Strong Langmuir turbulence in a pulsar emission region: statistical analysis

Abstract

We test a turbulent plasma emission model previously proposed to interpret micropulses in individual pulses received from a certain number of pulsars. In this model, we assumed that pulsar radio emissions can be related to the development of a strong Langmuir turbulence in a pulsar emission region. As shown, the elements of such a turbulence in this region are stable Langmuir solitons which have electrostatic and electromagnetic components at the same time. Consequently, they radiate electromagnetic waves likely to reach an observer. On this basis, we assumed that such a strong Langmuir turbulence would give rise to a lattice of stable Langmuir structures, regularly spaced, all with the same amplitude, width, position and velocity along the open magnetic field lines of the pulsar magnetosphere. Properties of such radiating Langmuir structures were associated with micropulses observed in radio pulses. Actually, such Langmuir structures in strongly turbulent pulsar plasmas should have random amplitudes, positions and velocities. Considering these as elementary structures in strongly turbulent pulsar plasmas, we propose a statistical theory for such plasmas. We start with the elementary soliton-like solutions of a non-linear Schrodinger equation, describing the strong turbulence in terms of a set of random solitons. The initial amplitudes, positions and velocities of these solitons are themselves random variables whose distributions act as free parameters for our statistical description. Assuming an ensemble of initial conditions, we are able to determine the mean number of solitons, the dynamical form factor, the resulting energy spectrum, the associated intensity and the intensity distribution. The energy spectrum qualitatively agrees with some of the observed pulsar spectra. The variation with time of the intensity distribution shows a realistic behaviour in a large part of the domain of the intensities.