In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile $q=q_{\boldsymbol {B}}$. A corresponding profile, $q_{\boldsymbol {J}}$, can be defined for the current density field lines. Ampère's law relates any mode of current perturbation $\delta \boldsymbol {J}_{m,n}$ with a mode of magnetic perturbation $\delta \boldsymbol {B}_{m,n}$. It is shown that the knowledge of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ allows us then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\boldsymbol {J}}$ in the flux coordinate is derived. Including this calculation in real-time Grad–Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ would then allow us to investigate the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of $q_{\boldsymbol {B}}$ and $q_{\boldsymbol {J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated with magnetic islands but with non-resonant magnetic modes. It remains to be explored to what extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial.

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, $\beta \gg 1$, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-$\beta$, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (${\sim }5\,\%$) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

We draw attention to an interesting possibility in the design and operation of stellarator fusion reactors, which has hitherto been considered unrealistic under burning-plasma conditions. Thanks to recent advances in stellarator optimisation theory, it appears possible to create a positive (outward-pointing) radial electric field in the plasma core by carefully tailoring the geometry of the magnetic field. This electric field is likely to expel highly charged impurities from the centre of the plasma through neoclassical transport and thus eliminate, or at least mitigate, a long-standing problem in stellarator physics. Further out, the electric field is expected to suddenly change sign from positive to negative, thus creating a region of strongly sheared flow, which could locally suppress turbulent transport and enhance overall energy confinement.

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalized Faraday rotation in pulsars and magnetars.

We present a framework for analysing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device CMFX (centrifugal magnetic fusion experiment), which will employ more sophisticated physics and realistic magnetic field geometries.

In the radiation hydrodynamic simulations used to design inertial confinement fusion (ICF) and pulsed power experiments, nonlinear radiation diffusion tends to dominate CPU time. This raises the interesting question of whether a quantum algorithm can be found for nonlinear radiation diffusion which provides a quantum speedup. Recently, such a quantum algorithm was introduced based on a quantum algorithm for solving systems of nonlinear partial differential equations (PDEs) which provides a quadratic quantum speedup. Here, we apply this quantum PDE (QPDE) algorithm to the problem of a non-equilibrium Marshak wave propagating through a cold, semi-infinite, optically thick target, where the radiation and matter fields are not assumed to be in local thermodynamic equilibrium. The dynamics is governed by a coupled pair of nonlinear PDEs which are solved using the QPDE algorithm, as well as two standard PDE solvers: (i) Python's py-pde solver; and (ii) the KULL ICF simulation code developed at Lawrence-Livermore National Laboratory. We compare the simulation results obtained using the QPDE algorithm and the standard PDE solvers and find excellent agreement.

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.

The propagation of electromagnetic waves in a linearly varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim \delta _a \sqrt {L}$ ($L$ being the medium length scale normalized by the Airy skin depth $\delta _a$), at which point the wave behaviour is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $\eta = \sqrt {L}/f_{\#}$ is large, with $f_{\#}$ being the f-number of the launching aperture. When $\eta \ll 1$, a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling.

Where and under what conditions the transfer of energy between electromagnetic fields and particles takes place in the solar wind remains an open question. We investigate the conditions that promote the growth of kinetic instabilities predicted by linear theory to infer how turbulence and temperature-anisotropy-driven instabilities are interrelated. Using a large dataset from Solar Orbiter, we introduce the radial rate of strain, a novel measure computed from single-spacecraft data, which we interpret as a proxy for the double-adiabatic strain rate. The solar wind exhibits high absolute values of the radial rate of strain at locations with large temperature anisotropy. We measure the kurtosis and skewness of the radial rate of strain from the statistical moments to show that it is non-Gaussian for unstable intervals and increasingly intermittent at smaller scales with a power-law scaling. We conclude that the velocity field fluctuations in the solar wind contribute to the presence of temperature anisotropy sufficient to create potentially unstable conditions.

We perform experiments in the Large Plasma Device at the University of California, Los Angeles, studying how different end-electrode biasing schemes modify the radial potential profile in the machine. We impose biasing profiles of different polarities and gradient signs on a set of five concentric electrodes placed 12 m downstream from the plasma source. We find that imposing concave-down profiles (negative potential radial gradient) on the electrodes creates radial potential profiles halfway up the plasma column that are comparable to those imposed on the electrodes and a few electron temperature in height, regardless of the biasing polarity. On the other hand, imposing concave-up profiles (positive potential radial gradient) leads to non-monotonic radial potential profiles. This observation can be explained by the current drawn through the electrodes and the parallel plasma resistivity, highlighting their important role in controlling the rotation of plasma. Concave-down plasma potential profiles, obtained by drawing electrons on the axis, are predicted to drive azimuthal drift velocities that can approach significant fractions of the ion sound speed in the central region of the plasma column.

Between a plasma and a solid target lies a positively charged sheath of several Debye lengths $\lambda _{D}$ width, typically much smaller than the characteristic length scale $L$ of the main plasma. This scale separation implies that the asymptotic limit $\epsilon = \lambda _{D} / L \rightarrow 0$ is useful to solve for the plasma-sheath system. In this limit, the Bohm criterion must be satisfied at the sheath entrance. A new derivation of the kinetic criterion, admitting a general ion velocity distribution, is presented. It is proven that, for $\epsilon \rightarrow 0$, the distribution of the velocity component normal to the target, $v_x$, and its first derivative must vanish for $|v_x| \rightarrow 0$ at the sheath entrance. These two conditions can be subsumed into a third integral one after it is integrated by parts twice. A subsequent interchange of the limits $\epsilon \rightarrow 0$ and $|v_x| \rightarrow 0$ is invalid, leading to a divergence which underlies the misconception that the criterion gives undue importance to slow ions.

A collisionless shock structure results from the nonlinear interaction between charged particles and electromagnetic fields. Yet, a collisionless shock is globally governed by the mass, momentum and energy conservation requirements. A stable shock structure must ensure that the fluxes of the conserved quantities are constant on average, and, therefore, is determined by this necessity. Here, we study an observed high upstream temperature high Mach number shock and show that the conservation laws cannot be fulfilled unless the shock is spatially inhomogeneous along the shock front and time-dependent.

A fusion neutron source (FNS) based on the gas-dynamic trap (GDT, Budker Institute, Novosibirsk) is considered for confinement of two-species plasma heated by neutral beam injection in a regime where the fast ion distribution function is far from Maxwellian. Kinetic instabilities are expected to develop in this regime, and in this paper we investigate the ion-cyclotron instability evolving in moderate densities of pure hydrogen and mixed deuterium–hydrogen target plasmas. The properties of the studied unstable mode, such as its azimuthal wavenumbers, propagation direction and its being affected by changes in the bulk plasma density and composition, allow us to identify it as the drift cyclotron loss cone (DCLC) instability. This mode scatters fast ions and thereby leads to drops in diamagnetic flux signals and increases longitudinal energy and particle losses, with the average energy of the lost ions estimated to be far above the temperature of warm Maxwellian ions. Our interpretation is that the unstable wave grows due to interaction with the fast ions located near the loss cone in the velocity space and scatters them. Applying the method of suppressing the DCLC instability by filling the loss cone with warm plasma, we have determined the values of plasma density and deuterium percentage that allow us to suppress the DCLC instability in the GDT. These findings justify using mixed bulk plasmas in fusion neutron source operation.

A careful theoretical analysis of the excitation of Alfvén eigenmodes (AEs), such as TAE (toroidicity-induced AE) and RSAE (reversed shear AE), by superalfvenic energetic particles is required for reliable predictions of energetic ion relaxation in present day fusion experiments. This includes the evaluation of different AE damping mechanisms including radiative and continuum dampings which are the focus of this study. A recent comprehensive benchmark of different eigenmode solvers including gyrokinetic, gyrofluid and hybrid magenetohydrodynamics (MHD) has shown that employed models may have deficiencies when addressing some of them (Taimourzadeh et al., Nucl. Fusion, vol. 59, 2019, 066006). In this paper, we are studying the radiative and continuum dampings of RSAEs in details which were missing in hybrid NOVA/NOVA-C calculations to prepare a NOVA-C package with a substantial upgrade. Both dampings require the finite Larmor radius (FLR) corrections to AE mode structures to be accounted for. Accurately calculating different damping rates and understanding their parametric dependencies, we resolve the limitation coming out of the perturbative approach. In particular, here, the radiative damping is included perturbatively, whereas the continuum damping is computed non-perturbatively. Our comparison leads to the conclusion that the non-perturbative treatment of the unstable RSAE modes is needed to find the agreement with the gyrokinetic calculations. We expect that the RSAE mode structure modification plays a dominant role in determining the RSAE stability.

Physics of the plasma rotation driven by biasing in linear traps is analysed for two limiting cases. The first, relevant for traps with low effective viscosity, considers the line-tying effects to be responsible for the drive as well as for the dissipation of the angular momentum. Meanwhile, in long and thin traps with collisional plasma or developed turbulence, the radial transport of the angular momentum becomes its primary loss channel. The momentum flux goes into the scrape-off layer, which makes conditions there partially responsible for the achievable rotation limits.

A first-order model is derived for quasisymmetric stellarators where the vacuum field due to coils is dominant, but plasma-current-induced terms are not negligible and can contribute to magnetic differential equations, with $\beta$ of the order of the ratio induced to vacuum fields. Under these assumptions, it is proven that the aspect ratio must be large and a simple expression can be obtained for the lowest-order vacuum field. The first-order correction, which involves both vacuum and current-driven fields, is governed by a Grad–Shafranov equation and the requirement that flux surfaces exist. These two equations are not always consistent, and so this model is generally overconstrained, but special solutions exist that satisfy both equations simultaneously. One family of such solutions is the set of first-order near-axis solutions. Thus, the first-order near-axis model is a subset of the model presented here. Several other solutions outside the scope of the near-axis model are also found. A case study comparing one such solution to a VMEC-generated solution shows good agreement.

Magnetic reconnection is a basic particle acceleration mechanism in laboratory and astrophysical plasmas. Two-dimensional models have been critical to understanding the onset of reconnection in laboratory experiments, but are fundamentally limited in diagnosing ion acceleration along open magnetic field lines. These shortcomings have opened the way to three-dimensional (3-D) models of torsional reconnection, where localized rotational perturbations to a fan-spine magnetic null point topology have demonstrated bulk particle acceleration along open magnetic field lines. Previous computational studies of the torsional fan reconnection mode using both solar and laboratory parameters demonstrated collimated jet formation and acceleration along the spine axis, wherein the bulk particle final kinetic energy spectra were shown to fall within a relatively narrow range (${\sim }2$ keV). This paper introduces typical laboratory plasma parameters in the torsional spine mode of 3-D reconnection models to diagnose its efficacy in inducing rapid ion acceleration. Using laboratory-scale length helium plasma parameters typical of capacitive discharges (singly ionized helium), we solve for relativistic particle trajectories using solutions to the steady-state, resistive, kinematic magnetohydrodynamic equations in the fan-spine topology. We find that particle acceleration at the reconnection site is highly dependent on the injection radius, and the peak accelerated particles ($\approx$3 keV) are trapped about the magnetic null point. While a jet is formed by ions injected close to the peak fan plane perturbation radius, their final ion kinetic energies are an order of magnitude lower ($\approx$0.3 keV) than the mirrored particles. Analysing the time dependence of their limited representative energy spectra shows the torsional spine mode particles follow an evolution much different than the narrow spectra of the torsional fan mode. These results have implications for diagnostic expectations of future laboratory plasma experiments designed to induce the torsional spine reconnection mode.

Continuum kinetic simulations are increasingly capable of resolving high-dimensional phase space with advances in computing. These capabilities can be more fully explored by using linear kinetic theory to initialize the self-consistent field and phase space perturbations of kinetic instabilities. The phase space perturbation of a kinetic eigenfunction in unmagnetized plasma has a simple analytic form, and in magnetized plasma may be well approximated by truncation of a cyclotron-harmonic expansion. We catalogue the most common use cases with a historical discussion of kinetic eigenfunctions and by conducting nonlinear Vlasov–Poisson and Vlasov–Maxwell simulations of singlemode and multimode two-stream, loss-cone and Weibel instabilities in unmagnetized and magnetized plasmas with one- and two-dimensional geometries. Applications to quasilinear kinetic theory are discussed and applied to the bump-on-tail instability. In order to compute eigenvalues we present novel representations of the dielectric function for ring distributions in magnetized plasmas with power series, hypergeometric and trigonometric integral forms. Eigenfunction phase space fluctuations are visualized for prototypical cases such as the Bernstein modes to build intuition. In addition, phase portraits are presented for the magnetic well associated with nonlinear saturation of the Weibel instability, distinguishing current-density-generating trapping structures from charge-density-generating ones.

The maser instability associated with the loss-cone distribution has been widely invoked to explain the radio bursts observed in the astrophysical plasma environment, such as aurora and corona. In the laboratory plasma of a tokamak, events reminiscent of these radio bursts have also been frequently observed as an electron cyclotron emission (ECE) burst in the microwave range ($\mathrm{\sim }2{f_{\textrm{ce}}}$ near the last closed flux surface) during transient magnetohydrodynamic events. These bursts have a short duration of ~10 μs and display a radiation spectrum corresponding to a radiation temperature ${T_{e,\textrm{rad}}}$ of over $30\ \textrm{keV}$ while the edge thermal electron temperature ${T_e}$ is only in the range of $1\ \textrm{keV}$. Suprathermal electrons can be generated through magnetic reconnection, and a loss-cone distribution can be generated through open stochastic field lines in the magnetic mirror of the near-edge region of a tokamak plasma. Radiation modelling shows that a sharp distribution gradient $\partial f/\partial {v_ \bot } > 0$ at the loss-cone boundary can cause a negative absorption of ECE radiation through the maser instability. The negative absorption then amplifies the radiation so that the microwave intensity is significantly stronger than the thermal value. The significant ${T_{e,\textrm{rad}}}$ from the simulations suggests the potential role of the loss-cone maser instability in generating the ECE burst in a tokamak.

We compare three different approaches to describe a magnetic island in a generic toroidal plasma: (i) perturbative, from the perspective of the equilibrium magnetic field and the related action in a variational principle formulation; (ii) again perturbative, based on the integrability of a system with a single resonant mode and the application of a canonical transformation onto a new island equilibrium system; and (iii) non-perturbative, making use of a full geometric description of the island considered as a stand-alone plasma domain. For the three approaches, we characterize some observables and discuss the respective limits.