Hans Schamel

Electron holes, ion holes and double layers: Electrostatic phase space structures in theory and experiment

Abstract The paper reviews the state-of-the-art in the observation and analytical description of localized electrostatic phase space structures. These structures occur on the Debye length scale and introduce a kind of intermittency in the dynamics of externally driven collisionless plasmas. Holes, the one group of structures investigated, are nonlinear saturated states of two-stream instabilities in which saturation is provided by particle trapping. They are ring-shaped vortices in phase space and are macroscopically manifest in local density depressions. Double layers, on the other hand, are narrow monotonic potential transitions and connect differently biased plasmas, resembling in some sense phase transitions. The controlling function of these nonlinearly excited d.c. states in the dynamical evolution of bounded plasmas exhibiting transient phenomena is discussed.

Plasma expansion into vacuum — A hydrodynamic approach

Abstract Based on the hydrodynamic description, the planar expansion of a plasma into vacuum is investigated numerically and analytically. Several dynamical structures are found and explained. In the inviscid case, ion wave collapse is the most striking feature. Viscosity prevents the collapse an d allows long-term calculations. Three phases in the evolution can be distinguished. In the time asymptotic regime the self-similar state is approached. This approach is preceded by a state of intermediate asymptotics and applies to charge separation as well.

The application of the spectral method to nonlinear wave propagation

Abstract We integrate the Korteweg-de Vries/Burgers equation numerically by using the spectral and pseudospectral method, respectively. Comparing the results with analytic solutions, we show that the aliasing interactions within the pseudospectral method lead to errors increasing in time, while the spectral method gives the correct time evolution. It is shown both analytically and by the numerical solutions that three invariants of the Korteweg-de Vries equation are conserved by both; therefore the number of invariants of any scheme is not decisive for a good approximation of the continuous solutions. Finally, we apply the spectral method to calculate the time evolution of turbulent sound waves in one and two space dimensions.

Role of Trapped Particles and Waves in Plasma Solitons-Theory and Application

In this tutorial and review paper, we investigate the influence of trapped particles on the propagation of ion acoustic solitons and the role of trapped waves on the propagation of Langmuir solitons. The classical potential method allows us to construct finite amplitude soliton solutions, and trapping phenomena are found to retard the motion of solitons. Thus, ion acoustic solitons have minimum speed when they are based on an isothermal electron equation of state since this corresponds to maximum electron trapping. In the small amplitude regime, deviations from the Boltzmann law lead to a new nonlinear term. Subsequently, the dynamics of the soliton is governed by a modified KdV-equation [e.g., (23)]. For Langmuir solitons an existence diagram is found and exhibits the comparison between experimentally observed localized structures and theory. The connection with the various small amplitude soliton solutions is also pointed out. Moreover, the inclusion of a pump and of dissipative terms in the coupled nonlinear Schrodinger-ion equation gives rise to a transient phenomenon called soliton flash, whose implication to the laboratory experiments is discussed. Finally, as an application in numerical analysis the propagation of solitons is followed by solving the KdV-equation in Fourier-space. This turns out to be an excellent tool to test stability and accuracy of numerical schemes. Our results reveal that the so-called aliasing interactions lead to erroneous solutions. The conservation of invariants does not guarantee the accuracy of a numerical algorithm, although it is needed for its stability.

Nonlinear dynamics in expanding plasmas

Abstract The expansion of a plasma occupying initially a half-space is investigated numerically and, by means of a novel description of the ion fluid, also analytically. A simple wave structure is found in the collisionless approximation. Stabilized by dissipation, the associated ion bunching gives rise to a fast ion component, similar to the ion blow-off in laser fusion. Three non-stationary regimes of this strongest nonlinear and inhomogeneous dynamical system are distinguished and discussed. For large t the ion front propagates with a speed proportional to (t−t 1 ) 1 2 where t1 is a reference time. A simple picture emerges, explaining the diverse experimental data.

SUNION-An Algorithm for One-Dimensional Laser-Plasma Interaction

Abstract SUNION solves the combined problem of ion expansion and of resonance absorption of p -polarized electromagnetic radiation. Well-posed initial and boundary conditions are derived within the ponderomotive approximation. Efficiency and accuracy of the code are checked by reproducing known results found in literature for various simplifications. A new type of numerical instability is exposed within the Lagrangian description of the expanding ions, pointing out a fundamental difficulty in treating plasma expansion into a vacuum. It originates from charge separation and is correlated with a singular behavior of the plasma flow. The solution method is considerably simplified by taking into account the first time-derivative in the complex second-order Schrodinger-type wave equation, and, by solving the latter by a Crank-Nicholson scheme, without reference to shooting methods. The absorption coefficient reaching values up to 60 per cent is found to be rather insensitive to the global density structure, and reflects more or less the local scale length at the critical density. Profile steepening caused by radiation pressure is accomplished within the first twenty ion plasma periods.

The dynamics of cavitons induced by the soliton flash

The dynamics of a caviton, its formation and evolution after saturation is studied by solving appropriate coupled mode equations. It is found that field trapping occurs in a flash-like manner, giving rise to the formation of a cavity and its subsequent splitting into two ion acoustic streamers. For this phenomenon, also seen in particle simulations and resonance absorption experiments, a simple analytical description is given.

The asymptotic velocity of fast ions in expanding plasmas

The front of an expanding plasma generally exposed to charge separation is shown to acquire asymptotically a speed given by self‐similar theory.

Linear modes in the presence of solitary ion holes

Abstract Linear perturbations of a plasma have been investigated which is structured by the presence of a kinetic ion hole equilibrium. A new dispersion relation, obtained by a two-dimensional stability analysis, exhibits two kinds of non-decaying modes. One is a transverse propagating ion acoustic type wave, which becomes dispersive in the long wave-length limit. The other branch represents aperiodic oscillations, which grow in time for k k cr , where k is the perpendicular wavenumber, and which destabilize the ion hole structure.

Energy Spectra of Turbulent Sound Waves

The dynamics of an irrotational compressible flow is considered in several space dimensions both theoretically and by numerical experiments. First we derive the nonlinear scalar wave equation (9) describing sound waves of small amplitude and small dissipation. The associated weak-turbulence equations in the limit of zero dissipation are solved by exact stationary power laws for the spectrum. But the numerical solutions of the inviscid equation (9) show the tendency of breaking down after a finite time, leading to shock spectra instead of the weak-turbulence spectra. This shows that an asymptotic analysis of cumulants does not account for “intermittency effects”.Finally it is argued that for the inviscid case no other closure of the hierarchy can take intermittency into account.