Professor Padma Kant Shukla passed away on the 26th of January in New Delhi, India, just after receiving the prestigious Hind Rattan (Jewel of India) Award. He was born in the village Tulapur, Uttar Pradesh (UP), India and was educated there. After his Ph.D. in Physics from Banaras Hindu University in Varanasi, he obtained his second doctorate degree in Theoretical Plasma Physics from Umea University under the supervision of one of us (Lennart Stenflo). He worked at the Faculty of Physics & Astronomy, Ruhr-University Bochum, Germany since January 1973, where he was a permanent faculty member and Professor of International Affairs, a position that was created for him to honour his international accomplishments and reputation.

This special issue is devoted to the memory of Professor Padma Kant Shukla, who passed away 26 January 2013 on his travel to New Delhi, India to receive the prestigious Hind Rattan (Jewel of India) award. Padma was born in Tulapur, Uttar Pradesh, India, 7 July 1950, where he grew up and got his education. He received a PhD degree in Physics at the Banaras Hindu University, Varanasi, Uttar Pradesh, India, in 1972, under the supervision of late Prof. R. N. Singh, and a second PhD degree in Theoretical Plasma Physics from Umeå University in Sweden in 1975, under the supervision of Prof. Lennart Stenflo. He worked at the Faculty of Physics & Astronomy, Ruhr-University Bochum, Germany since January 1973, where he was a permanent faculty member and Professor of International Affairs, a position that was created for him to honour his international accomplishments and reputation.

The concepts of ‘plasma edge’ and ‘collisionally modified Bohm criterion’ have occupied attention for many years since the publication of work by Bohm that gave rise to the Bohm criterion. He acknowledged that his description of the plasma-sheath transition was incomplete. We summarize work that shows that neither concept has precision, at the same time giving a critique.

The “International Topical Conference on Plasma Science: Advanced Plasma Concepts” was hosted by Instituto Superior Técnico, Lisbon and the University of Algarve, Faro, Portugal, during the period 24–28 September 2012. The conference was organized by Padma Kant Shukla, (Ruhr University Bochum, Germany), Robert Bingham (RAL, United Kingdom) and José Tito Mendonça, (IST, Portugal). The scientific activity belongs to a series of successful meetings, which started at the Abdus Salam International Centre for Theoretical Physics, Trieste, in 1989, and which has also been taking place at various other locations, including Faro and Lisbon in Portugal, and Santorini in Greece.

The propagation of a localized beam (cloud) of hot electrons and generation of Langmuir waves are investigated using numerical simulation of the quasi-linear equations in the presence of collisional effects for electrons and beam-driven Langmuir waves. It is found that inclusion of the collisional damping of Langmuir waves has remarkable effects on the evolution of the electron distribution function and the spectral density of Langmuir waves, while the effect of collision term for electrons is almost negligible. It is also found that in the presence of collisional damping of Langmuir waves, the relaxation of the beam distribution function in velocity space is retarded and the Langmuir waves are strongly suppressed. The average propagation velocity of the beam is not constant and is larger when collisional damping of Langmuir waves is considered. The collisional damping for electrons does not affect the upper boundary of the plateau but the collisional damping of Langmuir waves pushes it towards small velocities. It is also found that the local velocity of the beam and its width decrease when the collisional damping of Langmuir waves is included.

A strongly coupled dusty plasma system consisting of non-thermal electrons, Maxwellian ions, and negatively charged dust in presence of polarization force has been considered. The nonlinear propagation of dust-acoustic shock waves in such a dusty plasma system has been theoretically investigated by employing the reductive perturbation method. The effects of the polarization force and non-thermal electrons, on the properties of these dust-acoustic shock waves are briefly discussed. It is shown that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of the dust-acoustic shock waves. It has been found that the effects of polarization force and non-thermal electrons significantly modify the basic features of such shock waves. It has been proposed to design a new laboratory experiment, which will be able to identify the basic features of the dust-acoustic shock waves predicted in this present investigation.

The shock waves are important features in the analysis of transonic magnetohydrodynamical (MHD) flows where thermal radiation could also be significant. In this paper the effects of black-body radiation on non-relativistic shock waves in an ideal radiation MHD model for the optically thick case are discussed. Distilled shock conditions were derived and discussed for the case of a fixed ratio of specific heats of an ideal gas (γ) and ratio of gas to total pressure (b). The special case, when jumps in γ and/or b are allowed, was also considered.

By means of particle simulations of the equations of motion for ions interacting among themselves under the influence of newly discovered Shukla–Eliasson attractive force (SEAF) in a dense quantum plasma, we demonstrate that the SEAF can bring ions closer at atomic dimensions. We present simulation results of the dynamics of an ensemble of ions in the presence of the SEAF without and with confining external potentials and collisions between ions and degenerate electrons. Our particle simulations reveal that under the SEAF, ions attract each other, come closer, and form ionic clusters in the bath of degenerate electrons that shield ions. Furthermore, an external confining potential produces robust ion clusters that can have cigar- and ball-like shapes, which remain stable when the confining potential is removed. The stability of ion clusters is discussed. Our results may have applications to solid density plasmas (density exceeding 1023 per cm3), where the electrons will be degenerate and quantum forces due to the electron recoil effect caused by the overlapping of electron wave functions and electron tunneling through the Bohm potential, electron-exchange and electron-exchange and electron correlations associated with electron-1/2 spin effect, and the quantum statistical pressure of the degenerate electrons play a decisive role.

X-ray momentum coupling coefficients, CM, were determined by measuring stress waveforms in planetary materials subjected to impulsive radiation loading from the Sandia National Laboratories Z-machine. Velocity interferometry (VISAR) diagnostics provided equation-of-state data. Targets were iron and stone meteorites, magnesium-rich olivine (dunite) solid and powder (~5–300 μm), and Si, Al, and Fe calibration targets. Samples were ~1-mm thick and, except for Si, backed by LiF single-crystal windows. X-ray spectra combined thermal radiation (blackbody 170–237 eV) and line emissions from pinch materials (Cu, Ni, Al, or stainless steel). Target fluences of 0.4–1.7 kJ/cm2 at intensities of 43–260GW/cm2 produced plasma pressures of 2.6–12.4 GPa. The short (~5 ns) drive pulses gave rise to attenuating stress waves in the samples. The attenuating wave impulse is constant, allowing accurate CM measurements from rear-surface motion. CM was 1.9 − 3.1 × 10−5 s/m for stony meteorites, 2.7 and 0.5 × 10−5 s/m for solid and powdered dunite, 0.8 − 1.4 × 10−5 s/m for iron meteorites, and 0.3, 1.8, and 2.7 × 10−5 s/m respectively for Si, Fe, and Al calibration targets. Results are consistent with geometric scaling from recent laser hohlraum measurements. CTH hydrocode modeling of X-ray coupling to porous silica corroborated experimental measurements and supported extrapolations to other materials. CTH-modeled CM for porous materials was low and consistent with experimental results. Analytic modeling (BBAY) of X-ray radiation-induced momentum coupling to selected materials was also performed, often producing higher CM values than experimental results. Reasons for the higher values include neglect of solid ejecta mechanisms, turbulent mixing of heterogeneous phases, variances in heats of melt/vaporization, sample inhomogeneities, wave interactions at the sample/window boundary, and finite sample/window sizes. The measurements validate application of CM to (inhomogeneous) planetary materials from high-intensity soft X-ray radiation.

Time-dependent cylindrical and spherical dust-acoustic (DA) solitary and shock waves propagating in a strongly coupled dusty plasmas (containing strongly correlated negatively charged dust grains and weakly correlated adiabatic electrons and ions) are investigated. It is shown that cylindrical and spherical DA solitary and shock waves exist with negative potential, and that the strong correlation between the charged dust grains is a source of dissipation, and is responsible for the formation of cylindrical or spherical DA shock structures. It is also shown that the effects of a non-planar geometry (cylindrical and spherical) significantly modify the basic features (e.g. amplitude, width, speed, etc.) of DA solitary and shock waves. The implications of our results in laboratory experiments are briefly discussed.

Previous theory for stimulated Brillouin scattering is reconsidered and generalized. We introduce an effective ion sound velocity that turns out to be useful in describing scattering instabilities.

A description of the evolution of the initial disturbance in the fast magnetosonic (FMS) waveguide in transversely inhomogeneous plasma, given a weak coupling between FMS and Alfven modes, is made. It is shown that the Fourier transform of the FMS waveguide disturbance with respect to the coordinates along which plasma is homogeneous can be presented as a superposition of collective modes of the leading approximation with respect to the weak FMS–Alfven wave coupling from the initial instant of time. Frequencies of such collective modes and dependence of their structures on the coordinate along the inhomogeneity are found without taking the FMS–Alfven resonance into consideration, and the mode decrements are calculated using the perturbation technique. On the basis of such a representation of the FMS waveguide disturbance, the evolution of Alfven waves generating with waveguide mode packets produced by the initial disturbance of an arbitrary longitudinal structure is described. It is shown that the longitudinal structure of the Alfven disturbance generated by the collective mode packet is determined by the ratio between longitudinal scales of the initial disturbance and scales specified by resonance conditions (the resonance longitudinal wave number and the width of the range of the resonance longitudinal wave numbers). The structures of Alfven disturbances for the cases of such different ratios are described.

Nonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

Collisionless shocks are ubiquitous in astrophysics and in the laboratory. Recent numerical simulations and experiments have shown how these can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step toward a microscopic understanding of the process, we here analyze in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two unmagnetized, symmetric, and initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω=0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.

We present results from numerical simulations conducted to investigate a potential method for realizing the required fusion fuel heating in the fast ignition scheme to achieving inertial confinement fusion. A comparison will be made between collisionless and collisional particle-in-cell simulations of the relaxation of a non-thermal electron beam through the two-stream instability. The results presented demonstrate energy transfer to the plasma ion population from the laser-driven electron beam via the nonlinear wave–wave interaction associated with the two-stream instability. Evidence will also be provided for the effects of preferential damping of competing instabilities such as the Weibel mode found to be detrimental to the ion heating process.

An argon plasma is created from a general capacitively coupled plasma source and monitored by optical emission spectroscopy. A relation between the line intensity and the applied voltage is obtained and discussed. The plasma shows paraelectric behavior. A linear relation exists between the electric capacity of the capacitively coupled plasma and the applied voltage. This linear relation can be used in a new voltage measurement technique in which the applied voltage can be calculated from the measured line intensity.

We study the spin and ion effects in quantum plasma, where the two-fluid model of electrons is being used which treats the spin-up and -down populations relative to the magnetic field as different species. We find the susceptibility of electrons and ions where the ions are classical, but strongly coupled. The general dispersion relation is derived for wave propagation in homogeneous magnetized plasmas for arbitrary direction of propagation. We discuss the applicability of our results.

For the considered scheme of the external electron bunch injection in front of a laser pulse, the influence of the nonlinear driving laser pulse dynamics and electron bunch self-action to the processes of electron bunch compression and acceleration in the laser wakefield is analyzed. Self-consistent modelling results confirm that the nonlinear laser pulse dynamics limits the bunch compression due to variations of the phase velocity of the wake. A growth of the injected bunch charge leads to some extent to an increase of the trapped and accelerated bunch charge and to decrease of the trapped bunch radius and emittance due to increased self-focusing bunch. The three-dimensional theoretical model is elaborated and used to describe the propagation of laser pulses in dielectric capillary waveguides under imperfect coupling and focusing conditions with broken cylindrical symmetry. The role of cone entrances to the cylindrical part of a capillary is analyzed, and it is demonstrated that matching cones can considerably increase the transmission of laser pulses through the capillary, but cannot mitigate the requirements on the precision of the laser pulse focusing into a capillary. In order to avoid a speckle structure and strong transverse gradients of the fields, which can prevent the process of regular electron bunch acceleration, one has to ensure a small laser angle of incidence into the capillary not exceeding 1 mrad.

It is shown that the two-flavor neutrino oscillation equations admit an exact analytic solution for arbitrarily chosen normalized electron neutrino population, provided the electron plasma density is adjusted in a certain way. The associated formula for the electron plasma density is applied to the cases of exponentially decaying or oscillating electron neutrino populations.

Recently, there has been great interest around quantum relativistic models for plasmas. In particular, striking advances have been obtained by means of the Klein–Gordon–Maxwell system, which provides a first-order approach to the relativistic regimes of quantum plasmas. The Klein–Gordon–Maxwell system provides a reliable model as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli–Schrödinger or Dirac equations. In this work, a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein–Gordon–Poisson system, where the positive branch of the relativistic energy–momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared with the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas.