Nonlinear MHD Simulations Research Articles

Interstellar turbulence driven by the magnetorotational instability

The occurrence of the magnetorotational instability (MRI) in vertically stratified galactic disks is considered. Global 3D nonlinear MHD simulations with the ZEUSMP code are performed in a cylindric computational domain. Due to the evo- lution of the MRI toroidal and poloidal components of the mean magnetic fields are generated. The results are also applied to very young galaxies which are assumed to possess strong magnetic fields already after a few 10 8 years. The dependence of MRI growth rate on the shear strength is shown. The velocity dispersion grows with height and reaches values of about 5k m s −1 in good agreement with observations and close to the predictions of Sellwood & Balbus (1999). For strong magnetic fields the MRI is suppressed but it is not suppressed by turbulence initially present in the disk.

Modelling of PPCD in the reversed field pinch RFX by the transport code RITM

The modifications in plasma parameters and heating power under conditions of pulsed poloidal current drive (PPCD) in Reversed Field eXperiment (RFX) are modelled by the one-dimensional transport code RITM (Radiation from Impurities in Transport Model). Several channels for the PPCD effects on plasma confinement are taken into account: dissipation of externally driven poloidal currents, reduction in the electric field induced by the dynamo and decrease in magnetic fluctuations. It is demonstrated that the external currents are dissipated at the plasma edge and they cannot, alone, lead to any change in the temperature profile. The reduction in the dynamo electric field results in central peaking of the current and Ohmic power densities, accompanied, however, by a very modest rise in the central temperature. By taking into account the decrease in the level of magnetic fluctuations (predicted for PPCD conditions by non-linear MHD simulations) and the corresponding reduction of transport in the stochastic magnetic field, RITM reproduces, in agreement with experiments, a significant increase in the central temperature and a reduction in the loop voltage.

Theoretical investigation of field-line quality in a driven spheromak

Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear three-dimensional MHD simulations and analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces. Three-dimensional nonlinear MHD simulations confirm that field lines are predominantly open when there is a large-amplitude toroidal-mode-number n = 1 mode. However, an appreciable volume of good flux surfaces can be obtained either during the drive-off phase of a scheme with periodic pulsed drive or for an extended period under driven conditions, with oscillating volume, when the odd-n modes are suppressed. If a configuration with radially localized perturbations can be achieved, a scaling analysis for a Rosenbluth–Bussac spheromak equilibrium indicates a favourable (1/Lundquist number) scaling to larger, higher-field devices. A hyper-resistivity analysis, which also assumes small-scale perturbations, reproduces well magnetic probe data in the sustained spheromak physics experiment, while an analysis of the same experiment based on one-dimensional transport along open field lines contradicts experimental observations in several key ways. The scaling analysis is also applied to reversed-field pinches and indicates that a completely determined scaling can be obtained with less approximation to the resistive MHD equations than indicated in the previous literature.

Superthermal Electron Diffusion Processes in a Reversed Field Pinch

In reversed field pinches (RFPs), edge fast electrons play some important roles in the energy transport and RFP dynamo. There have been here detailed measurements of electron currents and floating potential with electrostatic probes at the edge region, showing that field-aligned current is carried by superthermal electrons, which results in reversed toroidal current outside the reversal surface. The time evolution of radial electric field, which is estimated from that of floating potential measured with insertable probes with some assumptions, revealed that radially outward electric field is formed in about 100 µs. Given that the radial electric field is a result of superthermal electron diffusion in a stochastic magnetic field line, then the estimated diffusion coefficient agrees well with the numerically calculated values, which were obtained by using Monte-Carlo particle orbit calculation in combination with a 3-dimentional nonlinear MHD simulation. It is concluded that the radial electric field is for...

The role of axisymmetric reconnection events inJET discharges with extreme shear reversal

Injection of lower hybrid heating and current drive into the currentramp-up phase of JET discharges can produce extremely reversedq-profiles characterized by a core region of very small or zero currentdensity (within motional Stark effect diagnostic measurement errors) andqmin>1. Te-profiles show sawtooth-like collapses and thepresence of an internal transport barrier. Accurate equilibriumreconstructions of these discharges are obtained using the ESC code,which was recently extended to allow equilibrium reconstructions inwhich a free boundary solver determines the plasma boundary and a fixedboundary solver provides the magnetic geometry and current densityprofile. The core current density does not appear to go negative,although current diffusion calculations indicate that sufficientnon-inductive current drive to cause this is present. This is explainedby nonlinear resistive MHD simulations in toroidal geometry whichpredict that these discharges undergo n = 0 reconnection events(axisymmetric sawteeth) that redistribute the current to hold the corecurrent density near zero.

Self-Gravitational Instability of an Isothermal Gaseous Slab under High External Pressure

In active massive star forming regions such as Orion and the Galactic center, the self-gravitational instability of a magnetized gaseous slab plays an important role as a trigger of star formation. In such high external pressure regions, the incompressible mode of self-gravitational instability (Elmegreen & Elmegreen 1978; Lubow & Pringle 1992) becomes dominant. Based on two-dimensional hydrodynamical simulations, Umekawa et al. (1999) proposed “Star formation by merging of the Jeans stable clumps” in a pressure bounded slab. In a magnetized slab confined by external pressure, Nagai et al. (1998) showed by linear analysis that the slab fragments to filaments parallel to the magnetic field lines. Here, we show by nonlinear three-dimensional MHD simulations that the filaments further fragment to Jeans stable clumps.

3-D MHD simulations of pellet injection and disruptions in tokamak plasmas

Non-linear MHD simulation results of pellet injection show that MHD forces can accelerate large pellets injected on the high field side of a tokamak to the plasma centre. Magnetic reconnection can produce a reverse shear q profile. Ballooning instability caused by pellets is also reduced by high field side injection. Studies are also reported of the current quench phase of disruptions, which can cause 3-D halo currents and runaway electrons.

8.10. Three-dimensional global MHD simulations of jet formation in active galactic nuclei

Magnetically driven jets from accretion disks are considered to be the most promising models of astrophysical jets. Uchida & Shibata (1985) and Shibata & Uchida (1986) first carried out two-dimensional nonlinear MHD simulations of jet formation from a magnetized disk. Matsumoto et al. (1996) applied the Uchida-Shibata model to a gas torus in active galactic nuclei and showed that the surface layer of the torus accretes faster than the equatorial region like an avalanche because magnetic braking most effectively extracts angular momentum from that layer. A magnetized torus subjects to global non-axisymmetric instabilities (Curry & Pudritz 1996) and local magnetorotational instability (Balbus & Hawley 1991). We carried out three-dimensional global MHD simulations to show the non-axisymmetric effects on the torus, avalanche flow and jet formation.

Extensions to single filament modelling of a tokamak plasma

Adjustments are described that should be made to a single filament description of a tokamak plasma if accurate modelling of a non-linear MHD simulation is to be achieved. It is shown that although the single filament model is excellent for purely radial, or purely vertical, fields, it does not describe the gradients of these fields. A simple scalar correction to the gradient terms in the model is found to facilitate the accurate prediction of the growth rate of the vertical instability. An extension to the modelling of X points is also presented. The corrected multi-pole model is shown to be appropriate for the design of robust controllers

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two‐dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfvén waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schrödinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one‐dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigenmode is found also for weakly two‐dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Magnetic Reconnection at Stressed X-Type Neutral Points

The reconnection and relaxation of two-dimensional stressed (non-potential) x-type neutral point magnetic fields are studied via solution of the nonlinear resistive 2-D MHD equations and by analytical solution of the linear eigenvalue problem. The linear dispersion relation was generalized for azimuthally nonsymmetric perturbations, and have found that for modes with azimuthal mode numbers m > 0, the relaxation can occur at a rate faster than that for n = m = 0, where n is the radial quantum'' number. One finds that for nearly azimuthally symmetric magnetic perturbations that are zero at the boundary; i.e. the frozen-in'' (sometimes called fine-tied'') boundary conditions, the fields relax incompressibly and nonlinearly to the unstressed x-type neutral point at a rate close to that predicted by linear theory. Also, fully compressible nonlinear MHD simulations have been performed, which show that the interaction between the plasma flow velocity and the magnetic field is the important physical effect, while the inclusion of thermodynamics does not affect the evolution considerably. A Lyapunov functional for the nonlinear incompressible 2-D resistive MHD equations is derived to show that the current-free x-point configuration is a global equilibrium to which general initial conditions relax.

Forced magnetic reconnection in a plasma sheet with localized resistivity profile excited by lower hybrid drift type instability

A forced magnetic reconnection process with a temporal evolution of resistivity is studied for a plasma sheet with a nonuniform resistivity profile based on the nonlocal mode structure of the lower hybrid drift type instability. The growth rate of the mode found is almost independent of the resistivity at the neutral sheet, but depends on the resistivity of the region of maximum density gradient away from the neutral sheet. We study this by using both a nonlinear numerical MHD simulation and a linear theory. The mode may be relevant to the prevalent theoretical concept of MHD reconnection and the localized anomalous resistivity profile based on the lower hybrid drift instability.

Dynamic processes in relaxation phenomena of RFP plasma

Research on causal mechanisms and dynamic processes of relaxation phenomena in a Reversed Field Pinch (RFP) plasma is reviewed in relation to toroidal flux generation, anomalous ion heating and loop voltage. The anomalous transport related to MHD fluctuations is briefly mentioned. Recent development of three dimensional, non-linear resistive MHD simulations and detailed measurements in RFP experiments reveal the behavior of MHD activity of RFP plasma more clearly.