic field, the electric-field fluctuations lead to an energy gain of the charged particle for all velocities. It has been shown that in the presence of strong magnetic field, this effect occurs only at low velocities. In the case of high velocities, the test particle systematically loses its energy due to the interaction with a stochastic electric field. The net effect of the fluctuations is the systematic reduction of the total energy loss (i.e., the sum of the polarization and stochastic energy losses) at vanishing magnetic field and reduction or enhancement at strong field, depending on the velocity of the particle. It is found that the energy loss of the slow heavy ion contains an anomalous term that depends logarithmically on the projectile mass. The physical origin of this anomalous term is the coupling between the cyclotron motion of the plasma electrons and the long-wavelength, low-frequency fluctuations produced by the projectile ion. This effect may strongly enhance the stochastic energy gain of the particle.

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

The results of a theoretical investigation of the low-velocity stopping power of ions in a magnetized collisional and classical plasma are reported. The stopping power for an ion is calculated through the linear-response (LR) theory. The collisions, which lead to a damping of the excitations in the plasma, are taken into account through a number-conserving relaxation time approximation in the LR function. In order to highlight the effects of collisions and magnetic field, we present a comparison of our analytical and numerical results obtained for nonzero damping or magnetic field with those for 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 the major objectives of this paper is to compare and to contrast our theoretical results with those obtained through a diffusion coefficient formulation based on the Dufty-Berkovsky relation evaluated for a magnetized one-component plasma modeled with target ions and electrons.

Binary collisions of charged particles in a magnetic field

Binary collisions between 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 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 nonsingular 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, and (ii) the collision between a magnetized electron and a 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 nonperturbative numerical classical trajectory Monte Carlo results agree excellently with the predictions of the perturbative treatment.

Dynamic polarization and energy dissipation for charged particles moving in magnetized two-component plasmas

Energy losses of test particles in magnetized two-component plasmas are investigated within the framework of the linearized Vlasov-Poisson theory, taking into account the dynamic polarization effects of both the plasma ions and electrons. General expressions of the potential and stopping power are obtained and calculations are performed for protons in a magnetized hydrogen plasma. The influences of the magnetic field, the angle between the proton velocity and magnetic field, and certain plasma parameters on the stopping power are studied. Numerical results show that for low particle velocities and strong magnetic field the dynamic polarization effects of the plasma ions become obvious and contribute mainly to the stopping power.

Low ion-velocity slowing down in a strongly magnetized plasma target

An ion projectile stopping at a velocity smaller than the target electron thermal velocity in a strong magnetic field is investigated within a different diffusion formulation, based on Green-Kubo integrands evaluated in magnetized one component plasma models, respectively framed on target ions and electrons. Analytic expressions are reported for slowing down orthogonal and parallel to an arbitrary large magnetic field, which are free from the usual uncertainties plaguing the standard perturbative derivations. Magnetic and target temperature dependences of the low velocity slowing down are thoroughly detailed for dense plasmas of fast ignition concern and ultracold plasmas envisioned for ion beam cooling, as well.

Coulomb explosions and energy loss of molecular ions in plasmas

Interactions of swift molecular ions with high-density plasma targets are studied by means of the linearized Vlasov-Poisson theory, allowing the dynamically screened interaction potential among the constituent ions to be expressed in terms of the classical plasma dielectric function. Coulomb explosions and the energy losses of a molecular ion are simulated by solving the equations of motion for the constituent ions. It is found that, due to the wakelike asymmetry of the interaction potential, the molecular axis tends to align itself along the beam direction. In addition, a strong enhancement of the energy loss of the molecular ion has been found in the initial stages of Coulomb explosions due to proximity of the constituent ions, but this effect diminishes at latter stages when the ions are sufficiently far apart.