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Linear stability analysis of strongly coupled incompressible dusty plasma in presence of shear flow has been carried out using the generalized hydrodynamical (GH) model. With the proper Galilean invariant GH model, a nonlocal eigenvalue analysis has been done using different velocity profiles. It is shown that the effect of elasticity enhances the growth rate of shear flow driven Kelvin- Helmholtz (KH) instability. The interplay between viscosity and elasticity not only enhances the growth rate but the spatial domain of the instability is also widened. The growth rate in various parameter space and the corresponding eigenfunctions are presented.

The paper presents an application of empirical mode decomposition (EMD) for the analysis of intermittent chaotic fluctuations from a glow discharge plasma. Here, the nature of the oscillations changes from an initial relaxation oscillation to a final chaotic oscillatory state via intermittent chaos. The time series data have been decomposed into several intrinsic mode functions (IMFs) using EMD. Furthermore, the estimation of the variance of the IMFs and the correlation of these IMFs with the original time series help us to identify the presence of coherent modes in the fluctuations. Through this analysis, we could clearly observe that initially during the relaxation oscillations the system was dominated by one type of coherent mode, whereas in the final chaotic state, it was dominated by another coherent mode. In the intermediate case, i.e., intermittent chaotic state, both the coherent modes are seen to be present. We have also used rescaled range ( R / S ) statistical method to identify the coherent mo...

Floating potential fluctuations associated with an anode fireball in a glow discharge plasma in the toroidal vacuum vessel of the SINP tokamak are found to exhibit different kinds of oscillations under the action of vertical magnetic field of different strengths. While increasing the vertical magnetic field, the fluctuations have shown transitions as: chaotic oscillation → inverse homoclinic transition → intermittency → chaotic oscillation. However, on decreasing the magnetic field, the fluctuations are seen to follow: chaotic oscillations → homoclinic transition → chaotic oscillation; that is the intermittent feature is not observed. Fireball dynamics is found to be closely related to the magnetic field applied; results of visual inspection with a high speed camera are in close agreement with the fluctuations, and the fireball dynamics is found to be closely related to the transitions. The statistical properties like skewness, kurtosis, and entropy of the fluctuations are also found to exhibit this hysteresis behaviour.

Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, Lmax, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time series is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.

A visco-elastic medium, such as a strongly coupled dusty plasma (SCDP), permits both the propagation of longitudinal dust acoustic mode due to compressibility and transverse shear mode due to elasticity. In the presence of finite velocity shear, these two modes get coupled with each other and eventually the coupled mode becomes unstable. In a non-Newtonian dust fluid, it has been found that the viscosity gradient has a modulating effect on this shear-driven instability under various parametric regimes. A detailed investigation has been carried out on the effect of viscosity gradient on the stability characteristics of a strongly coupled dusty plasma by using the conventional dust fluid equations; both analytically and numerically. These results can be helpful in understanding the phenomena associated with mechanical instabilities in highly viscous fluids; such as metallic glasses, Earth's mantle etc.

[1] Recent satellite observations show that current sheets in the space plasma environment are often characterized by bifurcated structures. The majority of the available models of the bifurcated current sheet in the literature are based upon equilibrium Vlasov-Maxwell kinetic theory. While in principle, kinetic models are more fundamental, investigations based on fluid theory can sometimes be advantageous. For instance, because of its inherent simplicity, fluid models of the current sheet can be used in the detailed nonlocal or global analysis of fluid stability. The present paper puts forth a two-fluid model of the bifurcated current sheet on the basis of the pseudo-potential method. According to the present model, double peaked current sheet is characterized by a transverse non-uniform flow and a profile of plasma density that has a plateau in the region between the current peaks. Further, the plasma pressure tensor associated with such a bifurcated current sheet is shown to be anisotropic and non-gyrotropic.

An attempt is made to develop an equilibrium kinetic equation for a weakly non ideal inhomogeneous gravitational system utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. It is shown that the pair correlational function explicitly depends upon the nature of binary interaction between particles. The corresponding kinetic equation containing pair correlation corrections is devoid of the degeneracy present in the collisionless Boltzmann equation with respect to the nature of the two particle interactions, unlike the Vlasov equation that cannot recognize the nature of two particle interaction. A net effect of the particle correlations can be realized only if the spatial symmetry of the correlation interaction is broken due to a spatial inhomogeneity. Such an inhomogeneity is inherently present in a bulk gravitational system in view of the unshielded long range nature of the two-particle interactions. In a finite gravitational system, the effects of pair correlations in the first order kinetic equation can be expressed in terms of the macroscopic gravitational potential to obtain a modified Boltzmann distribution that includes the effects of correlations.

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.

A nonlinear evolution equation governing the two dimensional propagation of fast and slow magnetosonic modes in a warm collisional plasma has been derived. This equation is a combination of Kadomtsev-Petviashvili (K-P) equation and the Burgers equation. The two dimensional K-P equation has two types of solitary wave solutions depending on the sign of the coefficients. One type is the usual planar type, the other is the lump solution. Both types of solitary wave solutions decay with time in the weak collisional limit. The two dimensional features of the amplitude and width of the lump or algebraic soliton have been discussed and the decay rates computed numerically. The decay rates depend on plasma beta and on the angle of propagation and the rates are different for the fast and the slow waves. At a certain angle of propagation the decay rates of both the modes are equal in the case of low beta plasma. Because of 2-D effects, the slow mode, although it has a lower collisional decay rate than the fast mode,...

Two dimensional shock structures of fast and slow magnetosonic waves, propagating in a dissipative warm magnetized plasma with a flow velocity are studied. The nonlinear evolution equation derived for such plasma, where dissipation is provided by electron ion collisions, is found to be a combination of Kadomtsev Petviashvili and Burger equation. Numerical solutions of this equation are obtained by transforming it to a moving frame of reference. These solutions, with appropriate boundary conditions show the development of shock structures both for fast and slow modes. Dependence of shock strength on plasma beta, angle of inclination of the magnetic field with the direction of flow velocity are shown. The most interesting feature is that, while for slow wave the shock strength persists for all angles of propagation but for the fast wave the shock strength vanishes below a certain critical Mach number and above a certain angle between the propagation vector and flow velocity.

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.

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 in plasma dynamics. The exponential growth of the time period is strongly indicative of homoclinic bifurcation in the system. The gradual decrease of skewness and increase of kurtosis with the increase of nT/nS also reflect growing complexity in the system. The visual change of recurrence plot and gradual enhancement of RQA variables DET, Lmax, and ENT reflects the bifurcation behavior in the dynamics. The combination of RQA and spectral analysis is a clear evidence that homoclinic bifurcation occurs due to the presence of plasma fireball with different density ratios. However, inverse bifurcation takes place due to the change of fireball voltage. Some of the features observed in the experiment are consistent with a model that describes the dynamics of ionization instabilities.

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived. >

In a RF produced magnetized argon plasma expanding into a larger expansion chamber, electrostatic modes propagating azimuthally in the direction of the electron diamagnetic drift and frequency greater than the ion cyclotron frequency are observed. In the radial direction, the mode amplitude peaks at a location where the radial density gradient is maximum. The modes are detected at axial locations up to 16 cm away from the entrance aperture. For fixed values of the neutral pressure and magnetic field, the mode frequency is found to be independent of the location at which it is measured. The modes exhibit drift wave characteristics revealing a radial structure with the azimuthal mode number m = 1 at the lower radial locations (r ∼ 3.0 cm) while the m = 2 mode is located in the outer region. Theoretical modeling using a local dispersion relation based on the fluid equations predicts destabilization of the modes with frequency greater than the ion-cyclotron frequency by electron-neutral collisions and exhibit...

In the strongly coupled limit, the generalized hydrodynamic model shows that a dusty plasma, acquiring significant rigidity, is able to support a “shear” like mode. It is being demonstrated here that in presence of velocity shear gradient, this shear like mode gets coupled with the dust acoustic mode which is generated by the compressibility effect of the dust fluid due to the finite temperatures of the dust, electron, and ion fluids. In the local analysis, the dispersion relation shows that velocity shear gradient not only couples the two modes but is also responsible for the instabilities of that coupled mode which is confirmed by nonlocal analysis with numerical techniques.

Floating potential fluctuations of a glow discharge plasma are found to exhibit different kinds of mixed mode oscillations. Power spectrum analysis reveals that with change in the nature of the mixed mode oscillation (MMO), there occurs a transfer of power between the different harmonics and subharmonics. The variation in the chaoticity of different types of mmo was observed with the study of Lyapunov exponents. Estimates of correlation dimension and the Hurst exponent suggest that these MMOs are of low dimensional nature with an anti persistent character. Numerical modeling also reflects the experimentally found transitions between the different MMOs.

In our work, we have proposed the arcade structures as minimum dissipative relaxed states (including both the viscous and resistive channels) pertaining to a two-fluid description of the plasma. The obtained relaxed state is non force-free in nature and appropriate to an open system with external drives. The Euler-Lagrange equations are solved in Cartesian coordinates subject to the existing photospheric boundary conditions. The solutions are seen to support flow-containing arcade like magnetic field configurations with inherent dissipative properties that may play an important role in the coronal heating. An interesting feature observed is the generation of different types of arcades with the variation of a single parameter characterizing the relaxed state. Also, recent observations with the LASCO coronagraph on board the SOHO spacecraft suggest that the helmet streamers originating from the sun may have an internal triple-arcade structure. The two-fluid relaxed state obtained here is also seen to support such structures., Comment: 18 pages and seven figures

[1] It has been suggested that Magnetic Holes (MHs) are caused by perpendicular proton energization due to the Ponderomotive Force (PF) associated with phase steepened Alfven waves. Here we include particle finite Larmor radius (FLR) effects and the effects of ion gyroharmonics in the PF expression. The general expression for the PF is derived by using the hot plasma dielectric tensor from kinetic theory. The fully kinetic expression has a multiple resonance character which is not revealed in the fluid picture. It will be shown that by including such effects, the expression for the PF will be significantly altered, both at the low frequency and high frequency limit. Also, an explicit analytic expression for the PF keeping only the first order FLR terms is given for conceptual purposes for the readers.

The stabilization of Rayleigh-Taylor (RT) instability is investigated in a non-Newtonian unmagnetized dusty plasma with an experimentally verified model of shear flow rate dependent viscosity. It has been found that non-Newtonian property has also a significant role in stabilization of RT instability along with velocity shear stabilization in the short wavelength regime. The effect of the non-Newtonian parameters is more profound in the higher velocity shear rate regime. A detailed study is reported on the role of non-Newtonian effect on RT instability with conventional dust fluid equations using standard numerical eigenvalue analysis.

Detection of nonlinearity has been carried out in periodic and aperiodic floating potential fluctuations of DC glow discharge plasma by generating surrogate data using iterative amplitude adjusted Fourier transform method. We introduce “delay vector variance” analysis (DVV) for the first time, which allows reliable detection of nonlinearity and provides some easy to interpret diagram conveying information about the nature of the experimental floating potential fluctuations (FPF). The method of false nearest neighbourhood is deployed on the FPF's to find a good embedding so as to be acquainted with the precise knowledge of m, which is desirable for carrying out DVV analysis. The emergence of nonlinearity with increase in discharge voltage has been ensured by taking into consideration the total energy present in different band of frequencies excited due to nonlinear processes. Rejection of null hypothesis has been verified by performing the rank test method that confirms the presence of nonlinearity quantitatively.

The principle of minimum dissipation of energy is utilized to obtain the spheromak configuration as a relaxed state. The Euler-Lagrange equation for the minimum dissipative relaxed state is solved in terms of Chandrasekhar-Kendall eigenfunctions analytically generalized in the complex domain. This state is non-force-free and further shows the nonconstancy of the ratio of parallel current to the magnetic field.

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 presence of Landau damping terms has been calculated assuming the Landau damping parameter $\alpha_1 = \sqrt{{m_e}/{m_i}}$ to be of the same order of the quantum parameter $Q = {\hbar^2}/({24 m^2 c^2_{s} L^2})$. The amplitude is shown to decay very slowly with time as determined by the quantum factor $ Q$., Comment: 9 pages, 1 figure

Two-dimensional (2-D) density and potential measurements have been carried out for plasma diffusing through an aperture in a diverging magnetic field. The radial density profile near the source is peaked on the axis but gradually evolves into a hollow profile away from the source. We observe a slow increase of the peak density along a hollow conical surface and correlate with the 2-D potential measurement reported earlier. It is also shown that the formation of 2-D structures with similar features are observed whenever plasma is allowed to diffuse through a physical aperture in such diverging magnetic field configuration, with or without the presence of electric double layer, i.e., the phenomenon is generic in nature.

Relaxed States of a slightly resistive and turbulent magnetized plasma is obtained by invoking the principle of minimum dissipation which leads to curl curl curl B = \lambda B . A solution of the above equation is accomplished using the analytic continuation of the Chandrasekhar-Kendall eigenfunctions in the complex domain. The new features of this theory is to show (i) a single fluid can relax to an MHD equilibrium which can support pressure gradient even without a flow, (ii) field reversal (RFP) in states that are not force free., Comment: LateX, 10 pages, 5 figures (ps), 18 references

Order-chaos-order was observed in the relaxation oscillations of a glow discharge plasma with variation in the discharge voltage. The first transition exhibits an inverse homoclinic bifurcation followed by a homoclinic bifurcation in the second transition. For the two regimes of observations, a detailed analysis of correlation dimension, Lyapunov exponent, and Renyi entropy was carried out to explore the complex dynamics of the system.

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noise level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.

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.

A nonresonant perturbative approach has been utilized to probe the modification of the equilibrium plasma distribution function due to plasma interaction with externally launched high-frequency large-amplitude RF waves in the presence of quantum effects. The quantum distribution function from the complete Wigner equation has been obtained for a high-frequency wave with constant amplitude. For waves with weak spatial or temporal modulation, the equilibrium distribution function has been obtained by solving the Wigner equation as an initial or boundary-value problem and retaining only lowest-order quantum effects. In the dipole approximation, a higher order diffusion has been identified in addition to quantum modified ponderomotive and quasilinear diffusion effects. Additional terms of the Wigner equation give the impression of higher order diffusion effects in the system.

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.

Nonlinear absorption of electromagnetic waves propagating through a plasma perpendicular to the uniform magnetic field at a frequency close to electron cyclotron subharmonic frequency is investigated by studying the dynamics of individual particle motion. The motion of the electron is described using a relativistic Hamiltonian formalism. Second-order canonical perturbation theory is carried out to explicitly obtain the subharmonic response. When the variation in the parameters of the dynamical system is slow, the motion of the particles is characterized by a conserved adiabatic invariant equal to the area embedded by the trajectory in phase space. The energy gain of an electron has been obtained in terms of the change in the adiabatic invariant resulting from a qualitative change in the phase orbit of the electron. A case of strong nonlinearity is considered in which the energy absorbed by an electron from the wave is greater than its thermal energy. The amount of absorbed power is computed analytically for the case of ordinary-mode polarization. (c) 1995 The American Physical Society

Plasma created by an inductive RF discharge is allowed to expand along a diverging magnetic field. Measurement of the axial plasma potential profile reveals the formation of an electric double layer near the throat of the expansion chamber. An accelerated ion beam has been detected in the downstream region, confirming the presence of the double layer. The 2-D nature of the ion energy distribution function of the downstream plasma has been studied by a movable ion energy analyser, which shows that the beam radius increases along the axial distance. The 2-D structure of the plasma potential has been studied by a movable emissive probe. The existence of a secondary lobe in the contour plot of plasma equipotential is a new observation. It is also an interesting observation that the most diverging magnetic field line not intercepting the junction of the discharge tube and the expansion chamber has an electric field aligned with it.

It is shown that the stationary collisionless single-particle Wigner equation in one dimension containing quantum corrections at the lowest order is satisfied by a distribution function that is similar in form to the Maxwellian distribution with an effective mass and a generalized potential. The distribution is used to study quantum corrections to electron hole solutions.

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.

The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger's equation. This has helped in obtaining some exact eigenmode solutions in both cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed., Comment: 10 pages, 4 figures

The properties of electrostatic transverse shear waves in a strongly coupled dusty plasma are examined using the nonlinear version of the generalized hydrodynamic equation. In the kinetic limit, it is shown that strongly coupled plasmas support localized dipolar vortexlike solutions with amplitude modulated periodically.

An attempt is made to develop an equilibrium kinetic equation for a weakly non-ideal non-uniform plasma utilizing the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations. The time-independent pair correlation function is shown to be a product of two single-particle non-uniform distribution functions and the binary interaction potential that is taken to be Coulombian. In order to obtain a closed form of kinetic equation, it is necessary to express the first-order corrections to the Vlasov equation arising out of correlations in terms of average plasma potential. The singular nature of the Coulomb potential gives rise to certain divergences that can be removed by the choice of Landau and Debye lengths as the lower and upper limits of the impact parameter. This procedure enables a representation of pairwise interaction potential in terms of average macroscopic potential. The first-order kinetic equation is utilized to obtain a modified Boltzmann distribution that includes the effects of correlations.

The first-order kinetic equation of the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations for an equilibrium inhomogeneous plasma is shown to contain an effective force resulting from pair correlations that depends on the gradient of the average electric field modulus. Such a kinetic equation is utilized to obtain a Boltzmann distribution that includes the effects of correlations. For an electron-ion plasma with stationary ions and finite electron-electron correlations, the nature of the Debye-screening potential is investigated.

A formalism is developed for flowing two-fluid stationary states for an externally driven system with dissipation. For the standard reduced model (neglecting electron inertia effects) and assuming quasineutrality to hold, a flow-field coupling equation is proposed as the governing equation for the steady-state plasma. In the presence of only azimuthal flow a modified Grad-Shafranov (GS) equation is obtained. The GS is solved for the topology relevant to field-reversed configuration (FRC). The external electric field required to attain the configuration is obtained self-consistently.

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.

The wake-field potentials produced by charged particles moving in a plasma are investigated in the presence of finite Landau-damping effects in the wave dispersion relation. In the frame of reference moving with the particle, the phase velocities of the spectrum of waves excited by the moving charge depend on the angle of propagation of the wave vector giving rise to a directional wave-particle resonance condition. As a consequence, the wake structure is seen to decay both along and transverse to the direction of motion of the charged particle.

Finite sized charged particles introduced into streaming dusty plasmas produce wake patterns in the downstream region. The structure of the wake potential is found to depend on values of the charge size and Mach number M, where M is the ratio of the flow speed to the dust acoustic speed.

The wake structure of a charged particle moving in a dusty plasma is analyzed for the cases where the charge speed is greater or less than the dust-acoustic speed. In the case of M 1, only lateral wakes are obtained.

Turbulent fluctuations are a common phenomena in most plasma systems. Most of the analysis is done by conventional Fourier techniques that extract information only in the frequency domain with temporal information usually missing. Also non-linear interaction between different modes cannot be identified. We present in this paper some new techniques using wavelet transforms and bispectral analysis that enable interpretation of non-stationary signals and also yield information about non-linear coupling between different basic modes of the system.

A Hamiltonian formulation of magnetic field line equations is derived for arbitrary magnetic field configurations in orthogonal curvilinear coordinate systems. The canonical equivalence of the different descriptions thus obtained are explicitly demonstrated and action-angle forms are given in cases where there is a geometrical symmetry. Examples of Hamiltonians are discussed for usual plasma machines like the tokamak and the levitron. Finally, generalisation to non-orthogonal coordinate systems is worked out.