Research topics Reinhard group

From Institute for Theoretical Physics II / University of Erlangen-Nuremberg

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The Institut für Theoretische Physik II is mainly concerned with the theory and computer simulation of many particle systems. Currently, the main fields of research are plasma, cluster and nuclear physics.

Areas of research

An entity is more than its parts - this is the challenge of many-body theory. For an example consider matter, which consists of positively charged atomic nuclei and negatively charged electrons. On vast scales of density and temperatures one may treat these constituents as point particles interacting through the well-known electrostatic force. Nevertheless the entire system appears in quite different forms depending on the values of external parameters: From an extremely thin and cold plasma in outer space to the hot and dense interior of stars with ordinary matter as encountered in daily life in between, see Fig.1.

Overview image.jpg

Fig. 1: Typical temperatures T and electron densities n on a doubly-logarithmic plot. Between the cold and thin interstallar gas and the hot and dense white dwarfs lie 30 orders of magnitude in density and 8 orders of magnitude in temperature. In between are near solid state density the metallic clusters, metallic hydrogen, the interior of Jupiter and the fusion plasma.

There arise problems like: What is the structure, e.g. unordered or crystalline? How reacts matter on a perturbation like an applied voltage, is isolating or does it conduct a current? - Our research on matter under extreme conditions concerns the following phenomena:

Hydrogen under high pressure

Hydrogen is the simplest atom consisting of a proton and an electron. The behaviour of hydrogen under extreme conditions is thus of large fundamental interest. Recent experiments suggest that hydrogen becomes conducting at pressures above 106 atm. There arises the question whether the molecules dissociate first into atoms which are subsequently ionize into protons and electrons or vice versa. Such research for the phase equilibria between molecular and atomic nonconducting fluids on one hand and conducting fluids on the other hand is not only of fundamental importance for a study of the structure of the giant planets Jupiter and Saturn, but has also actual applications in the planned inertial confinement fusion (ICF): There drops of hydrogen are to be compressed and heated by particle- and/or laser beams until the atomic nuclei fuse. For the outlay of such experiments one has to know how hydrogen behaves under the prevailing extreme conditions. For this purpose we perform numerical computer simulations.

Particle beams in accelerators and storage rings

The structure of atomic nuclei and elementary particles is studied by scattering of ions which have been accelerated to high energies. There arises a conflict of aims: The beams must be intensive, which requires a high density and they ought to be sharp in energy and well focused. However, at large densities this is prevented by the repulsion among the ions. In order to improve the quality of an ion beam it can be mixed with an electron beam, whose high quality is transferred successively to the ion beam by scattering between the electrons and the ions (electron cooling). Of course the cooling must proceed faster than the recombination between the electrons and the ions. A reliable estimate of the rates of these processes is particularly important for the planning and the operation of large accelerators like the Large Hadron Collider (LHC) at the european research center CERN in Geneva or for heavy ion induced ICF. Recent experiments on electron cooling of highly charged ion beams show recombination rates which are much higher than predicted by conventional theory. Detailed simulations point to the role of the polarization of the electrons by the ion. In Fig.2 it is shown that the density of the electrons grows in the vicinity of the ion. Because of the magnetic field which guides the beams, this enhancement is anisotropic. In the combined electric and magnetic fields the electrons move chaotically which requires a new theory for the recombination.

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Fig. 2: Density enhancement n/n0 in the vicinity of a highly charged (Z=51) ion in a magnetizes electron plasma. The arrow indicates the direction of the magnetic field.

Matter in intensive laser fields

Recently lasers have been developed which yield high intesities (1019 W/cm2)for short times ( 10-14 s). To get an impression: This intensity is as large as if the entire energy radiated from the sun to the earth had been focused into a small spot. Such laser fields exert forces on the constituents of matter that are much larger than the material binding forces. The electrons are accelerated to relativistic velocities and act themselves as strong sources of electromaagnetic radiation. The resulting X-ray impulses can be used to observe atomic and molecular processes in a time-resolved manner. Such experiments, in which matter perturbs the dominating light pose a challenge to theory. One must calculate suitable experimentally observable quantities which allow to draw conclusions on the extreme nonequilibrium conditions of the target. For example, the shift and shape of spectral lines yields information on the fields and teir fluctuations.

Metallic clusters

Metallic clusters are microscopically small drops of two to a few thousand metal atoms. Such systems lie between the atom and the bulk solid state. There are conducting electrons as in the solid state but also distinct surface- and quantum effects caused by the finite size of the cluster. Quantum shell effects are responsible for the magic numbers, i.e. the enhanced occurrence of certain cluster sizes, while surface forces determine the optical properties of clusters. Particular interest is paid to the highly nonlinear effects upon irradiation with intensive short laser pulses. These allow a temporal resolution of the electron dynamics during the transition from normal matter to highly excites gas on a very fine scale. As the cluster looses many electrons it becomes highly charged.The electric repulsion drives then its explosion on a somewhat slower scale (10-12 s). The analysis of the emitted electrons and explosion fragments yields information about the metallic structure under extreme conditions.

See also the website of the Erlangen-Toulouse collaboration

Atomic nuclei

In the research areas mentioned so far the atomic nucleus can be treated as a charged point. At higher spatial resolution, below 10-14 m, one has to account for its structure, consisting of interacting protons and neutrons. Quite similar as the metallic clusters the nucleus is a finite many-body system, a drop, whose structure is strongly determined by quantum shell effects and surface forces. Enhanced stability at certain magic proton and/or neutron numbers allows the existence of exotic unstable nuclei which can be produced in reactors or by accelerators. Exotic isotopes of known elements, i.e. extremely neutron- or proton rich nuclei play an important role in the nucleosynthesis in stars. There is also the quest for yet unknown superheavy elements with Z > 112. The new reactor in Garching is excellently suited for further experimental research in this area. This allows an improvement of the theories for the structure of the atomic nucleus and its dynamics.

Methods and algorithms

Research in these areas involves invariably coupled nonlinear partial differential equations. Their solution requires intricate numerical methods, which must be adapted to the physical problem under investigation. Continuous fields are treated on grids, particular attention must be paid to the long range part of the electric interaction, which must considered separately. Although the motion of particles can be desribed by a few coordinates one needs many of these for a realistic description of a many-body system. In order to keep the computing effort on an acceptable level hierarchical algorithms are developed, in which slow processes of long spatial range run on large scales, while fast short range processes are treated on fine scales. Full use is made of modern parallel computing techniques.

We employ therefore various computing methods and make use of our own and third party computing resources.