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In this work, we demonstrate a method for constructing the Solov'ev equilibrium with any given 2D shape surrounded by a vacuum region using external poloidal field coils, based on the method previously developed by T. Xu and R. Fitzpatrick [Nuclear Fusion, 59, 064002 (2019)]. The computational domain consists of two parts: the plasma region, where the solution is the same as the Solov'ev solution, and the vacuum region, where the magnetic field generated by external coils as well as plasma current is determined using the Green function method through a matching condition near the separatrix. However, the method is not limited to the Solov'ev equilibrium in particular. The accuracy, efficiency, and robustness of such a scheme suggest that this method may be applied to the 2D shaping of a tokamak plasma with a vacuum region using external coils in general.

Nonaxisymmetric magnetic fields such as the intrinsic error field and the externally applied resonant magnetic perturbation (RMP) in a tokamak are known to influence the plasma momentum transport and flow evolution through plasma response, which itself strongly depends on the plasma flow as well. The nonlinear interaction between plasma response and flow has been previously modeled in the conventional error field theory with the “no-slip” condition, which has been recently extended to allow the “free-slip” condition. In this work, we further target this specific process and numerically simulate the nonlinear plasma response and flow evolution in the presence of a single-helicity RMP in a circular-shaped model tokamak configuration, based on the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel (to k) flow or “slip frequency” profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Here, k is the wave vector of the propagating island. Good agreement with the extended theory with free-slip condition has been achieved for the parallel flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the no-slip condition tends to diminish as the plasma resistivity approaches zero.

Toroidal rotation is well known to play significant roles in the edge transport and L–H transition dynamics of tokamaks. Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma, purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself. In particular, the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher β regimes, which leads to the flattening or reversal of the local q (safety factor) profile. Here the formation of pressure pedestal along with the reversed magnetic shear region is shown to be the natural outcome of the MHD tokamak equilibrium in a self-consistent response to the presence of a localized toroidal rotation typically observed in high confinement-mode (H-mode) or quiescent H-mode.

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscous-resistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently., 17 pages

Flute instability produced by laser plasma expanding in a 10 T external magnetic field was studied in experiments. The plasma was generated by a 0.3 J ns laser ablating an aluminum target. The external magnetic field of approximately 10 T was provided by a pair of Helmholtz coils aligned parallel to the target surface. Initially, the plasma plume expands freely. The external magnetic field confines the plasma plume and, finally, forms a plasma cavity with a sharp plasma–field interface. Flute instability was observed at the plasma–field interface, which presents a salient kinetic feature rather than classical fluid instability. In the initial linear phase, the growth rate of the perturbation has good agreement with Large Larmor radius instability, which is larger than ion gyrofrequency. In the later nonlinear growth phase, the flute instability shows an obvious “fishbone” structure of kinetic instability, and the initial short wavelength perturbation shifts continually to longer wavelength mode and, finally, close to the density scale length. Our experiment reveals a new region of parameter space that reproduces the flute instability in the space experiments of an active magnetospheric particle tracer experiment and a combined release and radiation effects satellite.

The structural transition of a steady state dust flow from linear to nonlinear regimes is analyzed using a two-dimensional hydrodynamic model for the dust fluid confined in an axisymmetric toroidal system along with an unbounded streaming plasma. Numerical solutions of the employed hydrodynamical model not only confirms the analytical structure of the driven dust vortex flow in the linear limit as reported in the previous analysis but also shows how the dust vortices are strongly affected by the nonlinear convective transport of the flow at the higher Reynolds number (Re) regime. Effects of various system parameters including external driving field and the Reynolds number are investigated within the linear to nonlinear transition regime 0.001 ≤ Re < 50. In agreement with relevant experimental observations, the steady flow structure which is symmetric around the center in the linear regime begins to turn asymmetric in the nonlinear regime. The structure of the steady dust flow is found to be influenced mainly by the dissipation scales due to kinematic viscosity, ion drag, and neutral collision in the nonlinear regime, whereas, in the linear regime, it is mainly controlled by the external driving field and the confining boundaries.

Drift instabilities contribute to the formation of edge turbulence and zonal flows, and thus the anomalous transport in tokamaks. Experiments often found micro-scale tur- bulence strongly coupled with large-scale magnetohydrodynamic (MHD) processes, whereas a general framework has been lacking that can cover both regimes, in partic- ular, their coupling. In this paper, the linear resistive drift wave instability (DWI) is investigated using a full 2-fluid MHD model, as well as its numerical implementation in NIMROD code. Both analytical and numerical analyses reveal a macro-scale global drift wave eigenmode coupled with MHD dynamics and illustrate a non-monotonic dispersion relation with respect to both perpendicular and parallel wavenumbers. NIMROD results also reveal an edge-localized behavior in the radial mode structure as the azimuthal mode number increases, implying the dependence of the 2-fluid ef- fects due to the inhomogeneous density profile. The edge-localization introduces a non-trivial dependence of the effective perpendicular wavenumber to the perpendicular mode number, which may explain the quantitative difference between the global dispersion relation and its local approximation from the conventional local theory., 22 pages, 8 figures

Current ramping to achieve reversed shear confinement enhancement and peaked density profiles are important for achieving ignition conditions in the high-field tokamak IGNITOR [Coppi et al., Phys. Scri. 45, 112 (1992)]. Previous transport simulations used either fixed density profiles or obtained flat density profiles leading to a conclusion that a mechanism for peaking the density profile is required for ignition. In this paper an enhanced particle confinement regime that produces ignition before the sawtooth activity begins is explored. It is shown that fast current ramping is a general scheme leading to density profile peaking. In these simulations, peaked density profiles result from the formation of internal transport barrier due to reversed magnetic shear, which is produced by controlled plasma current and volume-averaged density ramping. Such a programmed Ohmic heating scheme is demonstrated to be an effective approach to achieve ignition of a deuterium-tritium plasma.

The ballooning stability of the magnetotail is considered within the framework of Hall magnetohydrodynamics (MHD). In particular, the extent to which Hall MHD effects modify ideal MHD ballooning modes is explored extensively. It is shown that Hall MHD effects primarily enter the stability analysis through changes introduced in the plasma compressibility. Hence, the incompressible ideal MHD modes are not affected, while the compressible ideal MHD modes are altered both quantitatively and qualitatively. In addition to modifying the growth rate of the compressible ideal MHD mode, Hall effects also introduce a new instability, called the entropy interchange instability, which is a variant of the ion temperature gradient instability, when the gradient ratio η≡d ln Ti/d ln ρ of the configuration becomes greater than 2/3, where Ti is the ion temperature and ρ is the plasma density. The theory is applied to two types of magnetotail configurations—analytic equilibria developed by Voigt [in Solar Wind-Magnetosphere...

The behaviors of atmospheric pressure plasma jet produced by a coplanar dielectric barrier discharge (CDBD) in helium in external electrostatic and magnetic field are investigated experimentally. Time-resolved ICCD images of jet in electric field, magnetic field, and floating metal ring are recorded, respectively. The results show that the jet dynamics is affected significantly by a metal ring, an electric, and/or a magnetic field. In a transverse electric field, the jet shows behavior of deflection, broadening, and shortening according to the structure of electric field. In a transverse magnetic field, the jet deflects to up or down depending on the magnetic direction. The jet can be slowed down or obstructed by a floating metal ring on the jet path, but will still pass through the tube at higher applied voltages of DBD, without significant change in jet length or shape out of the tube compared with that without metal ring. A positive DC voltage on the metal ring helps to improve the jet length, but a ne...

The stabilizing effects of enhanced edge resistivity on edge-localized instabilities in high confinement discharges due to lithium-conditioning in the National Spherical Torus Experiment are identified for the first time. Linear stability analysis of the experimentally constrained equilibrium suggests that the change in the equilibrium plasma density and pressure profiles alone due to lithium-conditioning may be insufficient for a complete suppression of low toroidal mode number peeling-ballooning modes. The enhanced resistivity due to the increased effective electric charge number Zeff after lithium-conditioning provides additional stabilization of the edge localized modes. Notably, this stabilizing effect by enhanced edge resistivity becomes evident only in two-fluid magnetohydrodynamic simulations.

The properties of the internal transport barriers are developed using theory and radial transport simulations that evolve local turbulent energy density with the temperature profiles. Standard ion temperature gradient models for the nonlinear radial fluxes driven by drift wave turbulence and stabilized by flow shear are implemented in a new high resolution multiple space–time transport code. A dimensionless parameterization of the input power is introduced and shown to characterize the bifurcation to an internal transport barrier. Examples of the interaction and feedback loops of the turbulence with the transport profiles are given for transport barriers as in the Tokamak Fusion Test Reactor [D. J. Grove et al. Nucl. Fusion 25, 1167 (1985)] and the Japan Atomic Energy Research Institute Tokamak-60 Upgrade (JT-60U) [Ninomiya et al., Phys. Fluids B 4, 2070 (1992)]. For the JT-60U the high performance discharge E 27969, which reached an equivalent QDT of unity, is modeled with an appropriate set of turbulent...

The formation of internal transport barriers observed in both Joint European Torus (JET) [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985)] and Doublet III-D Tokamak (DIII-D) [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] are reproduced in predictive transport simulations. These simulations are carried out for two JET-optimized shear discharges and two DIII-D negative central shear discharges using the Multi-Mode model in the time-dependent 1-1/2-D BALDUR transport code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)]. The Weiland model is used for drift modes in the Multi-Mode model in combination with either Hahm–Burrell or Hamaguchi–Horton flow shear stabilization mechanisms, where the radial electric field is inferred from the measured toroidal velocity profile and the poloidal velocity profile computed using neoclassical theory. The transport barriers are apparent in both the ion temperature and thermal diffusivity profiles of the simulations. The ti...

The hot electron plasmas (Te>2Ti) in Tore Supra (Equipe Tore Supra (presented by R. Aymar) in Plasma Physics and Controlled Nuclear Fusion Research [Proc. 12th Int. Conf., Nice, 1988 (IAEA, Vienna, 1989), Vol. 1, p. 9]) driven by fast wave electron heating (FWEH) are analyzed for thermal transport. Both neoclassical and anomalous transport processes are taken into account. The dominant power flow is through the electron channel of anomalous thermal diffusivity. The electron and ion temperature gradient driven instabilities are analyzed for a well documented discharge and shown to explain the diffusivities inferred from the steady state power balance analysis. The discharges are maintained in a quasi-steady state for periods up to 100 global energy replacement times. A large Tore Supra database is tested against two models for the turbulent electron thermal conductivity. Good correlation is obtained with an updated version of the collisionless skin depth formula. The electrostatic turbulence-based formula ...

Global drift wave map equations that allow the integration of particle orbits on long time scales are implemented to describe transport. Ensembles of test particles are tracked to simulate the low-confinement mode/reversed shear/enhanced reversed shear plasmas in the Tokamak Fusion Test Reactor (TFTR) tokamak and the Optimized Shear plasma in the Joint European Torus (JET) tokamak. The simulations incorporate a radial electric field, Ēr, obtained from a neoclassical calculation [Zhu et al., Phys. Plasmas 6, 2503 (1999)] and a model for drift wave fluctuations that takes into account change in the mode structure due to Ēr [Taylor et al., Plasma Phys. Controlled Fusion 38, 1999 (1996)]. Steady state particle density profiles along with two different measures of transport, the diffusion coefficient based on a running time average of the particle displacement and that calculated from the mean exit time, are obtained. For either weak or reversed magnetic shear and highly sheared Ēr, particle transport barriers...

The spatial and temporal evolutions of compound sawteeth were directly observed using 2D electron cyclotron emission imaging on experimental advanced superconducting tokamak. The compound sawtooth consists of partial and full collapses. After partial collapse, the hot core survives as only a small amount of heat disperses outwards, whereas in the following full collapse a large amount of heat is released and the hot core dissipates. The presence of two q = 1 surfaces was not observed. Instead, the compound sawtooth occurs mainly at the beginning of an ion cyclotron resonant frequency heating pulse and during the L-H transition phase, which may be related to heat transport suppression caused by a decrease in electron heat diffusivity.

The locking and unlocking thresholds for tearing modes are in general different. In this work, the physics origin for this difference is illustrated from theory analysis, and a numerical procedure is developed to find both locking and unlocking thresholds. In particular, a new scaling law for the unlocking threshold that is valid in both weak and strong rotation regimes has been derived from the lowest amplitude of the RMP (resonant magnetic perturbation) allowed for the locked-mode solution. Above the unlocking threshold, the criterion for the phase-flip instability is extended to identify the entire locked-mode states. Two different regimes of the RMP amplitude in terms of the accessibility of the locked-mode states have been found. In the first regime, the locked-mode state may or may not be accessible depending on the initial conditions of an evolving island. In the second regime, the locked-mode state can always be reached regardless of the initial conditions of the tearing mode. The lowest RMP ampli...

We demonstrate in theory that tearing mode locking and magnetic island suppression by resonant magnetic perturbations (RMPs) can correspond to different states of a same dynamic system governed by the torque balance and the nonlinear island evolution in the Rutherford regime. In particular, mode locking corresponds to the exact steady state of this system. A new exact analytic solution has been obtained for such a steady state, which quantifies the dependence of the locked mode island width on RMP amplitude in different plasma regimes. Furthermore, two different branches of mode locking have been revealed with the new analytic solution and the branch with suppressed island width turns out to be unstable in general. On the other hand, the system also admits stable states of island suppression achieved through the RMP modulation of tearing mode rotational frequency. When the RMP amplitude is above a certain threshold, the island suppression is transient until the tearing mode eventually gets locked. When the RMP amplitude is below the mode locking threshold, the island can be suppressed in a steady state on time-average, along with transient oscillations in rotational frequency and island width due to the absence of mode locking.

We report on a honeycomb superlattice pattern in a dielectric barrier discharge in argon/air for the first time. It consists of hexagon lattice and honeycomb framework and bifurcates from a hexagon pattern as the applied voltage increases. A phase diagram of the pattern as a function of the gas component and gas pressure is presented. The instantaneous images show that the hexagon lattice and honeycomb framework are ignited in turn in each half voltage cycle. The honeycomb framework is composed of filaments ignited randomly. The spatiotemporal dynamics of honeycomb superlattice pattern is discussed by wall charges.

In this work, we focus on examining a pure interchange process in a shear-less slab configuration as a prototype mechanism for blob formation. We employ full magnetohydrodynamic simulations to demonstrate that the blob-like structures can emerge through the nonlinear development of a pure interchange instability originating from a pedestal-like transition region. In the early nonlinear stage, filamentary structures develop and extend in the direction of the effective gravity. The blob-like structures appear when the radially extending filaments break off and disconnect from the core plasma. The morphology and the dynamics of these filaments and blobs vary dramatically with a sensitive dependence on the dissipation mechanisms in the system and the initial perturbation. Despite the complexity in morphology and dynamics, the nature of the entire blob formation process in the shear-less slab configuration remains strictly interchange without involving any change in magnetic topology.

Resistive MHD computations using the NIMROD code have found strong dependence of the low-n edge localized instabilities on edge current density distribution. The computations confirm that the low-n edge localized modes can be driven unstable by increasing the edge current density. When the edge peaked current density is sufficiently large, the q profile develops a region where the magnetic shear becomes negative. In these cases, the low-n edge instabilities are partially or fully stabilized. The stabilizing effects of edge current density in regions with reversed magnetic shear appear to be consistent with analytical predictions on a necessary condition for the stability of peeling modes. Nonlinear simulations indicate that the stabilizing effects of edge current density on the low-n edge instabilities through reverse shear can persist throughout the nonlinear exponential growth phase. Near the end of this nonlinear phase, the filament size in radial direction can exceed the pedestal width, and disconnect...

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1–20). The results use the compressible MHD model and depend on a precise representation of “ideal-like” and “vacuumlike” or “halo” regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 108 and 103 for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 105, which is much larger than experimentally measured values using Te values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.

A theory is developed for the description of ballooning instability in the intermediate nonlinear regime for general magnetic configurations including toroidal systems such as tokamaks. The evolution equations for the plasma filament growth induced by the ballooning instability are derived accounting for the dominant nonlinear effects in an ideal magnetohydrodynamic description. The intermediate nonlinear regime of ballooning modes is defined by the ordering that the plasma filament displacement across the magnetic surface is comparable to the linear mode width in the same direction. In the tokamak case, this regime could become particularly relevant for a transport barrier as the width of the barrier (or pedestal) region approaches the mode width of the dominant ballooning mode. A remarkable feature of the nonlinear ballooning equations is that solutions of the associated local linear ballooning mode equations continue to be valid solutions into the intermediate nonlinear regime. The filament growth equations for the intermediate nonlinear ballooning regime may be applicable to the precursor and precollapse phase of edge localized modes observed in both simulations and experiments.

A theoretical framework is developed for the study of the nonlinear gravitational (g) mode of a line-tied flux tube near marginal stability. The theory is based on an expansion using two small parameters, ϵ∼∣ξ∣∕Leq⪡1 and n−1∼k‖∕k⊥⪡1, with ξ denoting the plasma displacement, Leq the characteristic equilibrium length scale, and k‖ and k⊥ the dominant wavenumbers parallel and perpendicular to the equilibrium magnetic field, respectively. A particular nonlinear regime is described through the imposition of the ordering ϵ∼n−1. This regime corresponds to the nonlinear phase previously described by S. C. Cowley and M. Artun [Phys. Rep. 283, 185 (1997)], where the plasma is to lowest order incompressible and the lowest-order Lagrangian compression ∇0∙ξ is zero. In this regime, nonlinearity modifies the envelope equation of the linear global mode. The detonation regime, where the nonlinear growth of the mode dominates the linear response and becomes finite-time singular, is a narrower subset of the Cowley-Artun re...