We study the effect of negatively charged dust on the magnetic-field-aligned polarisation electrostatic field ($\boldsymbol {E}_{\parallel }$) using Cassini's RPWS/LP in situ measurements during the ‘ring-grazing’ orbits. We derive a general expression for $\boldsymbol {E}_{\parallel }$ and estimate for the first time in situ $\lVert \boldsymbol {E}_{\parallel } \rVert$ (approximately $10^{-5} \, \text {V}\, \text {m}^{-1}$) near the Janus and Epimetheus rings. We further demonstrate that the presence of the negatively charged dust close to the ring plane ($\vert \text {Z} \vert \lesssim 0.11 \, \text {R}_{s}$) amplifies $\lVert \boldsymbol {E}_{\parallel } \rVert$ by at least one order of magnitude and reverses its direction due to the effect of the charged dust gravitational and inertial forces. Such reversal confines the electrons at the magnetic equator within the dusty region, around $0.047 \, \text {R}_{s}$ above the ring plane. Furthermore, we discuss the role of the collision terms, in particular the ion–dust drag force, in amplifying $\boldsymbol {E}_{\parallel }$. These results imply that the charged dust, as small as nanometres in size, can have a significant influence on the plasma transport, in particular ambipolar diffusion along the magnetic field lines, and so their presence must be taken into account when studying such dynamical processes.

First-order-accurate degenerate variational integration (DVI) was introduced in Ellison et al. (Phys. Plasmas, vol. 25, 2018, 052502) for systems with a degenerate Lagrangian, i.e. one in which the velocity-space Hessian is singular. In this paper we introduce second-order-accurate DVI schemes, both with and without non-uniform time stepping. We show that it is not in general possible to construct a second-order scheme with a preserved two-form by composing a first-order scheme with its adjoint, and discuss the conditions under which such a composition is possible. We build two classes of second-order-accurate DVI schemes. We test these second-order schemes numerically on two systems having non-canonical variables, namely the magnetic field line and guiding centre systems. Variational integration for Hamiltonian systems with non-uniform time steps, in terms of an extended phase space Hamiltonian, is generalized to non-canonical variables. It is shown that preservation of proper degeneracy leads to single-step (one-step) methods without parasitic modes, i.e. to non-uniform time step DVIs. This extension applies to second-order-accurate as well as first-order schemes, and can be applied to adapt the time stepping to an error estimate.

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P $1\frac {1}{2}$-dimensional phase space is also considered and simulated numerically.

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

We analyse how the turbulent transport of $\boldsymbol {E}\times \boldsymbol {B}$ type in magnetically confined plasmas is affected by the intermittent features of turbulence. The latter are modelled via the non-Gaussian distribution $P(\phi )$ of the turbulent electric potential $\phi$. Our analysis is performed at an analytical level and confirmed numerically using two statistical approaches. We have found that the diffusion is inhibited linearly by intermittency, mainly via the kurtosis of the distribution $P(\phi )$. The associated susceptibility for this linear process is shown to be dependent on the poloidal velocity $V_p$ and on the correlation time $\tau _c$ (or the Kubo number $K_\star$, the ratio between $\tau _c$ and the specific time of flight $\tau _{{\rm fl}}$) with a maximum at $\tau _c\approx \tau _{{\rm fl}}$ ($K_\star \approx 1$). Intermittency does not affect the scaling of diffusion with the Kubo number.

A spacecraft during mission typically switches from chemical propulsion to electric propulsion once it lifts out of the Earth's gravity as the thrust requirement to drive it reduces substantially. Consequently, electric propulsion technology is commonly used for deep space mission, satellite orbit keeping and orbit correction. In the last few decades, the amount of man-made space junk (space debris) has increased enormously and has become a potential danger for space stations, space shuttles and other live satellites. A bi-directional plasma thruster, mounted on a satellite, can be used to remove space debris during satellite operation (Takahashi et al., Sci. Rep., vol. 8, 2018, p. 14417). A directed ion beam ejected from a plasma thruster imparts a net force on space debris to decelerate and facilitates manoeuvring and re-entry of space debris into the Earth's atmosphere where it can burn out. We present a detailed 1D3V PIC-MCC (particle in cell-Monte Carlo collision) simulation of a bi- directional plasma thruster. To this end, a PIC-MCC solver which resolves thruster axial direction and all three velocity dimensions is used to study a magnetic nozzle plasma thruster with both ends open (bi-directional plasma thruster). We show that such a bi-directional plasma thruster can be used to accelerate–decelerate a live satellite and also to remove space debris by altering the magnetic field spatial profile in the plasma expansion region. A detailed study is presented.

In the present work we investigate the dynamics of electrons under the action of wave packets of high-frequency electromagnetic carrier waves. When the group velocities of the packets are subluminal, electrons can be efficiently accelerated. We show that the whole process can be described by an accurate ponderomotive canonical formalism that includes relevant extensions of the original ponderomotive approach applied to carriers moving at the speed of light. Single-particle simulations validate our analytical approach and show that extended canonical methods provide better agreement with numerics than previous investigations. In particular, we obtain a precise relationship between the wave amplitude and group velocity for optimum acceleration of initially stationary targets.

Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon computational fluid dynamics (CFD) methods, allow the coronal features to be resolved using solar surface magnetograms as inputs. These computations are carried out in a full three-dimensional domain and, thus, selection of the correct mesh configuration is essential to save computational resources and enable/speed up convergence. In addition, it has been observed that for MHD simulations close to the hydrostatic equilibrium, spurious numerical artefacts might appear in the solution following the mesh structure, which makes the selection of the grid also a concern for accuracy. The purpose of this paper is to discuss and trade off two main mesh topologies when applied to global solar corona simulations using the unstructured ideal MHD solver from the COOLFluiD platform. The first topology is based on the geodesic polyhedron and the second on $UV$ mapping. Focus is placed on aspects such as mesh adaptability, resolution distribution, resulting spurious numerical fluxes and convergence performance. For this purpose, first a rotating dipole case is investigated, followed by two simulations using real magnetograms from the solar minima (1995) and solar maxima (1999). It is concluded that the most appropriate mesh topology for the simulation depends on several factors, such as the accuracy requirements, the presence of features near the polar regions and/or strong features in the flow field in general. If convergence is of concern and the simulation contains strong dynamics, then grids which are based on the geodesic polyhedron are recommended compared with more conventionally used $UV$-mapped meshes.

The Weibel instability is investigated theoretically and numerically under three scenarios: counterstreaming electron beams in background plasma, an electron–positron beam and an electron–proton beam in background plasma. These models occur widely in laboratory and astrophysical environments. The Weibel instability growth rates are determined numerically from the corresponding cold-fluid dispersion relations, which are confirmed with two-dimensional particle-in-cell simulations. The maximum growth rates for the counterstreaming beams in background plasma are an order of magnitude smaller than the maximum growth rates for the beams cases in the same range of density ratios and beam energies. The maximum growth rate for the electron–positron beam case is shown to be at most a factor $\sqrt {2}$ greater than the electron–proton beam case with similar dispersion behaviours. A non-monotonic relation is found between the maximum Weibel instability growth rates and the electron–positron beam energy, suggesting that increasing beam energies does not entail an increase in the Weibel instability growth rate.

Upper bounds on the growth of free energy in gyrokinetics are derived. These bounds apply to all local gyrokinetic instabilities in the geometry of a flux tube, i.e. a slender volume of plasma aligned with the magnetic field, regardless of the geometry of field, the number of particle species or collisions. The results apply both to linear instabilities and to the nonlinear growth of finite-amplitude fluctuations.

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project (R.L. Orbach, 2008, https://ncsx.pppl.gov/DOE_NCSX_052208.pdf). Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than $0.1\,\%$ of the cost of previous work, which considered solely local stochastic optimization.

This work numerically investigates the role of viscosity and resistivity in Rayleigh–Taylor instabilities in magnetized high-energy-density (HED) plasmas for a high Atwood number and high plasma beta regimes surveying across plasma beta and magnetic Prandtl numbers. The numerical simulations are performed using the visco-resistive magnetohydrodynamic equations. Results presented here show that the inclusion of self-consistent viscosity and resistivity in the system drastically changes the growth of the Rayleigh–Taylor instability (RTI) as well as modifies its internal structure at smaller scales. It is seen here that the viscosity has a stabilizing effect on the RTI. Moreover, the viscosity inhibits the development of small-scale structures and also modifies the morphology of the tip of the RTI spikes. On the other hand, the resistivity reduces the magnetic field stabilization, supporting the development of small-scale structures. The morphology of the RTI spikes is seen to be unaffected by the presence of resistivity in the system. An additional novelty of this work is in the disparate viscosity and resistivity profiles that may exist in HED plasmas and their impact on RTI growth, morphology and the resulting turbulence spectra. Furthermore, this work shows that the dynamics of the magnetic field is independent of viscosity and likewise the resistivity does not affect the dissipation of enstrophy and kinetic energy. In addition, power law scalings of enstrophy, kinetic energy and magnetic field energy are provided in both the injection range and inertial sub-range, which could be useful for understanding RTI induced turbulent mixing in HED laboratory and astrophysical plasmas and could aid in the interpretation of observations of RTI-induced turbulence spectra.

We study the time-dependent formation and evolution of a current sheet (CS) in a magnetised, collisionless, high-beta plasma using hybrid-kinetic particle-in-cell simulations. An initially tearing-stable Harris sheet is frozen into a persistently driven incompressible flow so that its characteristic thickness gradually decreases in time. As the CS thins, the strength of the reconnecting field increases, and adiabatic invariance in the inflowing fluid elements produces a field-biased pressure anisotropy with excess perpendicular pressure. At large plasma beta, this anisotropy excites the mirror instability, which deforms the reconnecting field on ion-Larmor scales and dramatically reduces the effective thickness of the CS. Tearing modes whose wavelengths are comparable to that of the mirrors then become unstable, triggering reconnection on smaller scales and at earlier times than would have occurred if the thinning CS were to have retained its Harris profile. A novel method for identifying and tracking X-points is introduced, yielding X-point separations that are initially intermediate between the perpendicular and parallel mirror wavelengths in the upstream plasma. These mirror-stimulated tearing modes ultimately grow and merge to produce island widths comparable to the CS thickness, an outcome we verify across a range of CS formation timescales and initial CS widths. Our results may find their most immediate application in the tearing disruption of magnetic folds generated by turbulent dynamo in weakly collisional, high-beta, astrophysical plasmas.

Extreme-ultraviolet pulses can propagate through ionised solid-density targets, unlike optical pulses and, thus, have the potential to probe the interior of such plasmas on sub-femtosecond timescales. We present a synthetic diagnostic method for solid-density laser-generated plasmas based on the dispersion of an extreme-ultraviolet attosecond probe pulse, in a pump–probe scheme. We demonstrate the theoretical feasibility of this approach through calculating the dispersion of an extreme-ultraviolet probe pulse propagating through a laser-generated plasma. The plasma dynamics is calculated using a particle-in-cell simulation, whereas the dispersion of the probe is calculated with an external pseudo-spectral wave solver, allowing for high accuracy when calculating the dispersion. The application of this method is illustrated on thin-film plastic and aluminium targets irradiated by a high-intensity pump pulse. By comparing the dispersion of the probe pulse at different delays relative to the pump pulse, it is possible to follow the evolution of the plasma as it disintegrates. The high-frequency end of the dispersion provides information on the line-integrated electron density, whereas lower frequencies are more affected by the highest density encountered along the path of the probe. In addition, the presence of thin-film interference could be used to study the evolution of the plasma surface.