Resistive Magnetohydrodynamic Instabilities Research Articles

Kinetic-magnetohydrodynamic hybrid simulation of infernal modes in circular tokamak plasmas with effects of kinetic thermal ions

Effects of the kinetic thermal ions (KTIs) on ideal infernal modes and resistive infernal modes have been investigated by using magnetohydrodynamic (MHD) simulation without KTIs and kinetic-MHD hybrid simulation with KTIs. For the ideal infernal modes, the pressure profile is significantly flattened at the saturated state for both the models with and without the KTIs. As the beta value decreases, the ideal infernal modes are stabilized while the resistive infernal modes are still unstable. For the resistive infernal modes, while the saturated pressure profile is significantly flattened in the MHD simulation without KTIs, the pressure profile is not flattened at the saturated state in the kinetic-MHD hybrid simulation with KTIs. The suppression of the saturation level by the effects of the KTIs results from the phase mismatch between the radial velocity and perturbed pressure mode structures. This indicates that KTIs play an essential role for the suppression of pressure profile flattening due to slowly growing resistive MHD instabilities.

Resistive instabilities in toroidal anisotropic plasmas

Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.

Effect of toroidal rotation on resistive magnetohydrodynamic instability with a nonmonotonic q profile in cylindrical geometry

The effect of plasma rotation on the linear stability of the resistive magnetohydrodynamic (MHD) instabilities with a nonmonotonic q profile is investigated numerically in the cylindrical geometry. The results have shown that the plasma rotation has a stabilization effect on the double tearing modes (DTMs) depending on the magnitude of the velocity, while the velocity shear has a relatively weak effect. The effect of rotation on DTMs is determined by the velocity at each rational surface. A toroidal velocity imposed on the innermost rational surface has a weak effect on m > 1 DTMs. When the velocity is imposed on the outboard resonant surface, the growth rates of the DTMs are reduced for m > 1 modes; however, it has an obvious destabilizing effect on both m = 1 (with m the poloidal mode number) DTM and single tearing mode branches if the distance between the two rational surfaces is sufficiently small. It is shown that the effect of plasma rotation on the growth rates of the MHD instabilities is in phase with the integrated value of the coupling between potential fluctuation and magnetic flux perturbation.

A model of energetic ion effects on pressure driven tearing modes in tokamaks

The effects that energetic trapped ions have on linear resistive magnetohydrodynamic (MHD) instabilities are studied in a reduced model that captures the essential physics driving or damping the modes through variations in the magnetic shear. The drift-kinetic orbital interaction of a slowing down distribution of trapped energetic ions with a resistive MHD instability is integrated to a scalar contribution to the perturbed pressure, and entered into an asymptotic matching formalism for the resistive MHD dispersion relation. Toroidal magnetic field line curvature is included to model trapping in the particle distribution, in an otherwise cylindrical model. The focus is on a configuration that is driven unstable to the m/n = 2/1 mode by increasing pressure, where m is the poloidal mode number and n is the toroidal. The particles and pressure can affect the mode both in the core region where there can be low and reversed shear and outside the resonant surface in significant positive shear. The results show that the energetic ions damp and stabilize the mode when orbiting in significant positive shear, increasing the marginal stability boundary. However, the inner core region contribution with low and reversed shear can drive the mode unstable. This effect of shear on the energetic ion pressure contribution is found to be consistent with the literature. These results explain the observation that the 2/1 mode was found to be damped and stabilized by energetic ions in δf-MHD simulations of tokamak experiments with positive shear throughout, while the 2/1 mode was found to be driven unstable in simulations of experiments with weakly reversed shear in the core. This is also found to be consistent with related experimental observations of the stability of the 2/1 mode changing significantly with core shear.

Ideal and resistive magnetohydrodynamic instabilities in cylindrical geometry with a sheared flow along the axis

The problem of the linear stability of internal magnetohydrodynamic modes in a cylindrical plasma with a sheared longitudinal flow is addressed. A Newcomb-like equation describing the perturbation is derived and exactly solved for a class of analytic profiles for rotational transform, equilibrium flow and pressure. A dispersion relation for ideal modes is then derived and analysed for different limits of the poloidal mode number (viz. m = 1, and ). In the resistive case, a simple and exact expression for the tearing stability index is derived using the same class of equilibrium profiles. It is found that a small flow shear has a destabilising effect, while if the flow shear is dominant over the magnetic shear the tearing mode is stabilised. Implications on the stability of the m = 1 resistive mode are also discussed.

Quasilinear perturbed equilibria of resistively unstable current carrying plasma

A formalism for consideration of island formation is presented using a model of a cylindrical resistively unstable plasma. Both current and pressure driven island formation at resonant surfaces are considered. The proposed formalism of perturbed equilibria avoids problems typical for linear analysis of resistive magneto-hydrodynamic instabilities related to extraction of the so-called small solution near the resonant surfaces. The matching technique of this paper is not sensitive to configuration parameters near the resonant surfaces. The comparison of the perturbed equilibrium method with the frequently used quasilinear mode analysis based on a perturbed averaged current density profile shows that the latter is limited in its applicability and underestimates the stability. Presented here for a cylindrical case, the perturbed equilibrium technique can be used in toroidal perturbed equilibrium codes with minor modifications.

The rotating wall machine: A device to study ideal and resistive magnetohydrodynamic stability under variable boundary conditions

The rotating wall machine, a basic plasma physics experimental facility, has been constructed to study the role of electromagnetic boundary conditions on current-driven ideal and resistive magnetohydrodynamic instabilities, including differentially rotating conducting walls. The device, a screw pinch magnetic geometry with line-tied ends, is described. The plasma is generated by an array of 19 plasma guns that not only produce high density plasmas but can also be independently biased to allow spatial and temporal control of the current profile. The design and mechanical performance of the rotating wall as well as diagnostic capabilities and internal probes are discussed. Measurements from typical quiescent discharges show the plasma to be high β (≤p>2μ(0)/B(z)(2)), flowing, and well collimated. Internal probe measurements show that the plasma current profile can be controlled by the plasma gun array.

Saturated ideal modes in advanced tokamak regimes in MAST

MAST plasmas with a safety factor above unity and a profile with either weakly reversed shear or broad low-shear regions, regularly exhibit long-lived saturated ideal magnetohydrodynamic (MHD) instabilities. The toroidal rotation is flattened in the presence of such perturbations and the fast ion losses are enhanced. These ideal modes, distinguished as such by the notable lack of islands or signs of reconnection, are driven unstable as the safety factor approaches unity. This could be of significance for advanced scenarios, or hybrid scenarios which aim to keep the safety factor just above rational surfaces associated with deleterious resistive MHD instabilities, especially in spherical tokamaks which are more susceptible to such ideal internal modes. The role of rotation, fast ions and ion diamagnetic effects in determining the marginal mode stability is discussed, as well as the role of instabilities with higher toroidal mode numbers as the safety factor evolves to lower values.

Effects of a poloidal divertor separatrix on resistive magnetohydrodynamic instabilities in a tokamak

A computer code package has been developed to simulate the linear and nonlinear evolution of long-wavelength resistive magnetohydrodynamic (MHD) instabilities in a four-node poloidal divertor tokamak (e.g., Wisconsin Tokapole II [Nucl. Fusion 19, 1509 (1979)]). Distinguishing features of this package include the use of a full set of three-dimensional (3-D) nonlinear resistive MHD equations and the inclusion of the divertor separatrix and the plasma outside the divertor separatrix in the computational domain. The present numerical results suggest that the plasma current outside the divertor separatrix tends to linearly stabilize the resistive MHD instability dominated by the m=2, n=1 mode, and, to a lesser extent, that dominated by the m=1, n=1 mode. (Here, m and n are poloidal and toroidal mode numbers, respectively.) However, the nonlinear evolution of the m=1, n=1 dominant instability is not significantly affected by the divertor configuration; the m=1, n=1 island is shown to reconnect totally by developing a large region of magnetic stochasticity. Hence, the cause of the partial reconnection observed in Tokapole II seems to lie beyond the scope of the classical resistive MHD model.

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Neoclassical viscosity effects on resistive magnetohydrodynamic modes in toroidal geometry

The flux-surface-averaged linearized resistive magnetohydrodynamic (MHD) boundary-layer equations including the compressibility, diamagnetic drift, and neoclassical viscosity terms are derived in toroidal geometry. These equations describe the resistive layer dynamics of resistive MHD modes over the collisionality regime between the banana plateau and the Pfirsch–Schlüter. From the resulting equations, the effects of neoclassical viscosity on the stability of the tearing and resistive ballooning modes are investigated numerically. Also, a study is given for the problem of how the neoclassical resistive MHD mode is generated as the collisionality is reduced. It is shown that the neoclassical viscosity terms give a significant destabilizing effect for the tearing and resistive ballooning modes. This destabilization comes mainly from the reduction of the stabilizing effect of the parallel ion sound compression by the ion neoclassical viscosity. In the banana-plateau collisionality limit, where the compressibility is negligible, the dispersion relations of the tearing and resistive ballooning modes reduce to the same form, with the threshold value of the driving force given by Δc=0. On the other hand, with the finite neoclassical effect it is found that the neoclassical resistive MHD instability is generated in agreement with previous results. Furthermore, it is shown that this later instability can be generated in a wide range of the collisionality including near the Pfirsch–Schlüter regime as well as the banana-plateau regime, suggesting that this mode is a probable cause of anomalous transport.

Numerical studies of toroidal resistive magnetohydrodynamic instabilities

A time-stepping code has been constructed to study the dominant resistive magnetohydrodynamic (MHD) instability of an axisymmetric toroidal plasma. The model used is based on the linearized, incompressible MHD equations with constant density and includes the toroidal ideal model if the resistivity is taken to be zero. The equations are solved fully implicitly using a coordinate system for which one set of coordinate surfaces coincides with a set of surfaces of constant poloidal flux. This is crucial for the accurate representation of modes for which the perturbed quantities vary rapidly near surfaces with rational values of the safety factor. The code is checked by comparison with an exactly soluble model, cylindrical resistive MHD codes and a toroidal ideal MHD code (ERATO). Results are presented showing the effect of resistivity on the unstable internal modes near nq 0 = 1 for an INTOR-like numerically generated equilibrium.

Resistive instabilities of current sheets in the solar wind

We present some numerical results on resistive magnetohydrodynamic instabilities and discuss their relevance to current sheets of the type indicated by spacecraft observations in the interplanetary plasma.

An unstable arch model of a solar flare

The theoretical consequences of assuming that a current flows along flaring arches consistent with a twist in the field lines of these arches are examined. It is found that a sequence of magneto-hydrodynamic (MHD) and resistive MHD instabilities driven by the assumed current (which we refer to as the toroidal current) can naturally explain most manifestations of a solar flare.

A numerical model for resistive magnetohydrodynamic instabilities

A hydromagnetic model has been developed to study resistive instabilities in cylindrical geometry, and the model is applied to study specific diffuse pinch configurations. The MHD equations include the effects of compressibility, finite resistivity, viscosity, and thermal conductivity. The plasma equilibrium configuration is assumed known and is specified by B θ 0 ( r), B z0 ( r), η 0( r), ϱ 0( r), T 0( r) and these functions can be chosen to describe a particular experiment. Perturbations of the form f 1( r, t)exp[ i( mθ + k 2 z)] are used for all plasma and field variables, and the resulting linear partial differential equations are solved numerically as an initial value problem using an implicit difference scheme. A set of seven equations for B r1 , B θ 1 , T 1 , ν r1 , ν θ 1 , ν z1 , ϱ 1, is obtained and the calculation is started by specifying an initial perturbation. For a particular problem, the parameters m, k z , and S = τ R / τ H , the ratio of resistive diffusion time to hydromagnetic transit time must be given, and for certain choices an exponential growth occurs and the growth rate p( m, k z , S) is calculated.