Klaus Elsässer

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.

Lagrangian stability of fluids and multifluid plasmas

Weber’s transformation is used to show how Lin’s constraint should be replaced if fluid equations are derived from Hamilton’s principle. The same technique is used to derive a three‐circulation theorem and a generalization of Ertel’s theorem for perfect multifluid plasmas. The Hamiltonian and Lagrangian formulation of the equations for fluid and electromagnetic potentials is given, with a discussion of their multivaluedness and their gauge and time dependence for static magnetohydrodynamic equilibria. The linear stability of these equilibria is shown to depend on the weight of a single negative eigenvalue of the internal energy variation, compared with all other (positive) contributions to the ‘‘energy’’ functional.

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.

Finite amplitude waves in ion-beam plasma systems

Abstract Several types of solitary waves can exist in an ion-beam plasma system. Their velocity is determined as a function of the beam velocity and the wave amplitude θ 0 . The region of existence is limited for θ 0 → 0 by the linear modes, and for finite θ 0 by the trapping of the beam or background ions.

Toroidal equilibria of an electron gas

Abstract A general formulation for investigating axisymmetric toroidal equilibria of pure electron clouds is given. The fluid and Maxwells equations are reduced to a set of three coupled equations for the (covariant) toroidal components of the generalized vorticity ( F ) and velocity ( j ), and the Bernoulli function ( U ). There appear two arbitrary flux functions I 0 and Ψ 0 , corresponding to the toroidal magnetic field and to the poloidal flux of the generalized vorticity. Experimentally relevant exact analytical and numerical solutions are presented for appropriate boundary conditions.

Uniqueness of the electrostatic solution in Schwarzschild space

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Greens identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.

Potential equations for plasmas round a rotating black hole

The generalized Helmholtz equations of relativistic multifluid plasmas can be integrated for axisymmetric equilibria in close analogy to the magnetic flux conservation law in ideal magnetohydrodynamics [J. D. Bekenstein and E. Oron, Phys. Rev. D 18, 1809 (1978)]. The results are, for each fluid component, two flux functions and a potential equation for the poloidal stream function. Amp\`eres equation for the four-potential

Plasma equations in general relativity

{A}_{\ensuremath{\nu}}

A three‐circulation theorem for relativistic plasmas

is reduced to two coupled equations for the time-like and the toroidal component. So we have altogether four potential equations for a two-component plasma; they can be derived from a variational principle.

Magnetic field perturbations correlated with large amplitude lower-hybrid waves in a high-voltage linear plasma discharge

Vlasov’s equation and the ideal multifluid equations are considered in manifestly covariant form. In the latter case, a thermodynamic closure (locally the first law of thermodynamics) leads to a generalized Kelvin/Helmholtz theorem. In the former case, the local dispersion relation for Langmuir waves in a strong gravitational field is derived and solved.