Solitary Langmuir waves in two-electron temperature plasma

Nonlinear interaction of Langmuir and ion-acoustic waves in two-electron temperature plasma is investigated. New integrable wave interaction regime was discovered, this regime corresponds to the Langmuir soliton with three-hump amplitude, propagating with a speed close to the ion–sound speed in the conditions of strong non-isothermality of electronic components. It was discovered that besides the known analytical solution in the form of one- and two-hump waves, there exists a range of solutions in the form of solitary waves, which in the form of envelope has multi-peak structure and differs from the standard profiles described by hyperbolic functions. In case of fixed plasma parameters, different group velocities correspond to the waves with different number of peaks. It is found that the Langmuir wave package contains both even and uneven numbers of oscillations. Low-frequency potential here has uneven number of peaks. Interrelation of obtained and known earlier results are also discussed.

Arbitrary amplitude Langmuir solitons in a relativistic electron–positron plasma

The arbitrary amplitude Langmuir solitons are investigated in an unmagnetized, warm, relativistic plasma, consisting of electrons and positrons. Both the species are considered to have equal non-relativistic temperatures, but can have arbitrary relativistic drift speeds, and their dynamics are governed by fluid equations. Using the Sagdeev psuedo-potential approach, the effects of drift speed, Mach number, and thermal temperature on the amplitude and width of the Langmuir solitons are investigated. For the parameters considered, only rarefactive solitons are found. These solitons represent dip in electron density or electron holes in the configuration space. Existence domain of the Langmuir solitons is limited by the minimum and maximum Mach numbers for given parameters. An increase in the electron (positron) temperature leads to an increase in the Langmuir soliton amplitude and their half-widths. On the other hand, increasing the electron (positron) drift speeds results in decreasing soliton amplitudes and their half-widths. For some typical parameters corresponding to the pulsar magnetosphere, namely electron density ~106 cm−3 and electron thermal velocity of one-tenth of the velocity of light, the electric field of the Langmuir solitons can be of the order of (3–24)kV/m. The presence of such large amplitude electrostatic solitary structures may accelerate electrons and positrons and also produce fine structures of (1–5) microseconds in pulsar radio emissions.

Coupled Langmuir and nonlinear ion acoustic waves in the presence of non-thermal electrons

A new set of equations describing the coupling of high-frequency electrostatic waves with ion fluctuations is obtained taking into account a non-thermal electron distribution. It is shown that there exist stationary envelope solitons which have qualitatively different structures from the solutions reported earlier. In particular, the Langmuir field envelopes are found with similar width and strong field intensities in comparison to the isothermal case. It is also shown that the presence of the fast or non-thermal electrons significantly modifies the nature of Langmuir solitons in the transition from a single-hump solution to a double-hump solution as the Mach number increases to unity. The low-frequency electrostatic potential associated with the high-frequency Langmuir field has the usual single-dip symmetric structure whose amplitude increases with increasing Mach number. Furthermore, the dip at the center of the double-hump Langmuir soliton is found to become smaller as the proportion of non-thermal electrons increases.

Testing the two-stream instability in a pulsar magnetosphere

Conditions for the development of a two-stream instability in a pulsar magnetosphere are deduced from specific dispersion relations for plane wave perturbations, that depend on the distribution functions of the involved particles. Three different approaches are investigated.Firstly, using relativistic one-dimensional Juttner Synge distribution functions appropriate to describe pulsar pair plasmas flows, we analytically derive the dispersion relation anew, precisely determining the dependence of its coefficients on the temperature, fluid velocity and associated Lorentz factor. We obtain modified frequencies for quasi-longitudinal waves and specific conditions for a two-stream instability to develop.Secondly, the importance of two-stream instabilities is tested numerically on two different timescales, that concern stationary and non-stationary properties of pair plasma flows. The linear analysis involves Gaussian distribution functions of the momentum, factorized with functions that depend on the localisation of the different groups of particles, and shows results that agree with observed luminosities.Finally as derived from fluid equations, the nonlinear evolution of such an instability process allows to associate the high level of radio radiation observed from pulsars with the existence of a lattice of radiating ‘Langmuir‘ soliton-like structures in a pulsar emission region. Actually, pair plasma particles follow the bundle of diverging magnetic field lines in the open magnetosphere and ‘Langmuir‘ soliton-like solutions, modified by magnetic field and density gradients, imply additional radiation.