M. S. Janaki

Study of nonlinear oscillations in a glow discharge plasma using empirical mode decomposition and Hilbert Huang transform

Hilbert Huang transform (HHT) based time series analysis was carried out on nonlinear floating potential fluctuations obtained from hollow cathode glow discharge plasma in the presence of anode glow. HHT was used to obtain contour plots and the presence of nonlinearity was studied. Frequency shift with time, which is a typical nonlinear behaviour, was detected from the contour plots. Various plasma parameters were measured and the concepts of correlation coefficients and the physical contribution of each intrinsic mode function have been discussed. Physically important quantities such as instantaneous energy and their uses in studying physical phenomena such as intermittency and non-stationary data have also been discussed.

Vlasov-Maxwell equilibria: Examples from higher-curl Beltrami magnetic fields

Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion and lead to linear or nonlinear functional relations between current and vector potential. The nonlinear relations support various special types of magnetic configurations including multiple current sheets and magnetic field discontinuities leading to singular current layers. It is demonstrated through the examples that in one dimension, the description of the equilibrium magnetic fields obeys double or higher-curl Beltrami equation. For the linear case, such representation gives the advantage of obtaining exact analytic solutions that are expressed as a superposition of the single-curl Beltrami fields.

Onset of normal and inverse homoclinic bifurcation in a double plasma system near a plasma fireball

Plasma fireballs are generated due to a localized discharge and appear as a luminous glow with a sharp boundary, which suggests the presence of a localized electric field such as electrical sheath or double layer structure. The present work reports the observation of normal and inverse homoclinic bifurcation phenomena in plasma oscillations that are excited in the presence of fireball in a double plasma device. The controlling parameters for these observations are the ratio of target to source chamber (nT/nS) densities and applied electrode voltage. Homoclinic bifurcation is noticed in the plasma potential fluctuations as the system evolves from narrow to long time period oscillations and vice versa with the change of control parameter. The dynamical transition in plasma fireball is demonstrated by spectral analysis, recurrence quantification analysis (RQA), and statistical measures, viz., skewness and kurtosis. The increasing trend of normalized variance reflects that enhancing nT/nS induces irregularity...

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrodinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.

Shear-wave Mach cones in a strongly coupled dusty plasma

Shear-wave Mach cones excited in a strongly coupled dusty plasma in the fluid regime are studied using the generalized hydrodynamic model. The Mach cones are excited by a laser beam that is modeled to sweep the three-dimensional dusty plasma with a velocity that is supersonic with respect to the phase velocity of the transverse shear waves. The formation of single Mach cone structures in vorticity maps reveals that they are formed due to shear motion. It is found that an asymmetry in the wake excitation technique gives rise to certain asymmetries in the Mach cone patterns.

A localized cathode glow in the presence of a bar magnet and its associated nonlinear dynamics

A localized glowing, fireball like structure, appears near the cathode surface of a glow discharge plasma device when it is subjected to a magnetic dipole field produced by a bar magnet placed outside the plasma chamber. It is seen that the plasma density in the localized glow region and the luminous intensity of this structure increases with the increase in the magnetic field strength. The effect of such localized glow region on the plasma floating potential fluctuation dynamics is investigated. Floating potential fluctuations show that the emergence of such localized structure leads the system towards nonlinear dynamical regimes. Increasing the magnetic field strength reveals a transition from order to chaos via period doubling bifurcation. This transition is analyzed by using bifurcation diagram, phase space plots, power spectrum plots, Hilbert Huang transform, and by estimating the largest Lyapunov exponent. The interaction of plasma with a dipole magnetic field produces a non-monotonic potential stru...

Quantum corrections to nonlinear ion acoustic wave with Landau damping

Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α1=me/mi to be of the same order of the quantum parameter Q=ℏ2/(24m2cs2L2). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.

Chaotic magnetic fields in Vlasov-Maxwell equilibria

Stationary solutions of Vlasov-Maxwell equations are obtained by exploiting the invariants of single particle motion leading to linear or nonlinear functional relations between current and vector potential. For a specific combination of invariants, it is shown that Vlasov-Maxwell equilibria have an associated Hamiltonian that exhibits chaos.

Nonlinear electrostatic structures in the presence of correlations

The nature of nonlinear electrostatic potential distribution in a dusty plasma is investigated in the presence of dust-dust correlations by developing an equilibrium kinetic equation that contains the effects of pair correlations. For a plasma in equilibrium, the role of pair correlations is to give rise to a force in the kinetic equation that is proportional to the dust density gradient. The solutions of such a kinetic equation with pair correlations and Poisson’s equation in the presence of a trapped particle population are obtained in the small-amplitude limit. The electrostatic potential represents a localized solitary wave-like structure with the amplitude and width varying with the correlation parameter.

Theoretical and numerical modelling of chaotic electrostatic ion cyclotron (EIC) oscillations by Jerk equation

In the last few years, third order explicit autonomous differential equations, known as jerk equations, have generated great interest as they show features of regular and chaotic motion. In this paper, we have modelled chaotic electrostatic ion cyclotron oscillations using a third order nonlinear ordinary differential equation (ODE) and investigated its nonlinear dynamical properties. The nonlinear ODE has been derived for a plasma system from a two fluid model in the presence of a source term, under the influence of an external magnetic field, which is perpendicular to the direction of the wave vector. It is seen that the equation does not require an external forcing term to obtain chaotic behaviour. The stability of the solutions of the equation has been investigated analytically as well as numerically, and the bifurcation diagram obtained shows a number of interesting phenomena for various regimes of parameters. The coexisting attractors as well as their corresponding basins are shown and the phase space portraits at different conditions are obtained numerically and shown here. The results obtained here are in agreement with preliminary experiments conducted for a similar configuration of a plasma system.