We present analytic solutions for three-dimensional magnetized axisymmetric equilibria confining rotating hot plasma in a gravitational field. Our up–down symmetric solution to the full Grad–Shafranov equation can exhibit equatorial plane localization of the plasma density and current, resulting in disk equilibria for the plasma density. For very weak magnetic fields and high plasma pressure, we find strongly rotating thin plasma disk gravitational equilibria that satisfy strict Keplerian motion provided the gravitational energy is much larger than the plasma pressure, which must be large compared to the magnetic energy of the poloidal magnetic field. When the rotational energy exceeds the gravitational energy and it is larger than the plasma pressure, diffuse disk equilibrium solutions continue to exist provided the poloidal magnetic energy remains small. For stronger magnetic fields and lower plasma pressure and rotation, we can also find gravitational equilibria with strong localization to the equatorial plane. However, a toroidal magnetic field is almost always necessary to numerically verify these equilibria are valid solutions in the presence of gravity for the cases considered in Catto & Krasheninnikov (J. Plasma Phys., vol. 81, 2015, 105810301). In all cases both analytic and numerical results are presented.

A novel method was experimentally demonstrated to produce a low-density electron plasma in a Penning–Malmberg trap, exploiting the static electric and magnetic confinement fields together with a periodic excitation with amplitudes as low as 0.5–5 V and frequencies in the MHz range. This unusual technique proved to be applicable as a replacement for conventional electron sources in Penning devices and presents interesting aspects both in terms of basic science and technological applications. Nevertheless, the experimental observations demonstrate the high sensitivity of plasma features of interest (charge, mean density and density distribution) to the experimental conditions, namely trap configuration and excitation parameters, and as a consequence clear trends have not been identified so far. We present an experimental campaign of measurements where several parameters were systematically changed leading to a better assessment of the plasma production mechanism and to the identification of common trends.

The Helicon-Cathode(HelCat) device is a medium-size linear experiment suitable for a wide range of basic plasma science experiments in areas such as electrostatic turbulence and transport, magnetic relaxation, and high power microwave (HPM)-plasma interactions. The HelCat device is based on dual plasma sources located at opposite ends of the 4 m long vacuum chamber – an RF helicon source at one end and a thermionic cathode at the other. Thirteen coils provide an axial magnetic field B ⩾ 0.220 T that can be configured individually to give various magnetic configurations (e.g. solenoid, mirror, cusp). Additional plasma sources, such as a compact coaxial plasma gun, are also utilized in some experiments, and can be located either along the chamber for perpendicular (to the background magnetic field) plasma injection, or at one of the ends for parallel injection. Using the multiple plasma sources, a wide range of plasma parameters can be obtained. Here, the HelCat device is described in detail and some examples of results from previous and ongoing experiments are given. Additionally, examples of planned experiments and device modifications are also discussed.

Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

The properties of dust ion acoustic rogue waves (DIARWs) in an unmagnetized collisionless plasma system composed of charged dust grains, superthermal electrons and warm ions as a fluid are studied. The multiple scale perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for DIARWs. From the coefficients of nonlinearity and dispersion, we have determined the critical wave number threshold kcr at which modulational instability sets in. This critical wave number depends on the various plasma parameters, viz. superthermality of electrons, ion temperature and dust concentration. Within the modulational instability region, a random perturbation of amplitude grows and thus, creates DIARWs. It is found that DIARWs are significantly affected by electron superthermality (via κ), ion temperature (via σ) and dust concentration (via f). In view of the crucial importance of DIARWs in space environments, our results may be useful in understanding the basic features of DIARWs that may occur in space plasmas.

The Culham Thesis Prize is awarded annually to the nominee who has displayed an excellence in the execution of the scientific method as witnessed by the award of Doctor of Philosophy in Plasma Science from a UK or Irish university. The thesis content should exhibit significant new work and originality, clearly driven by the nominee, be well explained and demonstrate a good understanding of the subject. The prize is awarded at the Institute of Physics Plasma Physics Group Spring Conference and the prize winner gives an invited talk about their thesis work. The prize is sponsored by Culham Centre for Fusion Energy.

The Lorentzian renormalization plasma shielding effects on the elastic electron–atom collision are investigated in generalized Lorentzian semiclassical plasmas. The eikonal analysis and the effective interaction potential are employed to obtain the eikonal scattering phase shift, differential eikonal collision cross section, and total eikonal collision cross section as functions of the collision energy, impact parameter, nonthermal renormalization parameter, and spectral index of the Lorentzian plasma. It is found that the influence of Lorentzian renormalization shielding suppresses the eikonal scattering phase shift and, however, enhances the eikonal collision cross section in Lorentzian semiclassical plasmas. Additionally, the energy dependence on the total collision cross section in nonthermal plasmas is found to be more significant than that in thermal plasmas.

We continue the study of collisionless systems governed by additive $r^{-{\it\alpha}}$ interparticle forces by focusing on the influence of the force exponent ${\it\alpha}$ on radial orbital anisotropy. In this preparatory work, we construct the radially anisotropic Osipkov–Merritt phase-space distribution functions for self-consistent spherical Hernquist models with $r^{-{\it\alpha}}$ forces and $1\leqslant {\it\alpha}<3$. The resulting systems are isotropic at the centre and increasingly dominated by radial orbits at radii larger than the anisotropy radius $r_{a}$. For radially anisotropic models we determine the minimum value of the anisotropy radius $r_{ac}$ as a function of ${\it\alpha}$ for phase-space consistency (such that the phase-space distribution function is nowhere negative for $r_{a}\geqslant r_{ac}$). We find that $r_{ac}$ decreases for decreasing ${\it\alpha}$, and that the amount of kinetic energy that can be stored in the radial direction relative to that stored in the tangential directions for marginally consistent models increases for decreasing ${\it\alpha}$. In particular, we find that isotropic systems are consistent in the explored range of ${\it\alpha}$. By means of direct $N$-body simulations, we finally verify that the isotropic systems are also stable.

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.

Saturation-power enhancement of a free-electron laser (FEL) amplifier by using tapered wiggler amplitude is based on the postponement of the saturation length of the uniform wiggler. In this paper, we qualitatively and quantitatively demonstrate that the saturation-power enhancement can be approached by means of the parameters adjustment, which is comparable to that by using a tapered wiggler. Compared to the method by tapering the wiggler amplitude, the method of parameters adjustment substantially shortens the saturation length, which is favorable to cutting down the manufacture and operation costs of the device.

Copper activation was used to characterize high-energy proton beam acceleration from near-critical density plasma targets. An enhancement was observed when decreasing the target density, which is indicative for an increased laser-accelerated hot electron density at the rear target-vacuum boundary. This is due to channel formation and collimation of the hot electrons inside the target. Particle-in-cell simulations support the experimental observations and show the correlation between channel depth and longitudinal electric field strength is directly correlated with the proton acceleration.

In collisional fluids, a number of key processes rely on the frequency of binary collisions. Collisions seem necessary to generate a shock wave when two fluids collide fast enough, to fulfill the Rankine–Hugoniot (RH) relations, to establish an equation of state or a Maxwellian distribution. Yet, these seemingly collisional features are routinely either observed or assumed, in relation with collisionless astrophysical plasmas. This article will review our current answers to the following questions: How do colliding collisionless plasmas end-up generating a shock as if they were fluids? To which extent are the RH relations fulfilled in this case? Do collisionless shocks propagate like fluid ones? Can we use an equation of state to describe collisionless plasmas, like MHD codes for astrophysics do? Why are Maxwellian distributions ubiquitous in particle-in-cell simulations of collisionless shocks? Time and length scales defining the border between the collisional and the collisionless behavior will be given when relevant. In general, when the time and length scales involved in the collisionless processes responsible for the fluid-like behavior may be neglected, the system may be treated like a fluid.

Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma–vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number $n=1$ distortions when the edge bootstrap current is large and higher $n$ corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch–Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch–Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

In this paper, the properties of photonic band gap (PBG) and surface plasmon modes in the three-dimensional (3D) magnetized plasma photonic crystals (MPPCs) with face-centered-cubic (fcc) lattices are theoretically investigated based on the plane wave expansion (PWE) method, in which the homogeneous magnetized plasma spheres are immersed in the homogeneous dielectric background, as the Voigt effects of magnetized plasma are considered (the incidence electromagnetic wave vector is perpendicular to the external magnetic field at any time). The dispersive properties of all of the EM modes are studied because the PBG is not only for the extraordinary and ordinary modes but also for the mixed polarized modes. The equations for PBGs also are theoretically deduced. The numerical results show that the PBG and a flatbands region can be observed. The effects of the dielectric constant of dielectric background, filling factor, plasma frequency and plasma cyclotron frequency (the external magnetic field) on the dispersive properties of all of the EM modes in such 3D MPPCs are investigated in detail, respectively. Theoretical simulations show that the PBG can be manipulated by the parameters as mentioned above. Compared to the conventional dielectric-air PCs with similar structure, the larger PBG can be obtained in such 3D MPPCs. It is also shown that the upper edge of flatbands region cannot be tuned by the filling factor and dielectric constant of dielectric background, but it can be manipulated by the plasma frequency and plasma cyclotron frequency.

In this paper, we consider a one-fluid model of electromagnetic hydrodynamics (EMHD) of quasi-neutral plasma, with ion and electron inertia fully taken into account. The EMHD and the MHD models are compared with regard to solving the classical problem of steady flow of incompressible plasma in a planar channel. In the MHD theory, the solution is given by the Hartmann flow, whereas in the EMHD model, the diagram of the longitudinal velocity is shown to be significantly different from the Hartmann profile: in particular, near-wall flows and a counterflow appear, while the flow velocity may significantly deviate from the direction of the antigradient pressure causing plasma to flow (the so-called hydrodynamic ‘Hall effect’). This study shows that the EMHD and the MHD planar channel theories are practically the same for liquid metal plasma and are very different for gas plasma.

Plasma expansion and soliton formation in laser created plasma are addressed. Nonlinear acoustic waves in plasma where the combined effect of trapped and non-thermal electrons are dealt with, in plasma expansion are studied. Using the perturbation method, a modified Korteweg–de Vries equation (mKdV) that describes how the ion acoustic waves (IAW) are derived. The plasma is modeled by a Cairns distribution function for non-thermal electrons combined with Gurevich distribution function for the trapped electrons. It is found that parameters taken into account have significant effects on the properties of nonlinear waves as well as on plasma expansion into vacuum. We point out, that this work has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, combined with trapped particles. Furthermore, this study is of interest in the context of the investigation of mono-energetic ion beams from intense laser interactions with plasmas.

This paper is dedicated to Vitaly Shafranov, who became increasingly interested in stellarators. Stellarators have a steady-state magnetic configuration, robust positional stability, and consistency with a plasma current below the level at which runaway electrons become a major issue. The development path for stellarators may be faster and cheaper than for tokamaks: stellarators are amenable to computer design validated by moderate scale experiments to circumvent issues that impede fusion development. This is distinct from the empirical explorations required to find an acceptable nonlinear, self-organized state of a tokamak. Fusion plasmas can be designed and controlled in stellarators in ways that are not possible in tokamaks. This paper outlines computational studies that could be carried at low cost during the next few years that would clarify the reactor potential of the stellarator and are needed for rational planning of the fusion program.

We present simulations that demonstrate the production of quasi-monoenergetic proton bunches from the interaction of a CO2 laser pulse train with a near-critical density hydrogen plasma. The multi-pulse structure of the laser leads to a steepening of the plasma density gradient, which the simulations show is necessary for the formation of narrow-energy spread proton bunches. Laser interactions with a long, front surface, scale-length (≫ c/ωp) plasma, with linear density gradient, were observed to generate proton beams with a higher maximum energy, but a much broader spectrum compared to step-like density profiles. In the step-like cases, a peak in the proton energy spectra was formed and seen to scale linearly with the ratio of laser intensity to plasma density.

Non-relativistic collisionless shock waves are widespread in space and astrophysical plasmas and are known as efficient particle accelerators. However, our understanding of collisionless shocks, including their structure and the mechanisms whereby they accelerate particles, remains incomplete. We present here the results of numerical modelling of an ion-acoustic collisionless shock based on the one-dimensional kinetic approximation for both electrons and ions with a real mass ratio. Special emphasis is paid to the shock-reflected ions as the main driver of shock dissipation. The reflection efficiency, the velocity distribution of reflected particles and the shock electrostatic structure are studied in terms of the shock parameters. Applications to particle acceleration in geophysical and astrophysical shocks are discussed.

It is shown that there exists a strong interaction between the magnetic and kinetic aspects of a multi-ion plasma. The interaction appears as a system of simultaneous equations which show the alignment of vortices to flows and satisfy the Beltrami condition. Solving these equations lead to a non-force-free magnetic field which can be cast as a superposition of three multiscale force-free magnetic field configurations. It is the consequence of different Beltrami parameters of positive and negative ion fluids. It is also shown that self-organized paramagnetic and diamagnetic field structures could be created by varying the vorticities and flows of ion fluids.