Protoplanetary discs are made of gas and dust orbiting a young star. They are also the birth place of planetary systems, which motivates a large amount of observational and theoretical research. In these lecture notes, I present a review of the magnetic mechanisms applied to the outer regions ($R\gtrsim 1\ \mathrm {AU}$) of these discs, which are the planet-formation regions. In contrast to usual astrophysical plasmas, the gas in these regions is noticeably cold ($T < 300\ \mathrm {K}$) and dense, which implies a very low ionisation fraction close to the disc midplane. In these notes, I deliberately ignore the innermost $(R\sim 0.1\ \mathrm {AU})$ region, which is influenced by the star–disc interaction and various radiative effects. I start by presenting a short overview of the observational evidence for the dynamics of these objects. I then introduce the methods and approximations used to model these plasmas, including non-ideal magnetohydrodynamics, and the uncertainties associated with this approach. In this framework, I explain how the global dynamics of these discs is modelled, and I present a stability analysis of this plasma in the local approximation, introducing the non-ideal magneto-rotational instability. Following this mostly analytical part, I discuss numerical models that have been used to describe the saturation mechanisms of this instability, and the formation of large-scale structures by various saturation mechanisms. Finally, I show that local numerical models are insufficient because magnetised winds are also emitted from the surface of these objects. After a short introduction on wind physics, I present global models of protoplanetary discs, including both a large-scale wind and the non-ideal dynamics of the disc.

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.

The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov–Maxwell simulations of collisionless plasmas, Hall magnetohydrodynamics and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer. This approach provides information on the structure of energy fluxes, under the assumption that the turbulent cascade transfers most of the energy that is then dissipated at small scales by various kinetic processes in these kinds of plasmas.

Accelerated particles are ubiquitous in the Cosmos and play a fundamental role in many processes governing the evolution of the Universe at all scales, from the sub-AU scale relevant for the formation and evolution of stars and planets to the Mpc scale involved in Galaxy assembly. We reveal the presence of energetic particles in many classes of astrophysical sources thanks to their production of non-thermal radiation, and we detect them directly at the Earth as cosmic rays. In the last two decades both direct and indirect observations have provided us a wealth of new, high-quality data about cosmic rays and their interactions both in sources and during propagation, in the Galaxy and in the Solar System. Some of the new data have confirmed existing theories about particle acceleration and propagation and their interplay with the environment in which they occur. Some others have brought about interesting surprises, whose interpretation is not straightforward within the standard framework and may require a change of paradigm in terms of our ideas about the origin of cosmic rays of different species or in different energy ranges. In this article, we focus on cosmic rays of galactic origin, namely with energies below a few petaelectronvolts, where a steepening is observed in the spectrum of energetic particles detected at the Earth. We review the recent observational findings and the current status of the theory about the origin and propagation of galactic cosmic rays.

The first detection of a binary neutron star merger through gravitational waves and photons marked the dawn of multimessenger astronomy with gravitational waves, and it greatly increased our insight in different fields of astrophysics and fundamental physics. However, many open questions on the physical process involved in a compact binary merger still remain and many of these processes concern plasma physics. With the second generation of gravitational wave interferometers approaching their design sensitivity, the new generation under design study and new X-ray detectors under development, the high energy universe will become more and more a unique laboratory for our understanding of plasma in extreme conditions. In this review, we discuss the main electromagnetic signals expected to follow the merger of two compact objects highlighting the main physical processes involved and some of the most important open problems in the field.

Charged particle motion in axisymmetric toroidal magnetic fields is analysed within the context of the canonical Hamiltonian guiding centre theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic field line is introduced and an analytical transformation to action-angle variables is obtained, under a zero drift width approximation. The latter is used to provide compact formulas for the orbital spectrum of the drift motion, namely the bounce/transit frequencies as well as the bounce/transit averaged toroidal precession and gyration frequencies. These formulas are shown to have a remarkable agreement with numerically calculated full drift width frequencies and significant differences from standard analytical formulas based on a pendulum-like Hamiltonian description. The analytical knowledge of the orbital spectrum is crucial for the formulation of particle resonance conditions with symmetry-breaking perturbations and the study of the resulting particle, energy and momentum transport.

Synchrotron radiation images from runaway electrons (REs) in an ASDEX Upgrade discharge disrupted by argon injection are analysed using the synchrotron diagnostic tool Soft and coupled fluid-kinetic simulations. We show that the evolution of the runaway distribution is well described by an initial hot-tail seed population, which is accelerated to energies between 25–50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. We find that, although the avalanche component carries the vast majority of the current, it is the high-energy seed remnant that dominates synchrotron emission. With insights from the fluid-kinetic simulations, an analytic model for the evolution of the runaway seed component is developed and used to reconstruct the radial density profile of the RE beam. The analysis shows that the observed change of the synchrotron pattern from circular to crescent shape is caused by a rapid redistribution of the radial profile of the runaway density.

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

This work addresses one-dimensional evolution of a collisionless plasma next to a solid surface that is immersed into the plasma instantaneously. In particular, we consider how the self-similar rarefaction wave (Allen & Andrews, J. Plasma Phys., vol. 4, 1970, pp. 187–194) establishes dynamically and how the electron reflection from the surface modifies the structure of the rarefaction wave and the Debye sheath. We demonstrate that a sufficiently strong reflection eliminates the Debye sheath and changes the wall potential and the plasma flow parameters significantly. The paper presents numerical results that illustrate the developed analytical theory.

We present experimental data providing evidence for the formation of transient (${\sim }20\ \mathrm {\mu }\textrm {s}$) plasmas that are simultaneously weakly magnetized (i.e. Hall magnetization parameter $\omega \tau > 1$) and dominated by thermal pressure (i.e. ratio of thermal-to-magnetic pressure $\beta > 1$). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $\lambda _{\textrm {gun}}=\mu _0 I_{\textrm {gun}}/\psi _{\textrm {gun}}$ of gun current $I_{\textrm {gun}}$ to applied magnetic flux $\psi _{\textrm {gun}}$ is an experimental knob for exploring the parameter space of $\beta$ and $\omega \tau$. These experiments were conducted on the Big Red Ball at the Wisconsin Plasma Physics Laboratory. The transient formation of such plasmas can potentially open up new regimes for the laboratory study of weakly collisional, magnetized, high-$\beta$ plasma physics; processes relevant to astrophysical objects and phenomena; and novel magnetized plasma targets for magneto-inertial fusion.

In this work we study the undesired effects of electron density fluctuations (in the form of blob structures which may exist in the edge region of tokamak plasmas) to the electron-cyclotron wave propagation and current drive in connection to the efficiency of neoclassical tearing mode stabilization. Our model involves the evaluation of the driven current in the presence of density perturbations, by using a combination of a wave solver based on the transfer matrix and electromagnetic homogenization methods for the propagation part prior to and inside the region of these structures (where standard asymptotic propagation methods may not be valid due to the short-wavelength limit breakdown), with a ray tracing code including island geometry effects and current drive computation for the propagation past the perturbed region. The computed driven current is input into the modified Rutherford equation in order to estimate the consequences of the wave deformation (driven by the density fluctuations) to the mode stabilization.

In this article, the electron trapping and acceleration in the wake field driven by an ultrarelativistic hollow electron beam is studied. When the hollow driver injects into plasma, there is a doughnut-shaped electron bubble formed because of the existence of a special ‘backflow’ beam in the centre of the electron bubble. At the same time, there is a transverse convergence of the hollow driver, which leads to the weakening of the backflow beam. This results in a local electron density transition at the rear of the bubble. During this process, there is an expansion of the longitudinal electron bubble size, and a bunch of background electrons is trapped by the wake field at the rear of the bubble. The tracks for the trapped electrons show that there are two sources: one is from the bubble sheath and the other is from the unique backflow beam. In the particle-in-cell simulation where the driving beam has initial energy of $1.0$ GeV per particle, the trapped beam can be accelerated to energy of more than $1.5$ GeV per particle and the corresponding transformer ratio is $1.5$. With the increase of driving beam energy up to $40.0$ GeV, a transformer ratio of $1.4$ still can be achieved. By adjusting the hollow beam density, it is possible to control the trapped beam charge value and beam quality, such as its energy spread and transverse emittance.

Thermal effects on the properties of four electromagnetic waves propagating in the pulsar magnetosphere are analysed. It is shown that thermal effects change only quantitatively the dispersion properties of superluminal ordinary O-mode freely escaping the pulsar magnetosphere; whereas properties of the extraordinary X-mode remain unchanged. The research shows that for two subluminal waves propagating along magnetic field lines thermal effects result in essential absorption. However, this attenuation occurs at considerable distances from the neutron star, and there is no doubt of their existence.

The behaviour of a strongly magnetised collisional electron–positron plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron–positron plasma experiments currently being developed, which will typically have very low densities and be confined in very strong magnetic fields. The constraint of strong magnetisation adds an additional complication in that long-range Coulomb collisions, which are usually negligible, must now be considered. A rigorous collision operator for these long-range collisions has never been written down. Nevertheless, we show that the collisional scattering can be accounted for without knowing the explicit form of this collision operator. The rate of radiation emission is calculated and it is found that the loss of energy from the plasma is proportional to the parallel collision frequency multiplied by a factor that only depends logarithmically on plasma parameters. That is, this is a self-accelerating process, meaning that the bulk of the energy will be lost in a few collision times. We show that in a simple case, that of straight field-line geometry, there are no unstable drift waves in such plasmas, despite being far from Maxwellian.

The behaviour of a collisional plasma that is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various time scales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collision frequency multiplied by a factor that only depends logarithmically on plasma parameters.

A one-dimensional (1-D) model for thinning of the Earth's plasma sheet (Chao et al., Planet. Space Sci., vol. 25, 1977, p. 703) according to the current disruption (CD) model of auroral breakup is extended to two dimensions. A rarefaction wave, which is a signature component of the CD model, is generated with an initial disturbance. In the 1-D gas model, the rarefaction wave propagates tailward at sound velocity and is assumed to cause thinning. Extending to a two-dimensional (2-D) gas model of a simplified plasma sheet configuration, the rarefaction wave is weakened, and the thinning ceases to propagate. Extending further to a 2-D plasma model by adding magnetic field into the lobes, the rarefaction wave is quickly lost in the plasma sheet recompression, but the plasma sheet thinning is still present. It propagates at a slower velocity than a 1-D model suggests, behind a wave train of pulses of increased pressure generated by the thinning process itself. This shows that the dynamics of plasma sheet thinning may be dominated by sheet–lobe interactions that are absent from the 1-D model and may not support the behaviour assumed by the CD model.

A warm degenerate plasma (containing ultra-relativistically or non-relativistically warm degenerate inertia-less electron species, non-relativistically warm degenerate inertial light nucleus species and stationary heavy nucleus species) is considered. The basic features of planar and non-planar solitary structures associated with the degenerate pressure-driven nucleus-acoustic waves propagating in such a warm degenerate plasma system are investigated. The reductive perturbation method, which is valid for small- but finite-amplitude solitary waves, is used. It is found that the effects of non-planar cylindrical and spherical geometries, non- and ultra-relativistically degenerate electron species and the temperature of degenerate electron species significantly modify the basic features (i.e. speed, amplitude and width) of the solitary potential structures associated with degenerate pressure-driven nucleus-acoustic waves. The warm degenerate plasma model under consideration is applicable not only to all cold white dwarfs, but also to many hot white dwarfs, such as DQ white dwarfs, white dwarf H1504+65, white dwarf PG 0948+534, etc.

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.

We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The solutions are also ‘nearly’ quasisymmetric. The primary idea is, given a desired quasisymmetry direction $\xi$, to change the smooth structure on space so that the vector field $\xi$ is Killing for the new metric and construct $\xi$–symmetric solutions of the magnetohydrostatic equations on that background by solving a generalized Grad–Shafranov equation. If $\xi$ is close to a symmetry of Euclidean space, then these are solutions on flat space up to a small forcing.

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.