C. Toepffer

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.

SEMICLASSICAL MOLECULAR DYNAMICS FOR STRONGLY COUPLED COULOMB SYSTEMS

Based on the time‐dependent variational principle for a Hartree wave function, a semiclassical approximation for a strongly correlated plasma is derived. This procedure maps the quantum dynamical problem to a classical one with one additional degree of freedom per particle and is considered the natural extension of classical molecular dynamics. As a test case, a single electron in a Coulomb potential is studied. For the full many‐body problem the pair distribution function, the velocity autocorrelation function, the conductivity, and the diffusion constants are calculated for a plasma. We also consider liquid molecular hydrogen and lithium as a further test case which is sensitive to the treatment of the Pauli exclusion principle.

Damping of giant resonances in a stochastic two-level model

Abstract We derive a theory for small amplitude motion about states in thermal equilibrium. This motion couples mean-field oscillations and occupation number relaxations. The theory contains the effects of two-body collisions treated beyond the Markov approximation. The damping of collective modes is studied in a stochastic two-level model. The widths of giant resonances in finite nuclei are estimated using sum rules.

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.

CORRELATIONS IN NUCLEI AND NUCLEAR DYNAMICS

A wide variety of schemes to compute short-range and long-range correlations is discussed. The emphasis lies on an overview and on the interrelations between the various schemes, rather than on a detailed presentation. The need for effective interactions, and their proper handling is outlined at the end.

On emittance growth of strongly coupled heavy ion beams

Abstract In intense, strongly coupled heavy ion beams collisions between beam particles become important. We investigate their influence on the beams phase-space dimensions in terms of averaged quantities. A model is developed where the emittance increases due to a temperature anisotropy driven by the envelope oscillations caused by a periodic focusing structure. A set of coupled differential equations is derived which extend the envelope equations by including the dynamics of the emittances. From these equations, estimates for the average emittance growth rates can be made. The predictions of the model are tested by comparison with numerical results obtained from molecular dynamics simulations.

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).

Relaxation in a strongly coupled particle beam

Abstract We investigate temperature relaxation processes in bunched and coasting ion beams at high phase-space densities using the molecular dynamics (MD) simulation technique. A simple model is presented which describes emittance growth in the framework of extended envelope equations. The relaxation rate τ c −1 for the temperature anisotropy is obtained from MD simulations. In the regime of strong coupling it decreases precursing the transition to an ordered beam. Some implications relevant for beam cooling and beam crystallization are discussed.