G. Zwicknagel

Stopping of heavy ions in plasmas at strong coupling

Abstract Standard approaches to the energy loss of ions in plasmas like the dielectric linear response or the binary collision model are strictly valid only in the regimes where the plasma is close to ideal and the coupling between projectile-ion and the plasma target is sufficiently weak. In this review we explore the stopping power in regimes where these conditions are not met. Actually relevant fields of application are heavy ion driven inertial fusion and the cooling of beams of charged particles by electrons. The conventional linear mean-field treatments are extended by many-body methods and particle simulations to account for strong correlations between the particles and for nonlinear coupling. We report the following important results in connection with the stopping at strong coupling: The energy loss of an ion scales with its charge approximately like Z 1.5 , the effective screening length depends on Z and is larger than the Debye length. Slow highly charged ions are surrounded by a cloud of electrons trapped by many body collisions. Quantum effects like the wave nature of the electrons and Pauli-blocking reduce the stopping power by mollifying the effective interactions.

On the importance of damping phenomena in clusters irradiated by intense laser fields

We study the dynamics of large clusters irradiated by intense and short laser pulses, within the framework of the nanoplasma model. Particular attention is paid to the influence of electron–surface collisions, which have not been considered in previous versions of the model. We show that they dominate inverse bremsstrahlung collisions when plasmon resonance occurs. The dynamics of the cluster changes considerably and the predictions of the model are significantly modified. Moreover, there is no evidence for the presence of highly charged ions and the hydrodynamic pressure is found to be smaller than the Coulomb one.

Molecular dynamic simulations of ions in electron plasmas at strong coupling

Molecular dynamic (MD) computer simulations are used to investigate the stopping of heavy ions in strongly coupled electron plasmas. Our results show, that in this regime collisions between the electrons as well as non-linear screening effects yield at low ion velocities a dependence of the stopping power on the ion chargeZ which scales like Z1.43 instead of the usual Z2 ln(const/Z)-scaling for weak coupling. This is connected with an enhanced local density of electrons around a highly charged, slow ion.

Stopping power of heavy ions in strongly coupled plasmas

We investigate the stopping power of heavy ions in strongly coupled electron plasmas by performing molecular dynamics (MD) computer simulations. A comparison with conventional weak coupling theories shows that these fail in describing the stopping power at low ion velocities and strong coupling. Then nonlinear screening effects become important and this causes a change in the dependence of the stopping power on the ion charge Z p at low ion velocities. From the MD simulation, we find the stopping power to behave like Z p 1.43 instead of the weak coupling behavior Z p 2 ln(const/Z p ). Similar results were recently obtained by experiments in connection with electron cooling at heavy ion storage rings.

Nonlinear energy loss of heavy ions in plasma

Abstract For the energy loss of highly charged heavy ions strong coupling effects in the energy transfer from the projectile-ion to a target plasma become important. A theoretical treatment of this nonlinear ion stopping has to go beyond the well established standard approaches for weak ion–target coupling. Here we review our investigations on the nonlinear energy loss based on extensive numerical simulations of the projectile–target system by both a test-particle method and full molecular dynamics (MD) simulations. The observed essential feature of nonlinear stopping is a dependency on the ion charge state like Zx, with x≲1.5, in contrast to the usual Z2 behavior. The numerical results are rather well reproduced by a theoretical approach, called the improved kinetic model, which considers both close collisions and collective effects. An additional study of the influence of nonlinear screening and strong correlations within the target shows that there are further significant effects on the stopping power at low velocities, which have to be taken into account.

Numerical simulation of the dynamic structure factor of a two-component model plasma

Using molecular dynamics simulations we investigate the dynamic structure factor S(k, ω) of a two-component model plasma where the Coulomb interaction is regularized at short distances. New simulation results are presented and discussed, and they are used to verify different theoretical treatments: the standard random-phase approximation, a dynamic local field correction with input from HNC calculations and a new approach, which includes a dynamic collision frequency via the Mermin ansatz.

Microfield distributions in strongly coupled two-component plasmas

The electric microfield distribution at charged particles is studied for two-component electron-ion plasmas using molecular dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account the quantum-diffraction effects. The potential-of-mean-force (PMF) approximation is deduced from a canonical ensemble formulation. The resulting probability density of the electric microfield satisfies exactly the second-moment sum rule without the use of adjustable parameters. The correlation functions between the charged radiator and the plasma ions and electrons are calculated using molecular dynamics simulations and the hypernetted-chain approximation for a two-component plasma. It is shown that the agreement between the theoretical models for the microfield distributions and the simulations is quite good in general.

Stopping power in anisotropic, magnetized electron plasmas

Abstract We performed particle-in-cell (PIC) computer simulations to investigate the stopping power on a heavy, highly charged ion in an anisotropic electron plasma in the presence of a static external magnetic field. The related energy transfer of the ion to the electrons can be viewed as the basic process of the interaction between an ion beam and the electron beam in the cooling section of a heavy ion storage ring. For low ion velocities, our simulations show an enhancement of the stopping power for ions moving transversal to the magnetic field compared to the case without magnetic field. Taking into account the velocity distribution of the ions in an ion beam also an enhancement of the longitudinal stopping power measured in experiments is expected. Our results are qualitatively in good agreement with an experiment at the test storage ring (TSR).

Nonlinear effects in stopping of partially ionized swift heavy ions

Abstract We present stopping power calculations for swift heavy ions in a hydrogen gas target. The point-like model is reviewed and compared to a new theory which includes the projectile elastic form factor. It is shown that, even for highly ionized ions, the projectile form factor yields a substantial modification over the standard stopping results.

Drag force on ions in magnetized electron plasmas

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 drag force and the energy loss are calculated in a model of binary collisions 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 energy loss is related to the transfer of relative velocity in a collision. Particular attention must be paid to the non-conservation of the center-of-mass motion in the presence of a magnetic field. Three kinetic regimes can be identified, depending on the relative magnitude of the distance of closest approach, the cyclotron radius and the pitch of the helical motion. Closed expressions for the energy loss are derived for monochromatic electron beams, which are folded with the velocity distribution of the electrons. Hard collisions are taken into account by regularizing the integrals with respect to the impact parameter at small distances. The resulting energy loss of the ion and the drag force are evaluated for anisotropic Maxwell velocity distributions of the electrons. The influence of the magnetic field is as follows: the energy loss is reduced if the ion moves parallel to the field, while it is enhanced if the ion velocity has a component transverse to the field. This enhancement is not as large as in the dielectric theory and in previous kinetic models.