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Register a new userCharged space debris induced nonlinear magnetosonic waves using inertial magnetohydrodynamics
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Added by
Siba Prasad Acharya
Publication date
2021
fields
Physics
and research's language is
English
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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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The excitations of nonlinear magnetosonic lump waves induced by orbiting charged space debris objects in the Low Earth Orbital (LEO) plasma region are investigated in presence of the ambient magnetic field. These nonlinear waves are found to be governed by the forced Kadomtsev-Petviashvili (KP) type model equation, where the forcing term signifies the source current generated by different possible motions of charged space debris particles in the LEO plasma region. Different analytic lump wave solutions that are stable for both slow and fast magnetosonic waves in presence of charged space debris particles are found for the first time. The dynamics of exact pinned accelerated lump waves is explored in detail. Approximate lump wave solutions with time-dependent amplitudes and velocities are analyzed through perturbation methods for different types of localized space debris functions; yielding approximate pinned accelerated lump wave solutions. These new results may pave new direction in this field of research.
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.
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.
We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schrodinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them.
A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamiltons Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross helicity and entropy, as the only constraints on variations of density, pressure, fluid velocity, and magnetic vector potential over a relaxation domain. A novel phase-space version of the MHD Lagrangian is derived, which gives Euler--Lagrange equations consistent with previous work on exact ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether $vec{E} + vec{u}timesvec{B} = 0$ should be a constraint is discussed.
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