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In this paper, multifractal detrended fluctuation analysis (MF-DFA) has been used to analyze the floating potential fluctuations obtained with a Langmuir probe from a dc glow discharge magnetized plasma device. The generalized Hurst exponents ( h ( q ) ) , local fluctuation function ( F q ( s ) ) , the Renyi exponents ( τ ( q ) ) and the multifractal spectrum F ( α ) have been calculated by applying the MF-DFA method. The result of the MF-DFA shows the multifractal nature of these fluctuations. We have investigated the influence of magnetic field on the multifractal nature of the fluctuations and it is seen that degree of multifractality is reduced with the increase in the magnetic field strength. The values of h ( q ) have been restricted between 0.7 and 1 for the magnetized fluctuations. This result is evidence of the existence of long-range correlations in the fluctuations. Furthermore, we employed shuffle and surrogate approaches to analyze the origins of multifractality. Comparing the MF-DFA results for the data set to those for shuffled and surrogate series, we have found that its multifractal nature is due to the existence of significant long-term correlation.

Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regime is sought from the power spectral analysis. The existence of PMS is confirmed using the order parameter M (here M α β for different combination pairs of oscillators), best suited to identify MS in coupled two-oscillator systems, and this definition is extended to obtain a new order parameter, M 3, aiding to distinguish complete MS of three oscillators from other forms of motion. The study of wavelet coefficient spectra sheds new light on the relative phase information of the oscillators in the QP PMS regions, also highlighting the intertwined role played by the various frequency components and their amplitudes as they vary temporally. Furthermore, this technique helps to draw a sharp distinction between CMS and chaotic unsynchronized states. Based on the Continuous Wavelet Transform coefficients of the three oscillators, an order parameter M w a v is defined to indicate the extent of synchronization of the various scales (frequencies) for different coupling strengths in the chaotic regime.Measure Synchronization (MS) is the generalization of synchrony to Hamiltonian Systems. Partial measure synchronization (PMS) and complete measure synchronization in a system of three nonlinearly coupled one-dimensional oscillators have been investigated for different initial conditions on the basis of numerical computation. The system is governed by the classical SU(2) Yang-Mills-Higgs (YMH) Hamiltonian with three degrees of freedom. Various transitions in the quasiperiodic (QP) region, namely, QP unsynchronized to PMS, PMS to PMS, and PMS to chaos are identified through the average bare energies and interaction energies route maps as the coupling strength is varied. The transition from quasiperiodicity to chaos is seen to be associated with a gradual transition to complete chaotic measure synchronization (CMS) which is followed by chaotic unsynchronized states, the most stable state in this case. The analyses illustrate the dependence on initial conditions. The explanation of the behavior in the QP regi...

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 bili- nearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathe- matical 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{\th}1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field., Comment: 11 pages, 8 figures

Recurrence quantification analysis (RQA) is used to study dynamical systems and to identify the underlying physics when a system exhibits a transition due to changes in some control parameter. The tendency of reoccurrence of different states after certain interval reflects and reveals the hidden patterns of a complex time series data. The present work involves the study of the floating potential fluctuations of a glow discharge plasma obtained by using a Langmuir probe. Determinism, entropy and Lmax are important measures of RQA that show an increasing and decreasing trend with variation in the values of discharge voltages and indicate an order-chaos transition in the dynamics of the fluctuations. Statistical analysis techniques represented by skewness and kurtosis are also supportive of a similar phenomenon occurring in the system.

The transport of magnetic field lines is investigated numerically by considering a static magnetic fluctuation with a uniform background field in which the fluctuating part is obtained as a particular solution of the double curl equation and is non force-free in nature. It is found that the transport of magnetic field lines is anomalous, in fact, subdiffusion for lower fluctuation level, δ B ∕ B 0 , relative to the mean field. The situation corresponds to weak chaos and closed magnetic surfaces in the phase space. Stochasticity increases by increasing the fluctuation level. Higher fluctuation levels with δ B ∕ B 0 > 1 lead to global stochasticity and almost normal diffusion. These results for transport characteristics are supported by analyzing the kurtosis of the displacement distribution of the chaotic field lines. A mixed phase space leads to non-Gaussian structure of the displacement probability distribution for the chaotic trajectories, whereas a wholly chaotic phase space supports nearly Gaussian distribution.

The possibility of finding chaos in a KdV like system in the absence of any external forcing is explored without reducing its order by treating it as a third order Jerk equation. While bounded solutions with periodic nature exist for both right and left traveling wave solutions of the KdV equation, inclusion of terms that signify damping lead to chaotic behavior only for left moving waves. The bifurcation diagram obtained for suitable choice of the parameters shows interesting phenomena such as Hopf and period doubling bifurcations. To characterize the chaotic behavior, the spectrum of Lyapunov exponent is studied. Domains of stable and unstable solutions with the boundaries marking transitions have been identified in the parameter space.

Single and double curl Beltrami magnetic fields are studied numerically in connection with their transport properties, and the results are compared and analyzed by characterizing the magnetic field lines. In the phase space of the single curl Beltrami field, islands of regular field lines are embedded into the chaotic sea, whereas the field lines for certain solutions of the double curl Beltrami field are chaotic over the entire space. Due to the presence of regular islands in phase space, the chaotic trajectories show stickiness phenomena which are characterized by the distribution of a chaotic field line. The dynamical traps in chaotic orbits due to stickiness phenomena are also characterized by the distribution of finite distance Lyapunov exponents. Finally, the recurrence length distribution of chaotic trajectories is plotted to understand their global behaviour.

The nonstationary and nonlinear dust-acoustic wave is considered in the framework of the Lagrangian fluid description. A single nonlinear equation and its solutions are obtained for dust-acoustic waves with nontrivial space and time dependence in both the large and small amplitude limit. In the absence of linear dispersion solutions in the large amplitude limit, it is demonstrated that under well-defined initial and boundary conditions the amplitude of the solutions is decreasing and the spatial profile spreads. This is a new class of nonlinear solutions leading to short-lived nonlinear structures. In the small amplitude limit, the soliton-like solution indicates close association with Korteweg–de Vries solitons.

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...

Experimental evidence of intrinsic noise induced coherence resonance in a glow discharge plasma is being reported. Initially the system is started at a discharge voltage (DV) where it exhibited fixed point dynamics, and then with the subsequent increase in the DV spikes were excited which were few in number and with further increase of DV the number of spikes as well as their regularity increased. The regularity in the interspike interval of the spikes is estimated using normalized variance. Coherence resonance was determined using normalized variance curve and also corroborated by Hurst exponent and power spectrum plots. We show that the regularity of the excitable spikes in the floating potential fluctuation increases with the increase in the DV, up to a particular value of DV. Using a Wiener filter, we separated the noise component which was observed to increase with DV and hence conjectured that noise can play an important role in the generation of the coherence resonance. From an anharmonic oscillator equation describing ion acoustic oscillations, we have been able to obtain a FitzHugh-Nagumo like model which has been used to understand the excitable dynamics of glow discharge plasma in the presence of noise. The numerical results agree quite well with the experimental results.

A mixture of dodecanethiol-capped Au nanoparticles (AuNPs) and the amphiphilic fatty acid, stearic acid, spread as a monomolecular layer on water surface, is observed with Brewster angle microscopy (BAM) to form a two-dimensional network of AuNP clusters through demixing, at concentration of AuNPs by weight (ρ[over ¯])>10% and the surface pressure (π)≥10mNm^{-1}. For π=15mNm^{-1}, the number of nodes (n) remains unchanged till ∼2 hours and then changes over to a lower n state, where the pattern consists of almost perfect circles with greater in-plane thickness of the AuNP lamellae. For the higher n state the mean-square fluctuation of BAM intensity remains flat and then decays as f(ξ)=ξ^{2α} with α∼0.6 (correlated fluctuations) over the length scales of 400μm-6μm and below 6μm, respectively. For the lower n state the fluctuation decays almost over the entire length scale with α=0.3, indicating emergence of aperiodicity from quasiperiodicity and a changeover to anticorrelated fluctuations. These patterns can be looked at as two distinct chaotic trajectories in the I-I^{'} phase space of the system (I being the scattered light intensity at any position of the pattern and I^{'} its gradient) with characteristic Lyapunov exponents.

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.

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.

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.

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. >

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.

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.

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

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.

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

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.

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.

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.

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.