We analyse, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a non-canonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Larmor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system.

Recent results of three astrophysically relevant experiments at Caltech are summarized. In the first experiment magnetohydrodynamically driven plasma jets simulate astrophysical jets that undergo a kink instability. Lateral acceleration of the kinking jet spawns a Rayleigh–Taylor instability, which in turn spawns a magnetic reconnection. Particle heating and a burst of waves are observed in association with the reconnection. The second experiment uses a slightly different setup to produce an expanding arched plasma loop which is similar to a solar corona loop. It is shown that the plasma in this loop results from jets originating from the electrodes. The possibility of a transition from slow to fast expansion as a result of the expanding loop breaking free of an externally imposed strapping magnetic field is investigated. The third and completely different experiment creates a weakly ionized plasma with liquid nitrogen cooled electrodes. Water vapour injected into this plasma forms water ice grains that in general are ellipsoidal and not spheroidal. The water ice grains can become quite long (up to several hundred microns) and self-organize so that they are evenly spaced and vertically aligned.

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.

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.

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.

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.

Clusters of galaxies are embedded in halos of optically thin, gravitationally stratified, weakly magnetized plasma at the system’s virial temperature. Owing to radiative cooling and anisotropic heat conduction, such intracluster medium (ICM) is subject to local instabilities, which are combinations of the thermal, magnetothermal and heat-flux-driven buoyancy instabilities. If the ICM rotates significantly, its stability properties are substantially modified and, in particular, also the magnetorotational instability (MRI) can play an important role. We study simple models of rotating cool-core clusters and we demonstrate that the MRI can be the dominant instability over significant portions of the clusters, with possible implications for the dynamics and evolution of the cool cores. Our results give further motivation for measuring the rotation of the ICM with future X-ray missions such as ASTRO-H and ATHENA.

Modelling the nucleation and growth of nanoparticles in liquid-phase laser ablation is very important to optimize and control the size and the structure of nanoparticles. However, the detailed formation process of nanoparticles after laser ablation is still unclear. In the present study we investigated for the first time the kinetic growth of nanoparticles synthesized by laser ablation in water, emphasizing the leading role of the plasma medium and in particular the electrostatic agglomeration due to the charging of the nanoparticle in the plasma plume. The importance of the confining role of the liquid medium on the plasma plume is revealed, showing how an isothermal expansion is able to produce smaller nanoparticles compared to an adiabatic cooling.

Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number $S$ , the magnetic Prandtl number $P_{m}$ , the amplitude of the boundary perturbation $\hat{{\it\Psi}}_{0}$ , and the perturbation wave number $\hat{k}$ . This new representation highlights the parameter regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of $S$ and $P_{m}$ , depending on the parameters that characterize the external drive, which have not been considered until now. These features are crucial to understanding the onset and evolution of magnetic reconnection in diverse physical systems.

The transverse dynamics of a pure electron plasma confined in a Penning–Malmberg trap is investigated, taking advantage of two-dimensional particle-in-cell numerical simulations. The evolution of the electron plasma turbulence is studied by means of a wavelet-based multiresolution analysis. In particular, a modified recursive denoising algorithm is developed to separate coherent and incoherent (not necessarily homogeneous) components of the flow. A set of simulations have been carried out changing systematically the radii of an initial annular density distribution of the electrons. The results of the multiresolution analysis indicate that the initial density configuration may have a considerable effect on the evolution of turbulence. Even very small initial density fluctuations can lead to quite different final states, especially in the presence of multiple active diocotron modes characterized by similar growth rates.

A plasma target for highly efficient neutralization of powerful negative ion beams is considered. The plasma is confined within a magnetic trap with multipole magnetic walls. It is proposed to use inverse magnetic mirrors to limit plasma outflow through the inlet and outlet holes in the trap. Using the particle-in-cell method, mathematical simulation of plasma dynamics in the trap has been performed. The estimates of plasma distribution and particle confinement efficiency in the region of the magnetic mirrors has been obtained. Simulation results were compared with experimental data.

The betatron radiation in the bubble regime is studied in the presence of resonant interaction between the accelerated electrons and the driver laser pulse tail. The calculations refer to experimental parameters available at the FLAME laser facility at the National Laboratories of Frascati (LNF), and represent the radiation spectra and spatial distributions to be expected in forthcoming experiments.

The origin of the 22-year solar magnetic cycle lies below the photosphere where multiscale plasma motions, due to turbulent convection, produce magnetic fields. The most powerful intensity and velocity signals are associated with convection cells, called granules, with a scale of typically 1 Mm and a lifetime of a few minutes. Small-scale magnetic elements (SMEs), ubiquitous on the solar photosphere, are passively transported by associated plasma flows. This advection makes their traces very suitable for defining the convective regime of the photosphere. Therefore the solar photosphere offers an exceptional opportunity to investigate convective motions, associated with compressible, stratified, magnetic, rotating and large Rayleigh number stellar plasmas. The magnetograms used here come from a Hinode/SOT uninterrupted 25-hour sequence of spectropolarimetric images. The mean-square displacement of SMEs has been modelled with a power law with spectral index ${\it\gamma}$ . We found ${\it\gamma}=1.34\pm 0.02$ for times up to ${\sim}2000~\text{s}$ and ${\it\gamma}=1.20\pm 0.05$ for times up to ${\sim}10\,000~\text{s}$ . An alternative way to investigate the advective–diffusive motion of SMEs is to look at the evolution of the two-dimensional probability distribution function (PDF) for the displacements. Although at very short time scales the PDFs are affected by pixel resolution, for times shorter than ${\sim}2000~\text{s}$ the PDFs seem to broaden symmetrically with time. In contrast, at longer times a multi-peaked feature of the PDFs emerges, which suggests the non-trivial nature of the diffusion–advection process of magnetic elements. A Voronoi distribution analysis shows that the observed small-scale distribution of SMEs involves the complex details of highly nonlinear small-scale interactions of turbulent convective flows detected in solar photospheric plasma.

In this paper we study transport features of a one-dimensional beam–plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analysed.

This study demonstrates a remarkable flexibility of advanced divertor configurations created with the remote poloidal field coils. The emphasis here is on the configurations with three poloidal field nulls in the divertor area. We are seeking the structures where all three nulls lie on the same separatrix, thereby creating two zones of a very strong flux expansion, as envisaged in the concept of Takase’s cusp divertor. It turns out that the set of remote coils can indeed produce a cusp divertor, with additional advantages of: (i) a large stand-off distance between the divertor and the coils and (ii) a thorough control that these coils exert over the fine features of the configuration. In reference to these additional favourable properties acquired by the cusp divertor, the resulting configuration could be called ‘a super-cusp’. General geometrical features of the three-null configurations produced by remote coils are described. Issues on the way to practical applications include the need for a more sophisticated control system and possible constraints related to excessively high currents in the divertor coils.

In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.

In this work we discuss an application of the Tetrad Dynamics approach, a stochastic dynamical theory already introduced in hydrodynamic turbulence, to incompressible magneto-hydrodynamics. This theoretical framework is capable of taking into account some crucial aspects of turbulent plasmas, namely, (i) its material nature, which is stressed through the adoption of Lagrangian variables, (ii) its probabilistic dynamics, which is fundamental to understand the intermittency and highly irregular nature of turbulence, and (iii) the multi-scale character of interactions, which is approached by promoting the space size of parcels to the role of a dynamical variable. In particular, here, we construct the probabilistic equations of motion for quantities describing the evolution of a turbulent plasma (a matrix ${\bf\varrho}$ describing the parcel’s shape, the plasma velocity and magnetic field coarse-grained gradient tensors, $\unicode[STIX]{x1D648}$ and $\unicode[STIX]{x1D652}$ ), resorting the functional formalism of classical statistical dynamics. Through the introduction of a stochastic action and using a path integral approach, the statistical properties of $({\bf\varrho},\unicode[STIX]{x1D648},\unicode[STIX]{x1D652})$ can be derived from those of noises appearing in their equations of motion, both at equilibrium and out of equilibrium.

Thanks to the presence of a transverse magnetic flux density ( $B_{x}$ and $B_{y}$ where $z$ is the extraction axis), the undesired extraction of electrons from a negative ion source is reduced and it is due to collisions. The electron transport is studied with a kinetic model, including Vlasov–Poisson effects and atomic collisions. The integrodifferential equations (IDE) resulting from a reduction to a one-dimensional problem (1-D) by integration on characteristic orbits are strongly affected by the trapped orbits, as here evaluated; a kernel calculation with a partial wave approximation is introduced. Dependencies from the local drift velocity $v_{d}$ and effective Larmor radius $L_{e}$ are found. Solutions are investigated in simple cases with a constant electron current (no additional electron production). Equilibrium solution and electron conductivity are analytically obtained. Presheath solutions are discussed; the approximated conversion to differential equations that are adequate for presheath only (with moderated electric field gradient $E_{z,z}>-eB_{x}^{2}/m$ ) and their numeric solutions coupled to Poisson equation are reported, and compared to iterative IDE solutions. Examples with different values of $L_{e}$ and mean free path (mfp) ratio are described.

In this paper, we analyse the linear stability of a stellar accretion disk having a stratified morphology. The study is performed in the framework of ideal magneto-hydrodynamics and therefore results in a characterization of the linear unstable magneto-rotational modes. The peculiarity of the present scenario consists of adopting the magnetic flux function as the basic dynamical variable. Such a representation of the dynamics allows us to take account of the co-rotation theorem as a fundamental feature of the ideal plasma equilibrium and to evaluate its impact on the perturbation evolution. According to the Alfvenic nature of the magneto-rotational instability, we consider an incompressible plasma profile and perturbations propagating along the background magnetic field. Furthermore, we develop a local perturbation analysis around fiducial coordinates of the background configuration and deal with very small-scale linear dynamics in comparison to the background inhomogeneity size. The main issue of the present study is that the condition for the emergence of unstable modes is the same in the stratified plasma disk as in the case of a thin configuration. Such a feature is the result of the cancellation of the vertical derivative of the disk angular frequency from the dispersion relation, which implies that only the radial profile of the differential rotation is responsible for the trigger of the growing modes.