Brahmananda Dasgupta

Coupled nonlinear Schrödinger equation for Langmuir and dispersive ion acoustic waves

Abstract A coupled pair of nonlinear Schrodinger equations for the Langmuir waves and the dispersive ion acoustic wave has been derived. The equations are valid for all values of the wave number k l of the low-frequency waves. It is shown that the ion acoustic wave is rendered modulationally unstable for all k l . If the amplitude of the ion acoustic wave is sufficiently large, the threshold for modulational instability of the Langmuir waves is diminished.

Relaxed States of a Magnetized Plasma with Minimum Dissipation

. A solution of thisequation is accomplished using the analytic continuation of the Chandrasekhar-Kendall eigenfunctionsin the complex domain. The new features of this theory show (i) that a single fluid can relaxto an MHD equilibrium which can support a pressure gradient even without a long-term couplingbetween mechanical flow and magnetic field, and (ii) field reversal in states that are not force free.[S0031-9007(98)07284-6]

Exact solution of damped nonlinear Schrödinger equation for a parabolic density profile

Abstract An exact single envelope soliton solution of the damped nonlinear Schrodinger equation in a medium with a parabolic density profile has been obtained. It is found that the condition of reflection of the soliton from the density hump is determined by its initial velocity and the scale lengths of the inhomogeneity.

Field-reversed configuration (FRC) as a minimum-dissipative relaxed state

Abstract The field-reversed configuration (FRC) with a completely null toroidal field and finite plasma beta is shown to result from a relaxation mechanism based on the principle of minimum dissipation of energy.

Solitary magnetosonic waves with Landau damping

The effect of Landau damping on nonlinear magnetosonic waves propagating obliquely to the magnetic field in a finite beta plasma has been studied. It has been found that such magnetosonic waves owing to their interaction with resonant particles are governed by a KdV equation with a damping term. This equation has solitary wave solutions whose amplitude decays with time as (1 + τ/τ0)−2. The decay rates of both fast and slow waves have been computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for fast and slow magnetosonic waves. At a certain angle of propagation, the decay rates of both modes are equal in the case of a low beta plasma. The fast mode has a higher damping rate for higher beta and becomes practically nonexistent for nearly perpendicular angles of propagation.

Surface waves in a magnetized plasma

Electrostatic surface waves propagating along the interface between a warm magnetized plasma and vacuum are investigated by deriving the relevant dispersion relations using a fluid model. The general dispersion relation for arbitrary orientation of the magnetic field and the propagation vector is derived in a closed form and certain special cases (when the magnetic field is directed parallel and perpendicular to the boundary surfaces) are analyzed numerically.

RF stabilization of ballooning modes in an axisymmetrically rotating plasma

Abstract It is known that ponderomotive forces produced by radial gradients in the RF energy can provide an effective stabilizing mechanism and create a stable window to the second stability regime. This problem is reexamined here with the introduction of axisymmetric toroidal rotation which itself is believed to have stabilizing influence on the ballooning modes on most flux surfaces except in the outer region. It is shown that the stabilizing effect is additive and an additional and important observation is that the outer region of the flux surfaces also gets stabilized by RF waves.

Multiple pulse homoclinic orbits in a nerve conduction equation

Abstract We demonstrate the existence of an infinite family of propagating multiple pulse solutions of a piecewise linear version of the FitzHugh-Nagumo nerve conduction equations. In this PWL version the eigenvalue conditions underlined in a recent work of Evans, Fenichel and Feroe fail to be satisfied.

Chaotic wavetrains in a nerve conduction model

Abstract Chaotic wavetrain solutions are constructed by explicit integration of a nerve conduction model which is a modified FitzHugh-Nagumo (FHN) system satisfying the Evans-Fenichel-Feroe (EFF) eigenvalue conditions. It is demonstrated that there exist non-denumerably many such solutions for each speed of propagation. The possible implication of such solutions in respect of information transfer along the nerve axon is briefly discussed.

On Dust-Bernstein Modes in a Dusty Plasma

Linear dispersion relations of low-frequency electrostatic dust-Bernstein modes have been derived by employing the Vlasov equation for the motions of electrons, ions, and dust particles in a uniformly magnetized dusty plasma. Because of the large mass of the dust grains, the finite Larmor radius effects become significant for dust dynamics giving rise to the existence of extreme low-frequency dust-Bernstein modes. The importance of these low-frequency electrostatic dust-modes on the dust-coagulation and dust-crystallization has also been pointed out.