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.

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.

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.

The effect of the electrostatic confinement potential on electron number densities and electron temperatures under bi-Maxwellian approximation for electron distribution function has been studied in an electrostatically plugged multi-dipole argon plasma system. Electrostatic plugging is implemented by biasing the electrically isolated multi-dipole magnetic cage. Experimental results show that the density ratio (N) and temperature ratio (T) of the two electron groups can be controlled by changing the voltage applied to the magnetic cage. Out of the two groups of electrons, one group has the cold electrons, which are plasma electrons produced by the ionization process, and the other group has the hot primary electrons.

The hydrodynamic equations of positive and negative ions, degenerate electrons, and the Poisson equation are used along with the reductive perturbation method to derive the three-dimensional Zakharov–Kuznetsov (ZK) equation. The G′/G-expansion method is used to obtain a new class of solutions for the ZK equation. At certain condition, these solutions can describe the solitary waves that propagate in our plasma. The effects of negative ion concentrations, the positive/negative ion cyclotron frequency, as well as positive-to-negative ion mass ratio on solitary pulses are examined. Finally, the present study might be helpful to understand the propagation of nonlinear ion-acoustic solitary waves in a dense plasma, such as in astrophysical objects.

A general formalism for calculating the potential distribution Φ(z) in the quasineutral region of a new class of plane Tonks–Langmuir (TL)-type bounded-plasma-system (BPS) models differing from the well-known ‘classical’ TL model (Tonks, L. and Langmuir, I. 1929 A general theory of the plasma of an arc. Phys. Rev. 34, 876) by allowing for arbitrary (but still cold) ion sources and arbitrary electron distributions is developed. With individual particles usually undergoing microscopic collision/sink/source (CSS) events, extensive use is made here of the basic kinetic-theory concept of ‘CSS-free trajectories’ (i.e., the characteristics of the kinetic equation). Two types of electron populations, occupying the ‘type-t’ and ‘type-p’ domains of electron phase space, are distinguished. By definition, the type-t and type-p domains are made up of phase points lying on type-t (‘trapped’) CSS-free trajectories (not intersecting the walls and closing on themselves) and type-p (‘passing’) ones (starting at one of the walls and ending at the other). This work being the first step, it is assumed that ε ≡ λD/l → 0+ (where λD and l are a typical Debye length and a typical ionization length respectively) so that the system exhibits a finite quasineutral ‘plasma’ region and two infinitesimally thin ‘sheath’ regions associated with the ‘sheath-edge singularities’ | dΦ/dz|z→±zs → ∞. The potential in the plasma region is required to satisfy a plasma equation (quasineutrality condition) of the form ni {Φ} =ne (Φ), where the electron density ne (Φ) is given and the ion density ni {Φ} is expressed in terms of trajectory integrals of the ion kinetic equation, with the ions produced by electron-impact ionization of cold neutrals. While previous TL-type models were characterized by electrons diffusing under the influence of frequent collisions with the neutral background particles and approximated by Maxwellian (Riemann, K.-U. 2006 Plasma-sheath transition in the kinetic Tonks–Langmuir model. Phys. Plasmas 13, 063508) or bi-Maxwellian (Godyak, V. A. et al. 1995 Tonks–Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23, 728) electron velocity distribution functions (VDFs), which satisfy the zero-CSS-term (Vlasov) kinetic equation and imply zero electron currents, we here propose a more general class of electron VDFs allowing, in an approximate manner, for non-zero CSS terms and finite electron currents inside the plasma region. The sheath-edge and floating-wall potentials are calculated by balancing the ion and electron current densities at sheath-edge singularities. In a first detailed application, the type-t and type-p electron VDFs are assumed to be ‘inner’ and ‘outer’ cut-off Maxwellians respectively, with different amplitudes and ‘formal’ temperatures, implying the perfectly CSS-free limit. For the special case of equal type-t and type-p electron VDF amplitudes and formal temperatures, the classical Boltzmann distribution for electrons is formally retrieved. Special cases with other amplitude and formal-temperature ratios show significant deviations from the classical case.

By investigating the dielectric response of the Fermi–Dirac plasma in the linear limit and evaluating the electrostatic potential around the positive stationary test charge, we find that the Shukla–Eliasson attractive force is present for the plasma density range expected in the interiors of large planets for a wide range of plasma atomic number. This research, which is based on the generalized electron Fermi-momentum, further confirms the existence of the newly discovered Lennard-Jones-like attractive potential and its inevitable role in plasma crystallization in the cores of planets. Moreover, it is observed that the characteristics of the attractive potential are strongly sensitive to the variation of plasma density and composition. Current research can also have applications in the study of strong laser-matter interactions and inertially confined plasmas.

This review describes the results of investigations on charged particle dynamics in a magnetic field carried out over a number of years. The studies have unravelled the existence of some very surprising and unusual phenomena. Though existing on the macro-scale, they are found to be of quantum origin, and are thereby not covered by the Lorentz equation, which has been regarded conventionally as the descriptor of electrodynamic phenomena on the macro-scale. These novel phenomena have been found to be attributed to the ‘quantum modulation’ of the de Broglie wave along the magnetic field. This is brought about through the scattering-induced transition across Landau levels, leading to the modulation of the plane wave state along the field as a result of the entanglement between the parallel and perpendicular degrees of freedom. These findings were motivated by the predictions of a formalism developed by the author and include such unusual phenomena as (i) macro-scale matter wave interference effects and (ii) the detection of curl-free vector potential also on the macro-scale, both attributed to quantum modulation which is a matter wave on the macro-scale. The formalism is thus described as ‘macro-quantization of guiding centre motion’.

Properties of dust-ion-acoustic shock waves (DIASWs) in an unmagnetized dusty plasma (containing inertial ions, Maxwellian electrons with two distinctive temperatures and negatively charged immobile dust) are investigated. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of two-electron-temperature and ion kinematic viscosity, which are found to significantly modify the basic features of the DIASWs, are discussed.

Among the theoretical and experimental situations of interest in plasma physics are the waves that rise into the plasma and are strongly affected from the plasma parameters. Therefore, the development of strong relations between unperturbed and perturbed quantities is proved to exist both experimentally and theoretically. In the present paper, the mathematical solution ended in a relation between drift and perturbed velocities, which presupposes the perturbed velocity value to be very small in comparison with the drift velocity. However, the experiment has shown that the presupposition of the small value of the perturbations is not satisfied in many laboratory instances; as a result the use of the perturbation theory is limited. To surpass this difficulty, the big perturbed quantity was divided into small and equal parts, and by using the equation between unperturbed and perturbed velocities as a repeating relation, the perturbed theory may be extended and generalized beyond the small disturbances. In addition, calculations with a little change in the initial conditions were carried out, to determine when the plasma obtains chaotic behavior.

The basic features of the nonlinear waves, which are associated with positive ion dynamics and dust charge fluctuation, have been investigated by employing the reductive perturbation method in a dusty electronegative plasma containing Boltzmann electrons, vortex-like negative ions, mobile positive ions, and charge fluctuating stationary dust (negatively charged). It has been observed that the basic features of the nonlinear waves (viz. amplitude, width, speed, etc.) in the plasma system under consideration have been significantly modified by the trapping parameter (introduced for vortex-like distribution of negative ions). The implications of the results (obtained from this investigation) in space and laboratory experiments have been briefly discussed.