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Register a new userNonlinear magnetoacoustic waves in a cold plasma
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The equations describing planar magnetoacoustic waves of permanent form in a cold plasma are rewritten so as to highlight the presence of a naturally small parameter equal to the ratio of the electron and ion masses. If the magnetic field is not nearly perpendicular to the direction of wave propagation, this allows us to use a multiple-scale expansion to demonstrate the existence and nature of nonlinear wave solutions. Such solutions are found to have a rapid oscillation of constant amplitude superimposed on the underlying large-scale variation. The approximate equations for the large-scale variation are obtained by making an adiabatic approximation and in one limit, new explicit solitary pulse solutions are found. In the case of a perpendicular magnetic field, conditions for the existence of solitary pulses are derived. Our results are consistent with earlier studies which were restricted to waves having a velocity close to that of long-wavelength linear magnetoacoustic waves.
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We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel-Korteweg-de Vries-Zakharov-Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio $b$ increases as the electron distribution becomes increasingly flat-topped. As $b$ and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle $theta$ at which the perturbation is applied. Solutions whose minimum value is zero and travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of $theta$ for which the first-order growth rate is not zero.
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earths magnetosphere where cold background plasma of sufficient density is present.
Compressible disturbances propagate in a plasma in the form of magnetoacoustic waves driven by both gas pressure and magnetic forces. In partially ionized plasmas the dynamics of ionized and neutral species are coupled due to ion-neutral collisions. As a consequence, magnetoacoustic waves propagating through a partially ionized medium are affected by the ion-neutral coupling. The degree to which the behavior of the classic waves is modified depends on the physical properties of the various species and on the relative value of the wave frequency compared to the ion-neutral collision frequency. Here, we perform a comprehensive theoretical investigation of magnetoacoustic wave propagation in a partially ionized plasma using the two-fluid formalism. We consider an extensive range of values for the collision frequency, ionization ratio, and plasma $beta$, so that the results are applicable to a wide variety of astrophysical plasmas. We determine the modification of the wave frequencies and study the frictional damping due to ion-neutral collisions. Approximate analytic expressions to the frequencies are given in the limit case of strongly coupled ions and neutrals, while numerically obtained dispersion diagrams are provided for arbitrary collision frequencies. In addition, we discuss the presence of cutoffs in the dispersion diagrams that constrain wave propagation for certain combinations of parameters. A specific application to propagation of compressible waves in the solar chromosphere is given.
The excitation and propagation of finite amplitude low frequency solitary waves are investigated in an Argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Kortweg-de Vries equation.
The excitations of nonlinear magnetosonic waves in presence of charged space debris in the low Earth orbital plasma region is investigated taking into account effects of electron inertia in the framework of classical magnetohydrodynamics, which is also referred to as inertial magnetohydrodynamics. Magnetosonic waves are found to be governed by a forced Kadomtsev-Petviashvili equation with the forcing term representing effects of space debris particles. The dynamical behaviors of both slow and fast magnetosonic solitary waves is explored in detail. Exact accelerated magnetosonic lump solutions are shown to be stable for the entire region in parameter space of slow waves and a large region in parameter space of fast waves. In a similar way, magnetosonic curved solitary waves become stable for a small region in parameter space of fast waves. These exact solutions with special properties are derived for specific choices of debris functions. These novel results can have potential applications in scientific and technological aspects of space debris detection and mitigation.
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