An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects ...related to the emission and transformation of energy have been considered as well. The results obtained can be used in analysing the recent experimental and simulation data.
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.
The dynamic Friedel sum rule (FSR) is derived within the second-order Born (B2) approximation for an ion that moves in a fully degenerate electron gas and for an arbitrary spherically-symmetric ...electron–ion interaction potential. This results in an implicit equation for the dynamic B2 screening parameter which depends on the ion atomic number Z1 unlike the first-order Born (B1) dynamic screening parameter reported earlier by some authors. Furthermore, for typical metallic densities our analytical results for the Yukawa and hydrogenic potentials are compared, for both positive and negative ions, to the exact screening parameters calculated self-consistently by imposing the exact dynamic FSR requirement to the scattering phase shifts. The B1 and B2 screening parameters agree excellently with the exact values at large velocities, while at moderate and low velocities the B1 approximation deviates from the exact solution whereas the B2 approximation still remains close to it. In addition, a Padé approximant to the Born series yields a further improvement of the perturbative approach, showing an excellent agreement on the whole velocity range in the case of antiprotons.
The low-velocity stopping power of ions in a magnetized collisional plasma is studied through the linear response theory. The collisions are taken into account through a number-conserving relaxation ...time approximation. One of the major objectives of this study is to compare and contrast our theoretical results with those obtained through a diffusion coefficient formulation based on Dufty-Berkovsky relation.
The effects of a radiation field (RF) on the unstable modes developed in a relativistic electron beam-plasma interaction are investigated assuming that ω(0) > ω(p), where ω(0) is the frequency of the ...RF and ω(p) is the plasma frequency. These unstable modes are parametrically coupled to each other due to the RF and are a mix between two-stream and parametric instabilities. The dispersion equations are derived by the linearization of the kinetic equations for a beam-plasma system as well as the Maxwell equations. In order to highlight the effect of the radiation field we present a comparison of our analytical and numerical results obtained for nonzero RF with those for vanishing RF. Assuming that the drift velocity u(b) of the beam is parallel to the wave vector k of the excitations two particular transversal and parallel configurations of the polarization vector E(0) of the RF with respect to k are considered in detail. It is shown that in both geometries resonant and nonresonant couplings between different modes are possible. The largest growth rates are expected at the transversal configuration when E(0) is perpendicular to k. In this case it is demonstrated that, in general, the spectrum of the unstable modes in the ω-k plane is split into two distinct domains with long and short wavelengths, where the unstable modes are mainly sensitive to the beam or the RF parameters, respectively. In the parallel configuration, E(0)∥k, and at short wavelengths the growth rates of the unstable modes are sensitive to both beam and RF parameters remaining insensitive to the RF at long wavelengths.
Screening effects are important to understand various aspects of ion–solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and ...scattering amplitudes for the quantum-mechanical elastic scattering within up to the second-order Born (B2) approximation are revisited for an arbitrary spherically-symmetric electron–ion interaction potential. The B2 phase shifts and scattering amplitudes are then used to derive the Friedel sum rule (FSR) involving the second-order Born corrections. This results in a simple equation for the B2 perturbative screening parameter of an impurity ion immersed in a fully degenerate electron gas which, as expected, turns out to depend on the ion atomic number Z1 unlike the first-order Born (B1) screening parameter reported earlier by some authors. Furthermore, our analytical results for the Yukawa, hydrogenic, Hulthén, and Mensing potentials are compared, for both positive and negative ions and a wide range of one-electron radii, to the exact screening parameters calculated self-consistently by imposing the FSR requirement. It is shown that the B2 screening parameters agree excellently with the exact values at large and moderate densities of the degenerate electron gas, while at lower densities they progressively deviate from the exact numerical solutions but are nevertheless more accurate than the prediction of the B1 approximation. In addition, a simple Padé approximant to the Born series has been developed that improves the performance of the perturbative FSR for any negative ion as well as for Z1=+1.
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.
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.
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