In this work, we investigate the generation of the ambipolar electric field in a gravitationally stratified, collisionless plasma atmosphere. In such environments, gravity tends to separate charged species. To prevent separation an electric field, classically described by the Pannekoek–Rosseland expression, is usually imposed externally. Here, we propose a self-consistent method to recover this field based on a multi-mode Fourier expansion of the electrostatic interaction. We show that, under suitable conditions, this approach naturally leads to the ambipolar electric field and restores charge neutrality. The method is tested in both isothermal and multi-temperature plasma configurations. This framework provides a foundation for future developments that may include collisions, ionisation and asymmetric boundary conditions to model more realistic stellar atmospheres.

We present an extended investigation of a recently introduced model of gravitationally confined, collisionless plasma (Barbieri et al. 2024a A&A vol. 681, p. L5), which showed that rapid temperature fluctuations at the base of the plasma, occurring on time scales much shorter than the electron crossing time, can drive the system into a non-thermal state characterised by anti-correlated temperature and density profiles, commonly referred to as temperature inversion. To describe this phenomenon, a temporal coarse-graining formalism was developed (Barbieri et al., 2024b J. Plasma Phys. vol. 90, p. 905900511). In this work, we generalise that approach to cover regimes where the time scales of temperature fluctuations are comparable to or exceed the electron crossing time. We derive a set of kinetic equations that incorporate an additional term arising from the coarse-graining procedure, which was not present in the earlier formulation. Through numerical simulations, we analyse the plasma dynamics under these broader conditions, showing that the electric field influences the system when fluctuation time scales approach the electron crossing time. However, for time scales much larger than the proton crossing time, the electric field becomes negligible. The observed behaviours are interpreted within the framework of the extended temporal coarse-graining theory, and we identify the regimes and conditions in which temperature inversion persists.

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

The properties of a collisional magnetized plasma sheath containing non-thermal electrons, multi-component ions (${\text{He}}^{+}$ and $ {\text{Ar}}^{+}$), neutral atoms and negatively charged dust particles are analysed. Using a one-dimensional fluid model, the parametric changes in sheath dynamics are investigated in the presence of nanometre-sized charged dust particles and an oblique magnetic field. The influence of charged dust, ionization, ion–neutral collisions, ion loss and non-thermal electrons on sheath parameters such as ion densities, velocities, electron density and potential is explored through theoretical modelling and numerical analysis. The results indicate that the ion density (${\text{He}}^{+}$ and $ {\text{Ar}}^{+}$) increases throughout the sheath region with rising ionization frequency in the absence of charged dust. However, when charged dust is present, the density of ${\text{He}}^{+}$ ions decreases while the density of $\text{Ar}^{+}$ ions increases, exhibiting a sharp peak near the sheath edge. It is also noted that the increase in ion–neutral collision frequency enhances the density, particularly near the sheath edge. Additionally, the presence of non-thermal electrons initially leads to an increase in ion density near the sheath edge, followed by a decrease within the sheath region. A qualitative explanation of the above phenomena, which occur due to different physical parameters, is provided.

Taking advantage of the invariance of the generalised canonical momentum associated with a translational symmetry along a given direction, we describe the dynamics of a plasma by solving an ensemble of $N$ relativistic reduced Vlasov equations coupled in a self-consistent way with the Maxwell equations. This approach, hereafter referred to as the multi-stream model, allows for a drastic reduction in the computational time compared with the full kinetic Vlasov–Maxwell approach. It is also well adapted to a parallel environment. In addition, we extend the model to a two-dimensional geometry in the configuration space, which makes it possible to treat the interaction between several instabilities of beam–plasma and Weibel type, with a relatively small number of streams. The model provides an exact description of current densities perpendicular to a cyclic coordinate, which are responsible, at both fundamental and microscopic levels, for key features of energy transfer, plasma heating and magnetic reconnection processes in collisionless plasmas.

Kinetic simulations of relativistic gases and plasmas are critical for understanding diverse astrophysical and terrestrial systems, but the accurate construction of the relativistic Maxwellian, the Maxwell–Jüttner distribution, on a discrete simulation grid is challenging. Difficulties arise from the finite velocity bounds of the domain, which may not capture the entire distribution function, as well as errors introduced by projecting the function onto a discrete grid. Here, we present a novel scheme for iteratively correcting the moments of the projected distribution applicable to all grid-based discretizations of the relativistic kinetic equation. In addition, we describe how to compute the needed nonlinear quantities, such as Lorentz boost factors, in a discontinuous Galerkin scheme through a combination of numerical quadrature and weak operations. The resulting method accurately captures the distribution function and ensures that the moments match the desired values to machine precision.

We describe a new model for the study of weakly collisional, magnetised plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle dynamics parallel to the magnetic field while approximating the perpendicular dynamics through a spectral expansion in the perpendicular degrees of freedom, analogous to moment-based fluid approaches. In so doing, a hybrid approach is obtained that is computationally efficient enough to allow for larger-scale modelling of plasma systems while eliminating a source of difficulty in deriving fluid equations applicable to magnetised plasmas. We connect this system of equations to historical asymptotic models and discuss advantages and disadvantages of this approach, including the extension of this parallel-kinetic-perpendicular moment beyond the typical region of validity of these more traditional asymptotic models. This paper forms the first of a multi-part series on this new model, covering the theory and derivation, alongside demonstration benchmarks of this approach that include shocks and magnetic reconnection.

We augment the ‘quasisisymmetric stellarator repository’ (QUASR) to include vacuum field stellarators with quasihelical symmetry using a globalized optimization workflow. The database now has over 300 000 quasisaxisymmetry and quasihelically symmetric devices along with coil sets, optimized for a variety of aspect ratios, rotational transforms and discrete rotational symmetries. This paper outlines a couple of ways to explore and characterize the data set. We plot devices on a near-axis quasisymmetry (QS) landscape, revealing close correspondence to this predicted landscape. We also use principal component analysis (PCA) to reduce the dimensionality of the data so that it can easily be visualized in two or three dimensions. The PCA also gives a mechanism to compare the new devices here with previously published ones in the literature. We are able to characterize the structure of the data, observe clusters and visualize the progression of devices in these clusters. The topology of the data are governed by the interplay of the design constraints and valleys of the QS objective. These techniques reveal that the data has structure, and that typically one, two or three principal components are sufficient to characterize it. The latest version of QUASR is archived at https://zenodo.org/doi/10.5281/zenodo.10050655 and can be explored online at quasr.flatironinstitute.org.