In the single fluid, non-relativistic, ideal magnetohydrodynamic (MHD) plasma description, magnetic field lines play a fundamental role by defining dynamically preserved ‘magnetic connections’ between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D magnetic connection hypersurfaces in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when $\boldsymbol{E}\boldsymbol{\cdot }\boldsymbol{B}=0$.

The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.

The fundamentals of the ‘resonance method’ are presented. The method relies on evaluating the dynamic response of one or more dust particles in the sheath of a laboratory plasma to small external perturbations. It allows one to make in situ high-precision measurements of particle properties. It is shown that the particle mass and charge and the strength of the interaction between two particles can be measured. Technical requirements, limitations and application examples are presented and discussed.

In this article, a detailed introduction of the light extinction spectrometry (LES) diagnostics is given. LES allows the direct in situ measurement of the particle size distribution and absolute concentration of dust clouds levitating in plasmas. Using a relatively simple and compact experimental set-up, the dust cloud parameters can be recovered with a good accuracy making minimum assumptions on their physical properties. Special emphases are given to the inversion procedure of light extinction spectra and all the required particle shape, refractive index and light extinction models. The parameter range and the limitations of LES are discussed. Two measurements in low-pressure gas discharges are presented: (i) in a direct-current (DC) glow discharge in which nanoparticles are growing from the sputtering of a tungsten cathode and (ii) in an argon–silane radio-frequency discharge. They demonstrate the capabilities of the LES technique to characterise, in situ and in real-time, the growth dynamics of nanoparticles in the size range 5–100 nm and volume concentrations in the range from a few ppb to a few ppm.

Successful phenomenological models of pulsar wind nebulae assume efficient dissipation of the Poynting flux of the magnetized electron–positron wind as well as efficient acceleration of the pairs in the vicinity of the termination shock, but how this is realized is not yet well understood. This paper suggests that the corrugation of the termination shock, at the onset of nonlinearity, may lead towards the desired phenomenology. Nonlinear corrugation of the termination shock would convert a fraction of order unity of the incoming ordered magnetic field into downstream turbulence, slowing down the flow to sub-relativistic velocities. The dissipation of turbulence would further preheat the pair population on short length scales, close to equipartition with the magnetic field, thereby reducing the initial high magnetization to values of order unity. Furthermore, it is speculated that the turbulence generated by the corrugation pattern may sustain a relativistic Fermi process, accelerating particles close to the radiation reaction limit, as observed in the Crab nebula. The required corrugation could be induced by the fast magnetosonic modes of downstream nebular turbulence; but it could also be produced by upstream turbulence, either carried by the wind or seeded in the precursor by the accelerated particles themselves.

The effect of the finite probe size in plasma fluctuation measurements is revisited for dusty plasmas, where it has been argued that dust leads to a significant low-frequency enhancement in the spectral densities of ion density fluctuations, which can constitute the physical basis of a dust diagnostic technique. Theoretical predictions for the spectral modifications are presented and the dust acoustic mode contribution is analysed. The finite probe size effect is treated within the volume average approach, which introduces geometry dependent form factors that are calculated for spherical and cylindrical probes. The volume average approach is compared with the typically employed cutoff wavenumber approximation for various dust and plasma parameters. The contribution of temperature fluctuations to the spectral density of current fluctuations is also evaluated.

This paper reviews key aspects of the problem of magnetic islands control by electron cyclotron current drive in fusion devices. On the basis of the ordering of the basic spatial and time scales of the magnetic reconnection physics, we present the established results, highlighting some of the open issues posed by the small-scale structures that typically accompany the nonlinear evolution of the magnetic islands and constrain the effect of the control action.

V. D. Shafranov was a key person in the fusion program. The paper presents the recollections of one of his close colleagues about Shafranov’s impact on the early days of tokamak research.

In recent papers, we show how accretion disks around massive black holes could act as dynamos producing magnetic jets similar to the jets that create spheromaks in the laboratory. In this paper, we discuss how these magnetic astrophysical jets might naturally produce runaway ion beams accelerated to $10^{20}$  eV or more, finally ejected as ultra high energy cosmic rays (UHECRs) long regarded as one of the mysteries of astrophysics. The acceleration is mainly due to the drift cyclotron loss cone kinetic instability known from plasma research. Experiments and simulations are suggested to verify the acceleration process.

Particle image velocimetry is a fluid measurement technique that has been used for more than 20 years to characterize the particle transport and thermal state of dusty plasma systems. This manuscript provides an overview of this diagnostic technique, highlighting the strengths and limitations that are associated with its use. Additionally, the variations of this technique that have been applied in the study of dusty plasma systems will be discussed, along with a small selection of measurements that can be made with the technique. Potential future directions for this diagnostic tool within the dusty plasma community will also be discussed.

Rotating plasmas have the potential to offer unique capabilities for isotope and mass separation. Among the various electric and magnetic field configurations offering mass separation capabilities, rotating plasmas produced through static or oscillating fields are shown to be a leading candidate for tackling the unsolved problem of large-scale plasma separation. The successful development and deployment of industrial-scale plasma separation technologies could, among many other applications, provide an innovative path towards advanced sustainable nuclear energy. In this context, the potential and versatility of plasma rotation induced by rotating magnetic fields is uncovered and analysed. Analytical stability diagrams are derived from rotating ion orbits as a function of ion mass. Based on these findings, the basic principles of a rotating field plasma separator are then introduced. In light of these results, challenges associated with this original separation process are underlined, and the main directions for a future research program aimed at this important unsolved problem of applied plasma physics are identified.

Methods of imaging and image analysis are presented for dusty plasma experiments. Micron-sized polymer spheres, electrically suspended in a partially ionized gas, are illuminated by a sheet of laser light and imaged by video cameras. Image analysis methods yield particle positions and velocities of individual particles in each video image. Methods to minimize errors in the particle positions and velocities, which are now commonly used in the dusty plasma community, are described.

The intense heat and energetic particle fluxes expected in ITER and future magnetic fusion reactors pose prohibitive problems to the design, selection and maintenance of the first wall and divertor. Micropellet injection (MPI) technologies can offer some innovative solutions to the material and extreme heat challenges. Basic physics of micropellet motion, ablation and interactions with high-temperature plasmas and energetic particles are presented first. We then discuss MPI technology options and applications. In addition to plasma diagnostic applications, controlled injection of micropellets of different sizes, velocities and injection frequencies will offer several possibilities: (1) better assessment of the core plasma cooling due to dust produced in situ; (2) better understanding of the plasma–material interaction physics near the wall; (3) new methods for plasma fuelling and impurity control; and (4) techniques for edge cooling with minimal impact on the plasma core. Dedicated small-scale laboratory experiments will complement major fusion experiments in development and applications of MPI.

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisp motions as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.

We consider two isolated, interacting dust particles confined in plasma. Measurements of normal mode frequencies are used to determine the dust charge, the Debye shielding length and the anisotropy of the confining potential well. For dust particles confined near the sheath edge, the vertical electric field and an effective electron temperature are also determined. This method is used to characterize the sheath above a short rectangular trench in the powered electrode of a radio-frequency discharge.

Charge carrier transport across interfaces of dissimilar materials (including vacuum) is the essence of all electronic devices. Ultrafast charge transport across a nanometre length scale is of fundamental importance in the miniaturization of vacuum and plasma electronics. With the combination of recent advances in electronics, photonics and nanotechnology, these miniature devices may integrate with solid-state platforms, achieving superior performance. This paper reviews recent modelling efforts on quantum tunnelling, ultrafast electron emission and transport, and electrical contact resistance. Unsolved problems and challenges in these areas are addressed.

Analytic solutions are presented for the orbit of a charged particle in the combination of a uniform axial magnetic field and parabolic electrostatic potential. These trajectories are shown to correspond to the sum of two individually rotating vectors with one vector rotating at a constant fast frequency and the other rotating in the same sense but with a constant slow frequency. These solutions are related to Penning trap orbits and to stochastic orbits. If the lengths of the two rotating vectors are identical, the particle has zero canonical angular momentum in which case the particle orbit will traverse the origin. If the potential has an inverse dependence on distance from the source of the potential, the particle can impact the source. Axis-encircling orbits are where the length of the vector associated with the fast frequency is longer than the vector associated with the slow frequency. Non-axis-encircling orbits are the other way around.

The proportion of metal ions in a high power impulse magnetron sputtering discharge is key information for the potential development of new materials and new layer architectures deposited by this technique. This paper aims to measure this proportion by using a homemade system consisting of a quartz crystal microbalance and a grid energy analyser assembly. Such a system yields relevant results on the composition of the post-discharge depending on the nature of the gas (Ar, Kr, Xe) and the target materials (Pt, Pd, Au, $\text{Pt}_{50}\text{Au}_{50}$ and $\text{Pt}_{5}\text{Pd}_{95}$ ). In our conditions, the highest proportion of metal ions in the post-discharge are obtained by using Ar gas and reaches 10 %, 12 %, 50 %, 19 % and 88 % for Pt, Au, Pd, $\text{Pt}_{50}\text{Au}_{50}$ and $\text{Pt}_{5}\text{Pd}_{95}$ targets, respectively.