The theory of terahertz (THz) wave emission at the oblique incidence of a focused s-polarized laser pulse on the boundary of a rarefied plasma is developed. The angular, spectral and energy characteristics of the THz signal as a function of the focal spot size and the incidence angle of laser radiation, as well as the plasma density, are investigated. It is shown that the THz radiation energy increases with a decrease in the laser pulse focal spot and has the maximum value when the tightly focused laser pulse is incident at the angle of total reflection on the plasma boundary.

Simulating plasmas in the Hall-magnetohydrodynamics (Hall-MHD) regime represents a valuable approach for the investigation of complex nonlinear dynamics developing in astrophysical frameworks and fusion machines. The Hall electric field is computationally very challenging as it involves the integration of an additional term, proportional to $\boldsymbol {\nabla } \times ((\boldsymbol {\nabla }\times \boldsymbol {B})\times \boldsymbol {B})$, in Faraday's induction law. The latter feeds back on the magnetic field $B$ at small scales (between the ion and electron inertial scales), requiring very high resolutions in both space and time to properly describe its dynamics. The computational advantage provided by the kinetic lattice Boltzmann (LB) approach is exploited here to develop a new code, the fast lattice-Boltzmann algorithm for MHD experiments (flame). The flame code integrates the plasma dynamics in lattice units coupling two kinetic schemes, one for the fluid protons (including the Lorentz force), the other to solve the induction equation describing the evolution of the magnetic field. Here, the newly developed algorithm is tested against an analytical wave-solution of the dissipative Hall-MHD equations, pointing out its stability and second-order convergence, over a wide range of the control parameters. Spectral properties of the simulated plasma are finally compared with those obtained from numerical solutions from the well-established pseudo-spectral code ghost. Furthermore, the LB simulations we present, varying the Hall parameter, highlight the transition from the MHD to the Hall-MHD regime, in excellent agreement with the magnetic field spectra measured in the solar wind.

The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in the present paper. It suggests that the reductive perturbation method (RPM) is valid if the amplitude of the CKdV solitary wave is small enough. However, for the KdV solitary wave, RPM is valid not only if the amplitude of the KdV solitary wave is small enough, but also if the nonlinear coefficient of the KdV equation is not tending to zero.

We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648) and Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) as benchmarks. We report that the GM approach converges more rapidly in capturing the nonlinear dynamics of the CBC than the continuum GENE code (Jenko et al., Phys. Plasmas, vol. 7, no. 5, 2000, pp. 1904–1910) when comparing the number of points representing the velocity space. Increasing the velocity dissipation improves the convergence properties of the GM approach, albeit yielding a slightly larger saturated heat flux. By varying the temperature equilibrium gradient, we show that the GM approach successfully reproduces the Dimits shift (Dimits et al., Phys. Plasmas, vol. 7, no. 3, 2000, pp. 969–983) and effectively captures its width, which is in contrast to the gyrofluid framework. In the collisional regime, the convergence properties of the GM approach improve and a good agreement with previous global particle-in-cell results on transport is obtained (Lin et al., Phys. Rev. Lett., vol. 83, no. 18, 1999, pp. 3645–3648). Finally, we report that the choice of collision model has a minimal impact both on the ion temperature gradient growth rate and on the nonlinear saturated heat flux, at tokamak-relevant collisionality.

Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB) formation in a number of tokamak devices. A simple model incorporating the fishbone dynamics and ion pressure gradient evolution is proposed in order to investigate the key physics parameters assisting the triggering of ITB. The time evolution of fishbone is described by the well-known predator–prey model. For each burst cycle, the energetic particles (EPs) resonantly interact with fishbone and are radially expelled from inner region leading to a radial current. A compensating bulk plasma return current and, hence, poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidal flow damping rate. When the shear of the poloidal flow exceeds a critical value, the turbulent fluctuations are suppressed and the bulk ion pressure gradient transits to the high-confinement state. It is shown that this process is only sensitive to the deposition rate of the trapped EPs within the $q=1$ surface, but not sensitive to other parameters. A quantitative formula for the shearing rate of poloidal flow induced by fishbone bursts is derived and verified numerically.

Plasma turbulence plays a critical role in the transport of energy from large-scale magnetic fields and plasma flows to small scales, where the dissipated turbulent energy ultimately leads to heating of the plasma species. A major goal of the broader heliophysics community is to identify the physical mechanisms responsible for the dissipation of the turbulence and to quantify the consequent rate of plasma heating. One of the mechanisms proposed to damp turbulent fluctuations in weakly collisional space and astrophysical plasmas is electron Landau damping. The velocity-space signature of electron energization by Landau damping can be identified using the recently developed field–particle correlation technique. Here, we perform a suite of gyrokinetic turbulence simulations with ion plasma beta values $\beta _i = 0.01, 0.1, 1$ and $10$ and use the field–particle correlation technique to characterize the features of the velocity-space signatures of electron Landau damping in turbulent plasma conditions consistent with those observed in the solar wind and planetary magnetospheres. We identify the key features of the velocity-space signatures of electron Landau damping as a function of varying plasma $\beta _i$ to provide a critical framework for interpreting the results of field–particle correlation analysis of in situ spacecraft observations of plasma turbulence.

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in the presence of resonances due to both parallel streaming and constant magnetic drifts. These integrals are written in terms of the well-known plasma dispersion function (Faddeeva & Terent'ev, Tables of Values of the Function $w(z)=\exp (-z^2)(1+2i/\sqrt {\pi }\int _0^z \exp (t^2) \,\mathrm {d} t)$ for Complex Argument, 1954. Gostekhizdat. English translation: Pergamon Press, 1961; Fried & Conte, The Plasma Dispersion Function, 1961. Academic Press), rendering the subsequent expressions simpler to treat analytically and more efficient to compute numerically. We demonstrate that our results converge to the well-known ones in the straight-magnetic-field and two-dimensional limits, and show good agreement with the numerical solver by Gürcan (J. Comput. Phys., vol. 269, 2014, p. 156). By way of example, we calculate the exact dispersion relation for a simple electrostatic, ion-temperature-gradient-driven instability, and compare it with approximate kinetic and fluid models.

Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time.

The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite–Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a two-dimensional Z-pinch is considered within a flux-tube configuration. In the collisionless regime, our gyromoment approach shows very good agreement with nonlinear simulations carried out with the continuum gyrokinetic code GENE, even with fewer gyromoments than required for the convergence of the linear growth rate. By using advanced linear collision operators, the role of collisions in setting the level of turbulent transport is then analysed. The choice of collision operator model is shown to have a crucial impact when turbulence is quenched by the presence of zonal flows. The convergence properties of the gyromoment approach improve when collisions are included.

A full-F isothermal gyro-fluid model and code (which is based on the full distribution function F compared to only small fluctuations) is extended to handle self-consistent coupling of multiple quasi-neutral ion species via the polarisation equation in the long wavelength approximation. The numerical model is used to determine two-dimensional interchange driven ‘blob’ transport in a plasma with intrinsic impurity content for a range of impurity parameters. With the same model, the self-consistent advective interaction of a main plasma species blob with a non-trace impurity cloud is studied. For homogeneous impurity distributions an increased effective mass reduces blob transport, whereas it is found that localised impurity clouds can lead either to acceleration or slowing down of blob propagation depending on the alignment of the impurity density gradient during the acceleration phase of the main ion species blob.

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

Angular momentum coupling between a rotating magnetized plasma and torsional Alfvén waves carrying orbital angular momentum (OAM) is examined. It is demonstrated not only that rotation is the source of Fresnel–Faraday rotation – or orbital Faraday rotation effects – for OAM-carrying Alfvén waves, but also that angular momentum from an OAM-carrying Alfvén wave can be transferred to a rotating plasma through the inverse process. For the direct process, the transverse structure angular rotation frequency is derived by considering the dispersion relation for modes with opposite OAM content. For the inverse process, the torque exerted on the plasma is derived as a function of wave and plasma parameters.

Significant progress has been made in designing magnetic fields that provide excellent confinement of the guiding-centre trajectories of alpha particles using quasisymmetry (QS). Given the reduction in this transport channel, we assess the impact of resonant Alfvén eigenmodes (AEs) on the guiding-centre motion. The AE amplitudes are chosen to be consistent with experimental measurements and large-scale simulations. We evaluate the drift resonance condition, phase-space island width and island overlap criterion for quasisymmetric configurations. Kinetic Poincaré plots elucidate features of the transport, including stiff transport above a critical perturbation amplitude. Our analysis highlights key departures from the AE-driven transport in tokamaks, such as the avoidance of phase-space island overlap in quasihelical configurations and the enhanced transport due to wide phase-space islands in low magnetic shear configurations. In configurations that are closer to QS, with QS deviations $\delta B/B_0 \lesssim 10^{-3}$, the transport is primarily driven by the AE, while configurations that are further from QS, $\delta B/B_0 \sim 10^{-2}$, experience significant transport due to the QS-breaking fields in addition to the AE.

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$, and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Machine learning techniques are used to construct models capable of inferring plasma state variables from non-emissive (LP) and emissive (EP) cylindrical Langmuir probes under conditions in which standard analytic theories are not applicable. Synthetic data sets, consisting of plasma parameters and probe characteristics computed kinetically in the orbital motion theory framework, are used to train and test regression models to infer electron densities, temperatures, and plasma potentials. Model skill metrics are introduced to determine uncertainty margins on inferred parameters, when models are applied to test sets not involved in the model optimization process. The different scalings and transformations required to obtain optimal accuracy are described in each case considered for both LPs and EPs. Excellent inferences are made for all three parameters considered from LP characteristics, but owing to the strong dependence on the plasma potential, and weak dependences on electron temperature and density with EPs, only plasma potential inferences are reported with acceptable accuracy for this type of probe. Our findings demonstrate that the combination of kinetic simulations and machine learning techniques is a promising and practical way to infer plasma parameters efficiently from cylindrical probes, under conditions beyond, and more general than those under which commonly used analytic approximations are valid.

We present a numerical method to solve the Vlasov–Maxwell equations for spin-1/2 particles, in a semiclassical approximation where the orbital motion is treated classically while the spin variable is fully quantum. Unlike the spinless case, the phase-space distribution function is a $2\times 2$ matrix, which can also be represented, in the Pauli basis, as one scalar function $f_0$ and one three-component vector function $\boldsymbol f$. The relationship between this ‘vectorial’ representation and the fully scalar representation on an extended phase space first proposed by Brodin et al. (Phys. Rev. Lett., vol. 101, 2008, p. 245002) is analysed in detail. By means of suitable approximations and symmetries, the vectorial spin-Vlasov–Maxwell model can be reduced to two-dimensions in the phase space, which is amenable to numerical solutions using a high-order grid-based Eulerian method. The vectorial model enjoys a Poisson structure that paves the way to accurate Hamiltonian split-time integrators. As an example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, and compare the results with those obtained earlier with the scalar spin-Vlasov–Maxwell model and a particle-in-cell code.

In typical heliospheric collisionless shocks most of the mass, momentum and energy are carried by ions. Therefore, the shock structure should be most affected by ions. With the increase of the Mach number, ion reflection becomes more and more important, and reflected ions participate in shaping the shock profile. Ion reflection at the collisionless shock is a non-local process: the reflected–transmitted ions re-enter the shock front far from the reflection point. The direction and the magnitude of this shift depend on the shock angle. The distance between the reflection point and the re-entry point is of the order of the upstream ion convective gyroradius and exceeds the shock width. The non-locality of ion reflection may have implications for shock rippling since reflected ions may carry perturbations along the shock front.