Plasma physics is a large and fundamental area of physics, a subject that is intellectually rigorous and mathematically sophisticated and which has many applied branches. Because there are many applications, the field tends to suffer from compartmentalisation in people's minds, in terms of published output and institutional and funding arrangements. JPP will strive to be the intellectual home of those who think of plasma physics as a fundamental discipline.

The standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A45, 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics, Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D13, 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas19, 102106; Fedele, R. et al. 2012b AIP Conf. Proc.1421, 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrödinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherer's equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci.NS-18, 1105). Conversely, in the quantum regime and in Hartree's mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.

Models for traveling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron–proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the traveling waves can be reduced to a single first-order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron–proton or an electron–positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton–electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic traveling waves consisting of hot electron and cold proton fluids.

Knowledge of the structure of coronal magnetic field originating from the photosphere is relevant to the understanding of many solar activity phenomena, e.g. flares, solar prominences, coronal loops, and coronal heating. In most of the existing literature, these loop-like magnetic structures are modeled as force-free magnetic fields (FFMF) without any plasma flow. In this paper, we present several exact solution classes for nonlinear FFMF, in both translational and axisymmetric geometries. The solutions are considered for their possible relevance to astrophysics and solar physics problems. These are used to illustrate arcade-type magnetic field structures of the photosphere and twisted magnetic flux ropes through the coronal mass ejections (CMEs), as well as magnetic confinement fusion plasmas.

The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.

The plasma sheath dynamics adjacent to the cathode in the presence of electrons, ions, and doubly ionized ions have been simulated in this work. The aim of the present investigation is, therefore, to study the effect of the doubly ionized ions on the characteristics of the plasma sheath dynamics such as potential distribution, sheath length, and ions dose and velocity near the surface (cathode). It was shown that the presence of the doubly ionized ions can increase the normalized potential of all positions in sheath region, sheath length, and ion/doubly ionized ions density ratio on the target. Obtained results may be helpful for analyzing the practical results of the surface operations such as ion implantation and plasma polymerization, etc.

Dispersion relations of dust-lattice waves in three-dimensional body-centered cubic (bcc) and face-centered cubic (fcc) dusty plasma crystals are derived taking into account particle–wake interactions. Results show that resonance coupling between the longitudinal and out-of-plane transverse wave modes set in if the vertical confinement is below a certain critical value. The imaginary part of the wave frequency shows that the hybrid mode cannot propagate in the crystal.

The head-on collision of dust magnetoacoustic solitary waves (DMASWs) is studied in magnetized electron–ion–dust plasma. The extended Poincaré–Lighthill–Kuo perturbation method is used to derive the Korteweg de Vries equations for DMASWs in this three-component plasma. The effects of the magnetic field intensity B0, the number of electrons residing on dust surface Zd, the ratio of electron to dust number density δ, the ratio of electron to ion temperature σ, and the ratio of dust acoustic velocity to dust Alfvén velocity β on the phase shift are investigated. It is found that these parameters can significantly influence the phase shifts of colliding DMASWs. The present investigation may be beneficial to understand the interaction between two DMASWs that may occur in plasma with dust impurities situations.

In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, i.e. ρ=ρ(J,z), while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential, i.e. ρ=ρ(J,V). We show that, in the case of slow varying charge density, the space-charge-limited current is reduced up to 50%. Our approach gives the well-known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child–Langmuir formulation.

We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.

The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrücken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ ≳ c/ωpe).