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Analytical models for nonlinear electron plasma waves in weakly magnetized plasmas are developed for single as well as multi-mode conditions, with continuous wave spectra being a limiting case. The conditions for wave decay as well as modulational instabilities are analysed. Our results demonstrate that slow or nearly stationary plasma density variations can be found for weakly magnetized plasmas even for weakly nonlinear electron plasma waves without involving cavitation of large amplitude plasma waves. A reduction of the growth rates for decay as well as modulational instabilities are found when the spectral width of the wave spectrum is increased. Some of our results are relevant for the interpretation of the nonlinearly enhanced ion acoustic lines often observed in non-equilibrium ionospheres.

Analytical models for weakly nonlinear electron plasma waves are considered in order to obtain dynamic equations for the space-time evolution of their local power spectra. The model contains the wave kinetic equation as a limiting case for slow, long wavelength modulations. It is demonstrated that a finite spectral width in wavenumbers has a stabilizing effect on the modulational instability. The results invite a simple heuristic relation between the spectral width and the root-mean-square amplitude of stable stationary turbulent Langmuir wave spectra. A non-local average dispersion relation is derived as a limiting form by using the formalism developed for the spectral dynamics.

Previous results obtained for modulational instability of a Langmuir wave spectrum are extended to account also for the Langmuir wave decay. The general model is tested by considering first the parametric decay of single-mode Langmuir waves, and also two-wave models, where several combinations are considered: one wave is modulationally unstable, another decay unstable and one where both waves are unstable with respect to decay. For the general case with continuous wave spectra it is found that distribution of the Langmuir wave energy over a wide wavenumber band reduces the decay rate when the correlation length for the spectrum becomes comparable to the wavelength of the most unstable sound wave among the possible decay products.

Small solid metallic objects in relative motion to thermal plasmas are studied by numerical simulations. We analyze supersonic motions, where a distinctive ion wake is formed behind obstacles. At these plasma drift velocities, ions enter the wake predominantly due to deflections by the electric field in the sheath around the obstacle. By irradiating the back side of the object by ultraviolet (UV) light, we can induce also an enhanced photo-electron population there. The resulting charge distribution gives rise to a pronounced local potential and plasma density well behind the object. This potential variation has the form of a three-dimensional ion acoustic double layer, containing also an ion phase space vortex. The analysis is supported also by one-dimensional numerical simulations to illustrate the importance of boundary conditions, Dirichlet and von Neumann conditions in particular.

The formation and propagation of ion phase-space vortices are observed in a numerical particle-in-cell simulation in two spatial dimensions and with three velocity components. The code allows for an externally applied magnetic field. The electrons are assumed to be isothermally Boltzmann-distributed at all times, implying that Poisson's equation becomes nonlinear for the present problem. Ion phase-space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. We consider the effect of a finite beam diameter and a magnetic field, in particular. A vortex instability is observed, appearing as a transverse modulation, which slowly increases with time and ultimately breaks up the vortex. When many vortices are present at the same time, we find that it is their interaction that eventually leads to a gradual filling-up of the phase-space structures. The ion phase-space vortices have a finite lifetime, which is noticeably shorter than that found in one-dimensional simulations. An externally imposed magnetic field can increase this lifetime considerably. For high injected beam velocities in magnetized plasmas, we observe the excitation of electrostatic ion-cyclotron instabilities, but see no associated formation of ion phase-space vortices. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.

Dynamical equations are derived for the evolution of weakly nonlinear electron plasma waves when the electron distributions are characterized by more than one temperature component. The presence of electron-acoustic modes in multi- temperature plasmas opens a new decay channel. By considering an explicit example, it is demonstrated that these distributions imply significant modifications of the standard models for the decay spectrum of electron plasma waves. In particular, long-wavelength Langmuir waves can decay to shorter wavelengths. The results can have implications for ionospheric heating experiments.

Particle diffusion is investigated in a strictly two-dimensional collisionless guiding-centre model for a strongly magnetized plasma. An analytical expression is presented for the entire time variation of the mean square test-particle displacement in the limit of low-frequency, strongly turbulent, electric field fluctuations. The analysis relies on an explicit integral expression for the Lagrangian autocorrelation function in terms of the Eulerian wavenumber spectrum and a time-varying weight function. Bohm diffusion is discussed by means of a simple model spectrum. The analysis applies for turbulent transport associated with electrostatic convective cells, magnetostatic cells and drift wave turbulence with the assumption of local homogeneity and isotropy in two dimensions.

The nonlinear transient evolution of a suddenly applied monochromatic wave in a homogeneous plasma is considered, with particular emphasis on the magnetized case, where ordinary and extraordinary electromagnetic waves travelling normal to B are treated. Two important features are described. First, the penetration of the wave front is shown to be accompanied by ‘radiation’ of low-frequency waves, of which ion cyclotron and lower-hybrid waves are considered here. Next, the presence of a nonlinear, second-harmonic precursor is predicted, containing two natural modes of oscillation, one with exactly twice the frequency of the fundamental, and the other a slightly frequency-shifted contribution. The analysis is readily generalized to waves other than those considered here.

The equilibrium properties of a two-dimensional plasma are examined theoretically, using a model where the finite-Larmor-radius corrections to the simple guiding-centre description are included. The analysis is carried out in a truncated Fourier representation of the resulting equations. This system has three ‘rugged’ quadratic invariants. A canonical-ensemble probability distribution characterized by three temperatures is derived. The resulting partition function is obtained and the equilibrium spectral energy density is calculated. The possibility of negative-temperature states leading to an inverse energy cascade is pointed out.

Two coupled equations describing the nonlinear evolution of modified convective cells with a finite but small wavenumber parallel to the external magnetic field B are derived. It is found that, for oblique propagation, the electrostatic and magnetostatic convective mode do not decouple as in the strictly perpen-dicular case. Various aspects of the governing equations are investigated. In the weakly nonlinear lirait, a three-wave interaction study shows the possibility of dual energy cascading, or of cascading to larger wavenumbers only, depending on the direction of the parallel wavenumber component of the pump wave. Furthermore, solitary wave solutions in the form of double vortices are considered.