J. Trulsen

Regularized Smoothed Particle Hydrodynamics: A New Approach to Simulating Magnetohydrodynamic Shocks

Smoothed particle hydrodynamics (SPH) has proven to be a useful numerical tool in studying a number of different astrophysical problems. Still, used on other problems, such as the modeling of low-β MHD systems, the method has so far not performed as well as one might have hoped. The present work has been motivated by the desire to accurately model strong hydrodynamic and magnetohydrodynamic shocks, and a key issue has therefore been to achieve a near-optimal representation of the simulated system at all times. Using SPH, this means combining the Lagrangian nature of the method with a smoothing-length profile that varies in both space and time. In this paper, a scheme containing two novel features is proposed. First, the scheme assumes a piecewise constant smoothing-length profile. To avoid substantial errors near the steps in the profile, alternative forms of the SPH equations of motion are used. Second, a predictive attitude toward optimizing the particle distribution is introduced by activating a mass, momentum, and energy conservation regularization process at intervals. The scheme described has been implemented in a new code called regularized smoothed particle hydrodynamics (RSPH), and test results for a number of standard hydrodynamic and magnetohydrodynamic tests in one and two dimensions using this code are presented.

Numerical simulation of jetstreams. II. The two-dimensional case

The dynamics of jetstreams have been studied by following the evolution of a simulation particle population. The self-gravitational field of the stream has been neglected, the individual small bodies interacting through hard, partially inelastic collisions only, no fragmentation or accreaction taking place. The chosen collision model — the beta-model — is given by Equation (4). The collisions will quickly establish a Rayleigh distribution of both eccentricities and inclinations, the average amplitude of the oscillations associated with eccentricity being up by approximately a factor √2. The velocity distribution inside the stream is highly non-Maxwellian. If the collisions are sufficiently inelastic, the stream is focused, the individual orbits becoming more and more circular (for azimuthally symmetric streams) and ecliptic. In the opposite case the collisions destroy the stream configuration rapidly. The beta collisional model is unable to produce any radial focusing.

Characterization of low frequency oscillations at substorm breakup

Field and particle data recorded on the geostationary satellite GEOS 2 are used to investigate the electric and magnetic signatures of a substorm characterized by a dispersionless injection of energetic electrons and ions. Three types of field variations are observed: (1) Long-period oscillations with period of ∼ 300 s, interpreted as oscillations of entire field lines. These oscillations develop as second harmonic standing waves and correspond to coupled shear Alfven-slow magnetosonic modes. They grow after the most active period of the breakup. (2) Short-period transient oscillations with periods of ∼ 45–65 s, interpreted as wave modes trapped in a current layer which develops prior to the substorm breakup and is disrupted at breakup. These oscillations also correspond to a coupled shear Alfven-slow magnetosonic mode (coupled via magnetic field curvature effects in a high-β plasma). The short-period transient oscillations are only observed during the most active period of the breakup. (3) A nonoscillatory sharp increase observed on both the parallel magnetic component and the energetic ion flux, averaged over one satellite rotation, interpreted as evidence for the fast magnetosonic mode which in view of the simultaneous large impulsive increase in the azimuthal electric field, appears to propagate radially outwards, transporting the substorm breakup downtail.

Lower hybrid wave cavities detected by the FREJA satellite

Localized electrostatic wave packets in the frequency region of lower hybrid waves have been detected by the instruments on the FREJA satellite. These waves are often associated with local density depletions indicating that the structures can be interpreted as wave filled cavities. The basic features of the observations are discussed. On the basis of simple statistical arguments it is attempted to present some characteristics which have to be accommodated within an ultimate theory describing the observed wave phenomena. An interpretation in terms of collapse of nonlinear lower hybrid waves is discussed in particular. It is argued that such a model seems inapplicable, at least in its simplest form, by providing a timescale and a length scale which are not in agreement with observations. Alternatives to this model are presented.

Confinement and turbulent transport in a plasma torus with no rotational transform

In the BLAAMANN device a weakly ionized hydrogen plasma is produced by electrons accelerated from a hot, negatively biased tungsten filament and confined in a toroidal magnetic field of strength up to 0.4 T. The plasma is turbulent, with relative fluctuation levels in ne, phi and Te of 10% or more. The time-averaged state exhibits nested toroidal surfaces of constant potential and pressure, which requires an anomalous cross-field current to remove the space-charge injected by the cathode and the charge accumulated due to the Del B- and curvature drifts. Typical plasma parameters are ne approximately 1016 m-3, Te approximately 1-20 eV, Ti approximately 1 eV. The cross-field diffusion coefficient is typically Dperpendicular to approximately 30 m2 s

SPH in spherical and cylindrical coordinates

-1 approximately 104*Dperpendicular to classical approximately 101*Dperpendicular to Bohm. Evidence is presented in support of the hypothesis that the plasma goes turbulent because it needs to develop an anomalous current channel, and this turbulence in turn determines the plasma transport and the time-averaged state.

Statistics of the lower hybrid wave cavities detected by the FREJA satellite

New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH. The Lagrangian formalism is used to derive the corresponding set of modified SPH equations of motion. The results show good agreement both with analytical and numerical results, in the case of the Sod shock tube test, the Noh infinite shock problem, and the Sedov point explosion test. The formulation has also been included in a 3D cylindrically symmetric problem of two colliding spherical shocks. For this latter problem, the results are presented allowing both a constant and a variable resolution. The results clearly demonstrate the capability of the new formulation to solve the singularity problem at the symmetry axis.

Cavitation of lower hybrid waves in the Earth's ionosphere: A model analysis

Localized electrostatic wave packets in the frequency region of lower hybrid waves have been detected by the instruments on the FREJA satellite and also earlier by instrumented rocket payloads. These waves are often associated with local density depletions, indicating that the structures can be interpreted as wave-filled cavities which are strongly elongated along the magnetic field. The basic features of the observations are discussed, providing a survey of the conditions for occurrence and spatial distributions. The basic properties of the individual cavities and associated fluctuating electric fields are discussed as well, and typical densities, widths, and other characteristics are obtained for selected orbits.

A statistical analysis of numerically simulated plasma turbulence

Lower hybrid wave cavities detected by the Freja satellite are analyzed. On the basis of simple statistical arguments by use of signals from two density probes, it is possible to obtain rather general results concerning the individual shapes of these cavities. In particular, it is demonstrated that a cylindrically symmetric Gaussian density depletion seems to give a very good fit for a vast majority of cases. The validity of this model is shown to give a great simplification in the interpretation of the data. As a result, a number of well-defined characteristics are obtained which have to be accommodated within an ultimate theory describing the observed wave phenomena.

Ion-beam diagnostics by means of an electron-saturated plane Langmuir probe

Low‐level electrostatic ion acoustic turbulence generated by the ion–ion beam instability was investigated numerically. It is demonstrated that a conditional statistical analysis can reveal the formation, propagation, and decay of negative potential wells which correspond to ion phase‐space vortices. While the statistical analysis gives results in terms of averages over a conditionally selected subensemble, individual phase‐space structures can be investigated by small clusters of test particles placed at selected positions in phase space. The predictions of the conditional statistical analysis can be tested and their accuracy estimated by this method. A discussion of various aspects of test particle dynamics in turbulent plasmas follows naturally, with particular emphasis on conditioned particle release and relative diffusion of particles. The statistical properties of the fluctuating electric fields sampled along Lagrangian particle orbits is analyzed.