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This paper investigated a multi-modular magnetic microrobot/millirobot (MMM) with a serial chain structure consisting of multiple identical modules. Depending on the magnet pattern used for the MMM's modules, an MMM can have different equilibrium postures under an external magnetic field, such as assembled ring and disassembled straight-line postures. In this study, we investigated the equilibrium and locomotion characteristics of the MMM by applying two different representative magnet patterns, considered to be effective for magnetic actuation, to the robots. We established various equations to determine and control the assembly, disassembly, and locomotion of the MMM with each magnet pattern. We also conducted various experiments demonstrating the assembly, disassembly, and cargo delivery capabilities of the MMM under different external magnetic fields. Results confirmed that each MMM and their magnet pattern have distinctive and useful characteristics, demonstrating that the two magnet patterns can be selectively and effectively used as MMM in different applications. [ABSTRACT FROM AUTHOR]

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have the potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and, thus, decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations and significantly reducing resistance and, hence, work. [ABSTRACT FROM AUTHOR]

We present an analytical model of the self-consistent equilibrium of a magnetic flux rope, which is obtained in cylindrical geometry. The equilibrium quantities, namely, the azimuthal magnetic field and plasma pressure, are determined in a self-consistent way through the current density, which is derived as a solution of a nonlinear equation. By minimizing the energy functional, it was shown that the constrained equilibrium state is stable. The obtained results are also applicable to the cylindrical tokamak magnetic configurations. It is shown that the analytically predicted radial profiles of equilibrium quantities are in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]

The Z-pinch configuration offers the promise of a compact fusion device owing to its simple geometry, unity beta, and absence of external magnetic field coils. Increasing the axial current compresses the plasma, resulting in a rapid rise of the fusion reaction rate. Historically, the Z pinch has been plagued by fast growing instabilities that limit plasma lifetimes. Recent progress has resulted from investigating approaches that provide stability. One approach exploits sheared-flow stabilization to produce an equilibrium Z pinch, which sustains the compressed plasma state for durations much longer than other plasma timescales. Recent experimental and simulation results encourage pursuit of the stabilized Z pinch to explore its fusion performance limits. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This coordinate system exists for magnetic fields with nested toroidal flux surfaces provided ∮ d l / B (j · ∇ ψ) = 0 , where symbols have their usual meaning, and the integral is taken along closed magnetic field lines. All quasisymmetric fields, regardless of their associated form of equilibria, must satisfy this condition. This coordinate system presents itself as a convenient form to describe general quasisymmetric configurations and their properties. Insight can be gained analytically into the difference between strong and weak forms of quasisymmetry, as well as axisymmetry, and the interaction of quasisymmetry with different forms of equilibria. [ABSTRACT FROM AUTHOR]

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. An example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples. [ABSTRACT FROM AUTHOR]

We study a model colloidal liquid crystal consisting of hard spherocylinders under the influence of an external aligning potential by Langevin dynamics simulation. The external field that rotates in a plane acts on the orientation of the individual particles and induces a variety of collective nonequilibrium states. We characterize these states by the time-resolved orientational distribution of the particles and explain their origin using the single particle behavior. By varying the external driving frequency and the packing fraction of the spherocylinders we construct the dynamical state diagram. [ABSTRACT FROM AUTHOR]

It is believed that plasma rotation can affect transitions to the advanced confinement regimes in tokamaks. In addition, in order to achieve fusion temperatures, modern tokamaks rely on auxiliary heating methods. These methods generate pressure anisotropy in the plasma. For incompressible rotation with pressure anisotropy, the equilibrium is governed by a generalized Grad–Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the effective pressure, p ̄ = ( p ∥ + p ⊥ ) / 2 , where p∥ (p⊥) is the pressure tensor element parallel (perpendicular) to the magnetic field. In the case of plasma rotation parallel to the magnetic field, the GGS equation can be transformed to one equation identical in form with the GS equation. In this study, by making use of the aforementioned property of the GGS equation for parallel plasma rotation, we have constructed ITER-like numerical equilibria by extending HELENA, an equilibrium fixed-boundary solver, and examined the impact of rotation and anisotropy on certain equilibrium quantities. The main conclusions are that the addition of pressure anisotropy to rotation allows the profile shaping of the equilibrium quantities to much more extent compared to the isotropic case, thus favoring the confinement, and allows extension of the parametric space of the Mach number corresponding to higher values. Furthermore, the impact of pressure anisotropy on the equilibrium quantities is stronger than that of the rotation for most of the quantities examined in view of respective experimental values. For the pressure components, the impact of the pressure anisotropy is the same, regardless of whether the power is deposited parallel or perpendicular to the magnetic surfaces, thus implying that there is no preferable heating direction, while for the current density, the heating parallel to the magnetic surfaces seems to be beneficial for the current gradient-driven instabilities. [ABSTRACT FROM AUTHOR]

3D equilibria with an anisotropic pressure component in the large helical device are analyzed with respect to their magnetic axis locations. The anisotropic extension of the 3D equilibrium solver variational moments equilibrium code, anisotropic neumann inverse moments equilibrium code, is used to compute fixed-boundary plasma equilibria based on a bi-Maxwellian distribution function describing the anisotropic particles. Different heating scenarios are assessed by means of parallel and perpendicular pressure anisotropies with different radial anisotropic pressure profiles imposed. A theoretical predicted scaling of the magnetic axis location with the auxiliary parameter βeq as predicted for classical stellarators and heliotrons by Hitchon [Nucl. Fusion 23, 383 (1983)] is found to be applicable to the large helical device in the case of a flat hot-particle profile for parallel or weak perpendicular dominated anisotropies with β ⊥ / β ∥ ≤ 2. For strong perpendicular or non-flat hot-particle profiles, a deviation from the predicted scaling of the magnetic axis location is found. Whereas center-peaked profiles show a stronger shift of the magnetic axis, edge-peaked profiles show no significant change of its radial location. High critical magnetic fields are identified as a necessary condition for strong perpendicular anisotropies. The observed deviations are ascribed to the magnetic field structure and negative pressure gradients. The invalidity of the theoretical predictions in the case of certain configurations is found to be caused by higher-order terms in the pressure components, which are not accounted for by the ordering on which the theory is based. [ABSTRACT FROM AUTHOR]

The vast majority of the existing lattice Boltzmann methods (LBMs) suggest to relax relevant quantities to a second-order truncated equilibrium state. Despite its simplicity and popularity, this choice does not fully exploit the potential of any lattice discretization. In this paper, an extended equilibrium state is adopted to evaluate the suitability of different LBMs (i.e., the Bhatnagar–Gross–Krook, the multiple-relaxation-time in terms of raw and central moments, and the simplified one) to simulate two-dimensional magnetohydrodynamic flows by means of the D2Q9 velocity space. Two sets of particle distribution functions are employed: one for the flow field and the other for the magnetic one. Even if the minimal five-velocities discretization is sufficient to represent the evolution of the latter, a nine-velocities model enhances the capability to enforce the divergence-free condition of the magnetic field, as shown. Therefore, a double-D2Q9 approach is herein devised. Eventually, the computational cost involved by all the schemes is discussed both in terms of virtual memory and run time. Interestingly, the simplified LBM for magnetohydrodynamic flows is herein presented for the first time. [ABSTRACT FROM AUTHOR]

In this work, we present a measurement system based on the thin layer of magnetic fluid aimed at scanning either the non-uniform magnetic field distribution applicable for magnetic levitation systems (MagLev) or determining small excess gas pressure. The key idea is based on the photo registration of a transparent air-filled cavity formed in a thin magnetic fluid layer due to balancing the gas pressure and the pressure emerging due to magnetic forces. As a result, the contour of the magnetic field lines in 3D space is visible. It is shown that the theoretical analysis and numerical simulations are consistent with experimental results. [ABSTRACT FROM AUTHOR]

We apply the near-axis expansion method for quasisymmetric magnetic fields with anisotropic pressure (developed in Paper I) [E. Rodriguez and A. Bhattacharjee, Phys. Plasmas 28, 012508 (2020)] to construct numerical solutions to circular axis stellarators. The solutions are found to second order in the distance from the axis, not possible in the standard Garren–Boozer construction [D. A. Garren and A. H. Boozer, Phys. Fluids B 3, 2822 (1991)], which assumes magnetostatic equilibria with isotropic pressure. In the limit of zero anisotropy, it is shown that a subset of coefficients can be chosen to avoid the overdetermination problem. [ABSTRACT FROM AUTHOR]

It is well known that the process of construction of quasisymmetric magnetic fields in magnetostatic equilibrium with isotropic pressure suffers from the problem of overdetermination. This has led to the widespread belief that global quasisymmetric solutions are likely not to exist. We develop a general near-axis expansion procedure that does not rely on the assumption of magnetostatic equilibria with isotropic pressure. We then demonstrate that in equilibria with anisotropic pressure, it is possible to circumvent the problem of overdetermination and carry out the power-series solutions to higher order. This suggests, contrary to current belief, that the existence of globally quasisymmetric fields is likely if one relaxes the assumption of magnetostatic equilibria with isotropic pressure. [ABSTRACT FROM AUTHOR]

Nonresonant internal modes can be difficult to anticipate as there is no resonant surface in the plasma. However, equilibria that are unstable to multiple nonresonant magnetohydrodynamic (MHD) modes may be more prone to global loss of confinement since these instabilities generate spatially extended linear displacements, potentially enhancing magnetic field line chaos via nonlinear interactions. Here, we successfully predict the unstable nonresonant pressure-driven modes for equilibria with zero shear in the plasma core, irrational q on axis, and a central pressure gradient, which is consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large-aspect-ratio limit. A criterion for identifying nonresonant modes most likely to be unstable is developed from the convergents of the continued fraction representation of q0. A higher-order analysis of the standard Energy Principle reveals the conditions under which these modes are expected to dominate. Linear growth rate spectra, as a function of toroidal mode number (up to n = 30), calculated using the initial-value extended-MHD code, M3D-C1, recover the characteristic dependence observed for ideal infernal modes. Nonresonant modes have also been invoked in some ideal sawtooth crash models. This work provides a mechanism to predict the mode numbers of infernal modes and, potentially, the width of some post-sawtooth-crash profiles. [ABSTRACT FROM AUTHOR]

We study the possibility of constructing steady magnetic fields satisfying the force balance equation of ideal magnetohydrodynamics with tangential boundary conditions in asymmetric confinement vessels, i.e., bounded regions that are not invariant under continuous Euclidean isometries (translations, rotations, or their combination). This problem is often encountered in the design of next-generation fusion reactors. We show that such configurations are possible if one relaxes the standard assumption that the vessel boundary corresponds to a pressure isosurface. We exhibit a smooth solution that possesses a Euclidean symmetry and yet solves the boundary value problem in an asymmetric ellipsoidal domain while sustaining a nonvanishing pressure gradient. This result provides a definitive answer to the problem of existence of regular ideal magnetofluidostatic equilibria in asymmetric bounded domains. The question remains open whether regular asymmetric solutions of the boundary value problem exist. [ABSTRACT FROM AUTHOR]

This study deals with the equilibrium beta limit for high-beta plasmas of the Large Helical Device using a 3D equilibrium calculation code, HINT, which is an initial value solver based on the relaxation method without an assumption of nested flux surfaces. For the finite beta equilibrium, due to the nonlinear 3D equilibrium response, the flux surface breaking begins, and the magnetic field line becomes stochastic in the peripheral region. However, although the magnetic axis shifts until the conventional theoretical beta limit, the separatrix limiting the equilibrium does not appear in the plasma core. For the high beta equilibrium, breaking of the force balance begins in the strongly stochastized region. To keep the force balance in that region, the pressure gradient decreases and the fixed profile is relaxed. As a result, the volume averaged beta, which is equivalent to the plasma stored energy, saturates, although the peak beta increases. The beta value, where the force balance begins breaking in the inside of the stochastic region, is proposed as a new index of the equilibrium beta limit for the typical heliotron-type stellarator. According to this new index of the equilibrium beta limit, the achieved beta value in the experiment of the Large Helical Device is still lower than the equilibrium beta limit. This suggests that if the heating power can be increased, the achieved beta value may still increase. [ABSTRACT FROM AUTHOR]

Using the variational method based on the Gaussian basis set, the authors investigate the 1u state of hydrogen molecular ion in a non-parallel magnetic field with respect to the fixed molecular axis. At sufficiently small field strength, the equilibrium configuration prefers the perpendicular orientation, in which the (relative) orientation θ between the magnetic field and the molecular axis is 90°. With increasing field strength, the orientation θ of the equilibrium configuration decreases, and is neither the parallel orientation nor the perpendicular orientation at field strength between 109 G and 2.35 × 1010 G. Meanwhile, more and more configurations with large orientations become unstable with respect to the dissociation H + p. [ABSTRACT FROM AUTHOR]

We investigated the optical properties of 4,4′-stilbenedinitrene at low temperature and in high magnetic fields and compared the results with complementary first principles calculations. Both physical tuning parameters allow us to manipulate the singlet-triplet equilibrium, and by doing so, control the optical contrast (which is on the order of -2.5 × 102 cm-1 at 555 nm and 35 T). Moreover, analysis of the magneto-optical response using a combined population and Beer's law framework reveals the singlet-triplet spin gap and identifies particular features in the absorption difference spectrum as deriving from singlet or triplet state excitations. These findings deepen our understanding of coupling in open shell molecules and show how chemical structure modification can modulate charge-spin interactions in organic biradicals. [ABSTRACT FROM AUTHOR]

The axion coupling in topological insulators (TI), which couples electric polarization (magnetization) with the magnetic (electric) field, is known to support a small-distance Casimir repulsion and a large-distance Casimir attraction with a zero-force stable equilibrium between TI plates. By enhancing the reflection properties of the TI interface through mirrors that introduce multiple reflections, we show that it is possible to maintain these trends while tuning the position of the zero-force point and its binding energy: the former by an order of magnitude and latter by over four orders. Moreover, surface charge on the TI allows for intermediate tuning of the zero-force point between coarse settings determined by the axion coupling. [ABSTRACT FROM AUTHOR]

A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma, conditions for quasisymmetry are constructed starting from the single-particle Lagrangian to the leading order. The conditions presented in the paper are less restrictive than the set recently obtained by Burby et al. ["Some mathematics for quasi-symmetry," arXiv:1912.06468 (2019)], and could facilitate ongoing efforts toward investigating the existence of global quasisymmetric MHD equilibria. It is also shown that quasisymmetry implies the existence of flux surfaces, regardless of whether the field corresponds to an MHD equilibrium. [ABSTRACT FROM AUTHOR]

The effect of magnetic field on the austenite (γ) to ferrite (α) transformation kinetics is studied in iron by means of dilatation measurements under magnetic field. In the frame of the Johnson–Mehl–Avrami-Kolmogorov analysis and considering a spherical growth mode for the ferrite grains, the Avrami exponent and the activation energy for the interface mobility are calculated. These parameters are found to be weakly influenced by the application of a 16 T magnetic field. This indicates that they are related mainly to the total amount of energy available for the transformation whatever its origin (whether magnetic or chemical). Whereas the magnetic field strongly affects the α/γ thermodynamic equilibrium through the Gibbs free energy of phases, it has a non noticeable influence on the transformation kinetics itself. [ABSTRACT FROM AUTHOR]

We consider colloidal platelets under the influence of gravity and an external aligning (magnetic) field. The system is studied using a fundamental measures density functional theory for model platelets of circular shape and vanishing thickness. In the gravity-free case, the bulk phase diagram exhibits paranematic-nematic phase coexistence that vanishes at an upper critical point upon increasing the strength of the aligning field. Equilibrium sedimentation profiles display a paranematic-nematic interface, which moves to smaller (larger) height upon increasing the strength of gravity (the aligning field). The density near the bottom of the system decreases upon increasing the strength of the aligning field at fixed strength of gravity. Using a simple model for the birefringence properties of equilibrium states, we simulate the color variation with height, as can be observed in samples between crossed polarizers. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of off-axis continuous intense relativistic beams propagating inside a circular conducting pipe. The equations of motion for the centroid and the envelope of slightly off-axis beams are derived and used to determine equilibrium and stability conditions for the beam transport. It is shown that depending on the parameters of the system, beams propagating along the pipe axis may become unstable due to the presence of the wall, imposing a fundamental limitation in the effective area that an equilibrium beam can occupy inside the conductor. [ABSTRACT FROM AUTHOR]

Several interrelated phenomena near the surface ablated into a discharge plasma, such as ablation and ionization in accelerated plasma are studied. Two characteristic ablation modes are identified, namely, ablation mode with a velocity at the Knudsen layer edge smaller than the local sound speed and a velocity at the Knudsen layer edge close to the sound speed. The existence of these two ablation modes is determined by the current density in the acceleration region. The nonequilibrium ionization region in the presence of strong electromagnetic plasma acceleration is studied. In the subsonic regime, the ionization region thickness is proportional to the ionization rate and inversely proportional to the magnetic field. Conditions for ionization equilibrium in the accelerating plasma are determined. The specific example of a micropulsed plasma thruster is considered. It is concluded that both the equilibrium and nonequilibrium ionization regimes occur in this device. [ABSTRACT FROM AUTHOR]

The shape formation of ferrofluid under magnetic field has been considered to be one of most difficult problems to analyze. In this paper we present a numerical implementation of the level set method for the equilibrium shape calculation of ferrofluid under magnetic field. The magnetic-fluid coupled system has an extremum value of electromagnetic system energy. When the system is composed of magnetic permeable material and current sources, the system energy is a maximum at the equilibrium state. The level set method is adopted for shape capturing since it can easily handle shape variations of fluid including topological changes such as merging, splitting, and even disappearing of connected material regions. The velocity field for the level set method is calculated using a shape derivative of continuum sensitivity analysis that is derived by employing the material derivative concept. The numerical results for a model problem of some ferrofluid on a glass plate show that the level set method works well for the ferrofluid shape formation. [ABSTRACT FROM AUTHOR]

A two-field reduced gyrofluid model including electron inertia, ion finite Larmor radius corrections, and parallel magnetic field fluctuations is derived from the model of Brizard [Brizard, Phys. Fluids B 4, 1213 (1992)]. It assumes low βe, where βe indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong uniform magnetic guide field, but permits an arbitrary ion-to-electron equilibrium temperature ratio. It is shown to have a noncanonical Hamiltonian structure and provides a convenient framework for studying kinetic Alfvén wave turbulence, from magnetohydrodynamics to sub-de scales (where de holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized cross-helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range, the generalized cross-helicity could display an inverse cascade if injected at small scales, for example by reconnection processes. [ABSTRACT FROM AUTHOR]

A Solovev-like solution describing equilibria with field aligned incompressible flows [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 19, 014504 (2012)] is extended to non parallel flows. The solution expressed as a superposition of Bessel functions contains an arbitrary number of free parameters which are exploited to construct a variety of configurations including ITER shaped ones. For parallel flows, application of a sufficient condition for linear stability shows that this condition is satisfied in an appreciable part of the plasma region on the high-field side mostly due to the variation of the magnetic field perpendicular to the magnetic surfaces. Also, the results indicate that depending on the shape of the Mach-function profile and the values of the free parameters the flow and flow shear may have either stabilizing or destabilizing effects. [ABSTRACT FROM AUTHOR]

Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium are studied analytically and numerically, where the plasma is confined by only poloidal magnetic field generated by an internal ring current. The plasma current due to finite pressure can be divided into two components; one remains at isotropic pressure and the other arises from pressure anisotropy. When p⊥, the pressure perpendicular to the magnetic field, is larger than p∥, the pressure parallel to the magnetic field, those two components of plasma current tend to cancel each other to reduce the total amount of plasma current. Equilibrium beta limit is also examined, where the beta is a ratio of the plasma pressure to the magnetic pressure. The equilibrium beta limit decreases as the pressure anisotropy becomes strong. The beta value is strictly limited by ellipticity of the equilibrium equation when p⊥>p∥ . On the other hand, when p⊥>p∥, although the tendency of the beta limit agrees with the ellipticity condition of the equilibrium equation, equilibria with a hyperbolic region can be obtained by iterative procedure with practically reasonable convergence criteria. [ABSTRACT FROM AUTHOR]

The 30 keV lithium beam diagnostic on DIII-D is suitable to measure both the radial electron density and poloidal magnetic field profiles in the pedestal. The refurbished system features a new setup to measure the Doppler shift allowing accurate alignment of the spectral filters. The injector has been optimized to generate a stable lithium neutral beam with a current of I = 15-20 mA and a diameter of 1.9 ± 0.1 cm measured by beam imaging. The typical temporal resolution is Δt = 1-10 ms and the radial resolution of ΔR = 5 mm is given by the optical setup. A new analysis technique based on fast Fourier transform avoids systematic error contributions from the digital lock-in analysis and accounts intrinsically for background light correction. Latest upgrades and a detailed characterization of the system are presented. Proof-of-principle measurements of the poloidal magnetic field with a statistical error of typically 2% show a fair agreement with the predictions modeled with the Grad-Shafranov equilibrium solver EFIT within 4%. [ABSTRACT FROM AUTHOR]

Theoretical studies of the plasmoid instability generally assume that the reconnecting magnetic fields are symmetric. We relax this assumption by performing two-dimensional resistive magnetohydrodynamic simulations of the plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic asymmetry modifies the onset, scaling, and dynamics of this instability. Magnetic islands develop preferentially into the weak magnetic field upstream region. Outflow jets from individual X-points impact plasmoids obliquely rather than directly as in the symmetric case. Consequently, deposition of momentum by the outflow jets into the plasmoids is less efficient, the plasmoids develop net vorticity, and shear flow slows down secondary merging between islands. Secondary merging events have asymmetry along both the inflow and outflow directions. Downstream plasma is more turbulent in cases with magnetic asymmetry because islands are able to roll around each other after exiting the current sheet. As in the symmetric case, plasmoid formation facilitates faster reconnection for at least small and moderate magnetic asymmetries. However, when the upstream magnetic field strengths differ by a factor of 4, the reconnection rate plateaus at a lower value than expected from scaling the symmetric results. We perform a parameter study to investigate the onset of the plasmoid instability as a function of magnetic asymmetry and domain size. There exist domain sizes for which symmetric simulations are stable but asymmetric simulations are unstable, suggesting that moderate magnetic asymmetry is somewhat destabilizing. We discuss the implications for plasmoid and flux rope formation in solar eruptions, laboratory reconnection experiments, and space plasmas. The differences between symmetric and asymmetric simulations provide some hints regarding the nature of the three-dimensional plasmoid instability. [ABSTRACT FROM AUTHOR]

Existing numerical tools for calculating the MHD stability of magnetically confined plasmas generally assume the existence of nested flux surfaces. These tools are therefore not immediately applicable to configurations with magnetic islands or regions with an ergodic magnetic field. However, in practice, these islands or ergodic regions are often small, and their effect on MHD stability can then be evaluated using a perturbation theory developed in the present paper. This procedure allows the effect of the broken magnetic topology on the stability of each eigenmode to be calculated without requiring any knowledge about the perturbed eigenfunctions. [ABSTRACT FROM AUTHOR]

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. [ABSTRACT FROM AUTHOR]

The fast termination phase of a vertical displacement event (VDE) in a tokamak is modeled as a sequence of shrinking equilibria, where the core current profile remains constant so that the safety-factor at the axis, qaxis, remains fixed and the qedge systematically decreases. At some point, the n = 1 kink mode is destabilized. Kink modes distort the magnetic field lines outside the plasma, and surface currents are required to nullify the normal component of the B-field at the plasma boundary and maintain equilibrium at finite pressure. If the plasma touches a conductor, the current can be transferred to the conductor, and may be measurable by the halo current monitors. This report describes a practical method to model the plasma as it evolves during a VDE, and determine the surface currents, needed to maintain equilibrium. The main results are that the onset conditions for the disruption are that the growth-rate of the n = 1 kink exceeds half the Alfven time and the associated surface current needed to maintain equilibrium exceeds one half of the core plasma current. This occurs when qedge drops below a low integer, usually 2. Application to NSTX provides favorable comparison with non-axisymmetric halo-current measurements. The model is also applied to ITER and shows that the 2/1 mode is projected to be the most likely cause of the final disruption. [ABSTRACT FROM AUTHOR]

Radiofrequency discharges used in industry often have centrally peaked plasma density profiles n(r) although ionization is localized at the edge, even in the presence of a dc magnetic field. This can be explained with a simple cylindrical model in one dimension as long as the short-circuit effect at the endplates causes a Maxwellian electron distribution. Surprisingly, a universal profile can be obtained, which is self-similar for all discharges with uniform electron temperature Te and neutral density nn. When all collisions and ionizations are radially accounted for, the ion drift velocity toward the wall reaches the Bohm velocity at a radius which can be identified with the sheath edge, thus obviating a pre-sheath calculation. For non-uniform Te and nn, the profiles change slightly but are always peaked on axis. For helicon discharges, iteration with the HELIC code for antenna-wave coupling yields profiles consistent with both energy deposition and diffusion profiles. Calculated density is in absolute-value agreement with experiment. [ABSTRACT FROM AUTHOR]

Coaxial helicity injection in the HIT-II [A. J. Redd et al., Phys. Plasmas 9, 2006 (2002)] spherical torus is modeled with time-dependent resistive magnetohydrodynamics computations run to steady state for conditions without strong relaxation. Laboratory and computed results on injector current and plasma current agree reasonably well as toroidal magnetic field and injector flux are scaled. The scalings are consistent with a dimensional estimate from the Grad-Shafranov equation that provides a new perspective on a previously published model based on a current-sheet equilibrium and the magnetic pressure required for the 'bubble-burst' criterion. Numerical solutions of the Grad-Shafranov equation with an assumed current profile also indicate large qualitative changes as the predicted criterion is crossed. [ABSTRACT FROM AUTHOR]

A blob-filament (or simply 'blob') is a magnetic-field-aligned plasma structure which is considerably denser than the surrounding background plasma and highly localized in the directions perpendicular to the equilibrium magnetic field B. In experiments and simulations, these intermittent filaments are often formed near the boundary between open and closed field lines, and seem to arise in theory from the saturation process for the dominant edge instabilities and turbulence. Blobs become charge-polarized under the action of an external force which causes unequal drifts on ions and electrons; the resulting polarization-induced E × B drift moves the blobs radially outwards across the scrape-off-layer (SOL). Since confined plasmas generally are subject to radial or outwards expansion forces (e.g., curvature and ∇B forces in toroidal plasmas), blob transport is a general phenomenon occurring in nearly all plasmas. This paper reviews the relationship between the experimental and theoretical results on blob formation, dynamics and transport and assesses the degree to which blob theory and simulations can be compared and validated against experiments. [ABSTRACT FROM AUTHOR]

It is shown that nonequilibrium filling of an upper surface subband induced by a microwave resonance can be the origin of absolute negative conductivity and zero-resistance states for a two-dimensional electron system on liquid helium in a perpendicular magnetic field. Contrary to a similar effect reported for semiconductor systems, an oscillating sign-changing correction to the dc-magnetoconductivity shows up as a result of quasi-elastic inter-subband scattering that does not involve photons. This analysis explains the remarkable magnetooscillations and zero-resistance states recently observed in electron systems on liquid helium. [ABSTRACT FROM AUTHOR]