Spatial profiles of impurity emission measurements in the extreme ultraviolet (EUV) spectroscopic range in radiofrequency (RF)-heated discharges are combined with one-dimensional and three-dimensional transport simulations to study the effects of resonant magnetic perturbations (RMPs) on core impurity accumulation at EAST. The amount of impurity line emission mitigation by RMPs appears to be correlated with the ion Z for lithium, carbon, iron and tungsten monitored, i.e. stronger suppression of accumulation for heavier ions. The targeted effect on the most detrimental high-Z impurities suggests a possible advantage using RMPs for impurity control. Profiles of transport coefficients are calculated with the STRAHL one-dimensional impurity transport code, keeping $\nu /D$ fixed and using the measured spatial profiles of $\textrm{F}{\textrm{e}^{20 + }}$, $\textrm{F}{\textrm{e}^{21 + }}$ and $\textrm{F}{\textrm{e}^{22 + }}$ to disentangle the transport coefficients. The iron diffusion coefficient ${D_{\textrm{Fe}}}$ increases from $1.0- 2.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ to $1.5- 3.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ from the core region to the edge region $(\rho \gt 0.5)$ after the onset of RMPs. Meanwhile, an inward pinch of iron convective velocity ${\nu _{\textrm{Fe}}}$ decreases in magnitude in the inner core region and increases significantly in the outer confined region, simultaneously contributing to preserving centrally peaked $\textrm{Fe}$ profiles and exhausting the impurities. The ${D_{\textrm{Fe}}}$ and ${\nu _{\textrm{Fe}}}$ variations lead to reduced impurity contents in the plasma. The three-dimensional edge impurity transport code EMC3-EIRENE was also applied for a case of RMP-mitigated high-Z accumulation at EAST and compared to that of low-Z carbon. The exhaust of ${\textrm{C}^{6 + }}$ toward the scrape-off layer accompanying an overall suppression of heavier ${\textrm{W}^{30 + }}$ is observed when using RMPs.

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$, the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$, where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al., J. Plasma Phys., vol. 85, issue 2, 2019; Paul et al., J. Plasma Phys., vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space (${\sim }50\text {--}500$) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks.

Fluid models that approximate kinetic effects have received attention recently in the modelling of large-scale plasmas such as planetary magnetospheres. In three-dimensional reconnection, both reconnection itself and current sheet instabilities need to be represented appropriately. We show that a heat flux closure based on pressure gradients enables a 10-moment fluid model to capture key properties of the lower-hybrid drift instability (LHDI) within a reconnection simulation. Characteristics of the instability are examined with kinetic and fluid continuum models, and its role in the three-dimensional reconnection simulation is analysed. The saturation level of the electromagnetic LHDI is higher than expected, which leads to strong kinking of the current sheet. Therefore, the magnitude of the initial perturbation has significant impact on the resulting turbulence.

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$, the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $. The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

We use three-dimensional (3-D) fully kinetic particle-in-cell simulations to study the occurrence of magnetic reconnection in a simulation of decaying turbulence created by anisotropic counter-propagating low-frequency Alfvén waves consistent with critical-balance theory. We observe the formation of small-scale current-density structures such as current filaments and current sheets as well as the formation of magnetic flux ropes as part of the turbulent cascade. The large magnetic structures present in the simulation domain retain the initial anisotropy while the small-scale structures produced by the turbulent cascade are less anisotropic. To quantify the occurrence of reconnection in our simulation domain, we develop a new set of indicators based on intensity thresholds to identify reconnection events in which both ions and electrons are heated and accelerated in 3-D particle-in-cell simulations. According to the application of these indicators, we identify the occurrence of reconnection events in the simulation domain and analyse one of these events in detail. The event is related to the reconnection of two flux ropes, and the associated ion and electron exhausts exhibit a complex 3-D structure. We study the profiles of plasma and magnetic-field fluctuations recorded along artificial-spacecraft trajectories passing near and through the reconnection region. Our results suggest the presence of particle heating and acceleration related to small-scale reconnection events within magnetic flux ropes produced by the anisotropic Alfvénic turbulent cascade in the solar wind. These events are related to current structures of the order of a few ion inertial lengths in size.

Rayleigh–Taylor (RT) and buoyancy-driven (BD) instabilities are driven by gravity in a fluid system with inhomogeneous density. The paper investigates these instabilities for a strongly coupled dusty plasma medium. This medium has been represented here in the framework of the generalized hydrodynamics (GHD) fluid model which treats it as a viscoelastic medium. The incompressible limit of the GHD model is considered here. The RT instability is explored both for gradual and sharp density gradients stratified against gravity. The BD instability is discussed by studying the evolution of a rising bubble (a localized low-density region) and a falling droplet (a localized high-density region) in the presence of gravity. Since both the rising bubble and falling droplet have symmetry in spatial distribution, we observe that a falling droplet process is equivalent to a rising bubble. We also find that both the gravity-driven instabilities get suppressed with increasing coupling strength of the medium. These observations have been illustrated analytically as well as by carrying out two-dimensional nonlinear simulations. Part 2 of this paper is planned to extend the present study of the individual evolution of a bubble and a droplet to their combined evolution in order to understand the interaction between them.

Magnetic wave perturbations are observed in the solar wind and in the vicinity of Earth's bow shock. For such environments, recent work on magnetic pumping with electrons trapped in the magnetic perturbations has demonstrated the possibility of efficient energization of superthermal electrons. Here we also analyse the energization of such energetic electrons for which the transit time through the system is short compared with time scales associated with the magnetic field evolution. In particular, considering an idealized magnetic configuration we show how trapping/detrapping of energetic magnetized electrons can cause effective parallel velocity ($v_{\parallel }$-) diffusion. This parallel diffusion, combined with naturally occurring mechanisms known to cause pitch angle scattering, such as whistler waves, produces enhanced heating rates for magnetic pumping. We find that at low pitch angle scattering rates, the combined mechanism enhances the heating beyond the predictions of the recent theory for magnetic pumping with trapped electrons.

The axisymmetric visco-resistive magnetohydrodynamic steady states allowing flows (i.e. non-vanishing velocity fields) are computed for a toroidal JET-like geometry. It is shown that a spatially inhomogeneous heating of moderate magnitude leads to an increase of typical toroidal speeds with respect to the situation with uniform temperature with identical mean Hartmann numbers. A symmetry argument is introduced to capture the symmetry breaking, induced by the temperature gradient, that produces a net toroidal plasma flow.

A growing body of evidence suggests that the solar wind is powered to a large extent by an Alfvén-wave (AW) energy flux. AWs energize the solar wind via two mechanisms: heating and work. We use high-resolution direct numerical simulations of reflection-driven AW turbulence (RDAWT) in a fast-solar-wind stream emanating from a coronal hole to investigate both mechanisms. In particular, we compute the fraction of the AW power at the coronal base ($P_\textrm {AWb}$) that is transferred to solar-wind particles via heating between the coronal base and heliocentric distance $r$, which we denote by $\chi _{H}(r)$, and the fraction that is transferred via work, which we denote by $\chi _{W}(r)$. We find that $\chi _{W}(r_{A})$ ranges from 0.15 to 0.3, where $r_{A}$ is the Alfvén critical point. This value is small compared with one because the Alfvén speed $v_{A}$ exceeds the outflow velocity $U$ at $r < r_{A}$, so the AWs race through the plasma without doing much work. At $r>r_{A}$, where $v_{A} < U$, the AWs are in an approximate sense ‘stuck to the plasma’, which helps them do pressure work as the plasma expands. However, much of the AW power has dissipated by the time the AWs reach $r=r_{A}$, so the total rate at which AWs do work on the plasma at $r>r_{A}$ is a modest fraction of $P_\textrm {AWb}$. We find that heating is more effective than work at $r < r_{A}$, with $\chi _{H}(r_{A})$ ranging from 0.5 to 0.7. The reason that $\chi _{H} \geq 0.5$ in our simulations is that an appreciable fraction of the local AW power dissipates within each Alfvén-speed scale height in RDAWT, and there are a few Alfvén-speed scale heights between the coronal base and $r_{A}$. A given amount of heating produces more magnetic moment in regions of weaker magnetic field. Thus, paradoxically, the average proton magnetic moment increases robustly with increasing $r$ at $r>r_{A}$, even though the total rate at which AW energy is transferred to particles at $r>r_{A}$ is a small fraction of $P_\textrm {AWb}$.

Ideally, binary-collision algorithms conserve kinetic momentum and energy. In practice, the finite size of collision cells and the finite difference in the particle locations affect the conservation properties. In the present work, we investigate numerically how the accuracy of these algorithms is affected when the size of collision cells is large compared with gradient scale length of the background plasma, a parameter essential in full-$f$ fusion plasma simulations. Additionally, we discuss implications for the conserved quantities in drift-kinetic formulations when fluctuating magnetic and electric fields are present: we suggest how the accuracy of the algorithms could potentially be improved with minor modifications.

Using mixed second-order structure functions, a compact exact law is derived for isothermal compressible Hall magnetohydrodynamic turbulence with the assumptions of statistical homogeneity, time stationarity and infinite kinetic/magnetic Reynolds numbers. The resulting law is written as the sum of a Yaglom-like flux term, with an overall expression strongly reminiscent of the incompressible law, and a pure compressible source. Being mainly a function of the increments, the compact law is Galilean invariant but is dependent on the background magnetic field if one is present. Only the magnetohydrodynamic source term requires multi-spacecraft data to be estimated whereas the other components, which include those introduced by the Hall term, can be fully computed with single-spacecraft data using the Taylor hypothesis. These properties make this compact law more appropriate for analysing both numerical simulations and in situ data gathered in space plasmas, in particular when only single-spacecraft data are available.

The interplay between toroidal drift-wave turbulence and tokamak profiles is investigated using a wave-kinetic description. The coupled system is used to investigate the interplay between marginally stable toroidal drift-wave turbulence and geodesic acoustic modes (GAMs). The coupled system is found to be unstable. Notably, the most unstable mode corresponds to the resonance between the turbulent wave radial group velocity and the GAM phase velocity. For a low-field-side ballooned drift-wave growth, a background flow shear breaks the symmetry between inwards- and outwards-travelling instabilities. Although this turbulence–GAM coupling may not be the primary driver for avalanches in standard core ion temperature gradient simulations, this mechanism is generic and displays many of the expected features, and should be of interest in several other regimes, which include towards the edge or in the presence of energetic particles.

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion, vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al., Nucl. Fusion, vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion, vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al., Nucl. Fusion, vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids, vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas, vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

One of the limitations in studying dusty plasmas is that many of the important properties of the dust (like the charge) are directly coupled to the surrounding plasma conditions rather than being determined independently. The application of high-intensity ultraviolet (UV) sources to generate discharging photoelectric currents may provide an avenue for developing methods of controlling dust charge. Careful selection of the parameters of the UV source and dust material may even allow for this to be accomplished with minimal perturbation of the background plasma. The Auburn Magnetized Plasma Research Laboratory (MPRL) has developed a ‘proof-of-concept’ experiment for this controlled photo-discharging of dust; a high-intensity, near-UV source was used to produce large changes in the equilibrium positions of lanthanum hexaboride ($\textrm {LaB}_6$) particles suspended in an argon DC glow discharge with negligible changes in the potential, density and temperature profiles of the background plasma. The shifts in equilibrium position of the dust are consistent with a reduction in dust charge. Video analysis is used to quantify the changes in position, velocity and acceleration of a test particle under the influence of the UV and Langmuir probes are used to measure the effects on the plasma.

Using particle-in-cell numerical simulations with electron–positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length $\lambda _0$ in relation to the system size $L$ of the two-dimensional ‘Arnold–Beltrami–Childress’ (ABC) magnetic field configurations. Topological constraints on the distribution of magnetic helicity in two-dimensional systems, identified earlier in relativistic force-free simulations, that prevent the high-$(L/\lambda _0)$ configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about $\epsilon _{\textrm {diss}} \simeq 60\,\%$. We find that the peak growth time scale of the electric energy $\tau _{E,{\textrm {peak}}}$ scales with the characteristic value of initial Alfvén velocity $\beta _{A,{\textrm {ini}}}$ like $\tau _{E,\textrm {peak}} \propto (\lambda _0/L)\beta _{A,{\textrm {ini}}}^{-3}$. The particle energy change is decomposed into non-thermal and thermal parts, with non-thermal energy gain dominant only for high initial magnetisation. The most robust description of the non-thermal high-energy part of the particle distribution is that the power-law index is a linear function of the initial magnetic energy fraction.

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\varDelta _d$. Electron inertia ensures $\varDelta _d\gtrsim c/\omega _{pe}$. The lines that lie within a magnetic flux tube of radius $\varDelta _d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$ vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega _{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.