Resistive MHD Model Research Articles

Viscous Effects on Nonlinear Double Tearing Mode and Plasmoid Formation in Adjacent Harris Sheets

In this paper, we study the effects of viscosity on the evolution of the double tearing mode (DTM) in a pair of adjacent Harris sheets based on the resistive MHD model in the NIMROD code. Similar to the tearing mode in the conventional single Harris sheet, a transition is observed in the generation of both normal and monster plasmoids at Prandtl number Pr=1. In the Pr<1 regime of the DTM, normal plasmoids (small plasmoids) are generated along with monster plasmoid, whereas in the single tearing mode (STM) cases, such a generation is not observed. When Pr is above the critical value, the generation of monster plasmoid is halted. Correspondingly, in the Pr<1 regime, a quadrupolar flow advects along the poloidal direction, but in the Pr>1 regime this flow advection is inhibited.

Secondary island induced during magnetic reconnection by an external sub-Alfvénic shear flow

Secondary tearing instability induced associated with sub-Alfvénic shear flow during magnetic reconnection processes is investigated using a compressible resistive MHD model. Compared to the without shear flow case, it is found that a secondary island can be built up during the reconnection process with an external sub-Alfvénic shear flow. For further investigation, we also found that the built-up island is not developed so larger due to the pairs of discontinuities formed in the inflow region of the reconnection. For the fixed initial asymptotic shear flow velocity v0, there existing a critical value λvc fastest to excite the secondary island. The critical value λvc may vary with different v0. Although, there is a significant gap for reconnection rates between the simulation results and observations, it can be deduced that the discontinuities can be formed in the situations with sheared flows associated with the magnetic reconnection. The results can be applied to interpret the multiple-X lines reconnections and discontinuities observations at the Earth's dayside magnetopause and magnetotail.

A resistive MHD model and simulation on plasma flow evolution in the presence of resonant magnetic perturbation in a tokamak

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.

Generation of B y in Earth’s magnetotail with the effect of IMF B y during southward interplanetary magnetic field

Based on the three-dimensional compressible resistive MHD models, the Earth’s dipole magnetic field is employed to investigate IMF By penetration driven by the solar wind during southward interplanetary magnetic field (IMF) with uniform resistivity. It is found that the magnetic field By is built up in the central plasma sheet of the Earth’s magnetotail. When θ = 30° (where BIMFy = BIMF sin θ), the magnetic field By in the plasma sheet is the strongest and even larger than the initial imposed BIMFy. In addition, BIMFy promotes the reconnection process of dayside magnetopause. With a further increase in θ, the reconnection rate of dayside magnetopause and the magnetic field By decrease, and the structure changes significantly. The results can be used to analyze the observed data of IMF By penetration.

Configurations of Earth’s magnetosphere in response to variations in z component Solar-wind flow during the southward IMF

Based on the compressible resistive MHD models, the Earth’s dipole magnetic field is employed to investigate magnetic reconnection driven by the solar wind with southward interplanetary magnetic field. By including the z-component solar wind velocity vswz in a three-dimensional compressible global resistive MHD simulation with uniform resistivity, we found that vswz does not affect the location of magnetic reconnection on the dayside magnetopause in the interaction of southward magnetic field of the solar wind with the Earth’s dipole field. However, significant deviation of the central plasma sheet in the magnetotail from equatorial plane can occur. Detailed study also shows that vswz promotes magnetic reconnection at the dayside magnetopause, and the reconnection rate and deviation of magnetotail current sheet both increase with vswz. In particular, the deviation angle increases linearly with vswz. The results here can be useful for understanding observed substorm behavior in the magnetosphere.

A discontinuous Galerkin method for a two dimensional reduced resistive MHD model

We are concerned with the numerical approximation of an incompressible ionized gas (plasma) flowing in a toroidal geometry. We also assume that the flow is independent of the toroidal coordinate and the resulting model is thus 2-D. We consider a symmetric formulation, the so-called Reduced Resistive MHD model, where the governing equation gives the evolution of the axial current and vorticity (scalar variables). These equations are written in a quasi conservative form and, using the Discontinuous Galerkin (DG) framework, an approximation strategy is proposed and analyzed for triangular meshes. This approach combines a Galerkin projection of the velocity stream function and magnetic flux to obtain divergence-free approximations, together with a DG approximation of the evolutionary equations for current and vorticity, while the integration is performed using Crank–Nicholson scheme. The designed methodology is validated on the kink-mode and the tilting MHD instabilities.

Unstable spectra of double tearing modes with anti-symmetric shear flow

The linear properties of both even and odd double tearing modes (DTMs) in the presence of plasma shear flow are studied based on a reduced resistive MHD model in slab geometry. It is found that for the anti-symmetric shear flow, the linear growth rates γ(ky) of the even (odd) eigenmode of DTMs decrease (increase) with increasing the strength of shear flow. Indeed, in the small wavenumber ky regime, γ(ky) of the even eigenmode is larger than that of the odd eigenmode, while γ(ky) of two kinds of eigen states coalesce with each other (the same growth rate and opposite frequencies) when the wavenumber ky exceeds a critical value kyC. It is demonstrated that kyC decreases with decreasing η for a fixed separation between two resonant surfaces xs, while decreasing xs increases the critical value of kyC for a fixed shear velocity. In the nonlinear regime for a low value of resistivity, it is observed that by increasing the strength of anti-symmetric shear flow, in the early phase of the abrupt regime a monster plasmoid and subsidary small plasmoids are generated, and later they are ejected from the DTM current sheet and merged with the main DTM islands.

Simulation study on a merging core fueling technique for an advanced fuel fusion spherical tokamak reactor

With respect to a particle fueling method in a spherical tokamak reactor with an advanced fuel, we investigate the availability of a merging process following the translation of a small torus plasma through which a plasma current flows in the same direction as the main plasma. A three-dimensional resistive MHD model is used to examine the particle fueling effect by reproducing the translation process and simultaneously performing an ion trajectory calculation. The simulation shows the merging process between the translated plasma and the main plasma and exhibits potential as a particle fueling method. The results of the study indicate that up to 30% of the ions in the secondary plasma are supplied to the main plasma.

Filaments in the edge confinement region of TJ-II

Floating potential measurements from two remote reciprocating probes in the plasma edge region of the TJ-II stellarator are analyzed using the transfer entropy, revealing the spatial dimensions and propagation properties of filamentary structures. The results are corroborated by performing simulations with a resistive MHD model and analyzing data from synthetic diagnostics. The transfer entropy captures the rotation of the filaments and allows the calculating of their rotation velocity. This deduced velocity was compared to the (known) poloidal velocity of the plasma and showed a relatively good agreement.

Kinetic modeling of 3D equilibria in a tokamak

External resonant magnetic perturbations (RMPs) can modify the magnetic topology in a tokamak. In this case the magnetic field cannot generally be described by ideal MHD equilibrium equations in the vicinity of resonant magnetic surfaces where parallel and perpendicular relaxation timescales are comparable. Usually, resistive MHD models are used to describe these regions. In the present work, a kinetic model is used for this purpose. Within this model, plasma response, current and charge density are computed with help of a Monte Carlo method, where guiding center orbit equations are solved using a semianalytical geometrical integrator. Besides its higher efficiency in comparison to usual integrators this method is not sensitive to noise in field quantities. The computed charges and currents are used to calculate the electromagnetic field with help of a finite element solver. A preconditioned iterative scheme is applied to search for a self-consistent solution. The discussed method is aimed at the nonlinear kinetic description of RMPs in experiments on Edge Localized Mode (ELM) mitigation by external perturbation coil systems without simplification of the device geometry.

On the magnetic reconnection of resistive tearing mode with the dynamic flow effects

Magnetic reconnection usually occurs in turbulent environments, which may not only provide anomalous resistivity to enhance reconnection rates but also significantly modify the reconnection process through direct nonlinear interaction with magnetic islands. This study presents numerical simulations investigating the effects of an imposed dynamic flow on magnetic reconnection, based on a two-dimensional reduced resistive MHD model. Results show that while the linear stability properties of the resistive tearing mode are moderately affected by the dynamic flow, nonlinear evolution is significantly modified by radial parity, amplitude, and frequency of the dynamic flow. After the slowly evolving nonlinear Rutherford stage, the reconnection process is found to progress in two phases by including the dynamic flow. A Sweet-Parker like current sheet is formed in the first phase. Afterwards, plasmoid instability is triggered in the second phase, where multiple plasmoids are continuously generated and ejected along the current sheet, leading to an impulsive bursty reconnection. The reconnection rate is considerably enhanced in the range of low resistivity as compared to without flow. We found that plasmoid instability onset and evolution are strongly influenced by the frequency and radial parity of the dynamic flows. The scaling of effective reconnection rates with the flow is found to be independent of resistivity.

A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

A positivity-preserving discontinuous Galerkin (DG) scheme [42] is used to solve the Extended Magnetohydrodynamics (XMHD) model, which is a two-fluid model expressed with a center-of-mass formulation. We prove that DG scheme with a positivity-preserving limiter is stable for the system governed by the XMHD model or the resistive MHD model. We use the relaxation system formulation [28] for describing the XMHD model, and solve the equations using a split level implicit–explicit time advance scheme, stepping over the time step constraint imposed by the stiff source terms. The magnetic field is represented in an exact locally divergence-free form of DG [23], which greatly improves the accuracy and stability of MHD simulations. As presently constructed, the method is able to handle a wide range of density variations, solve XMHD model on MHD time scales, and provide greatly improved accuracy over a Finite Volume implementation of the same model.

Eigenmode characteristics of the double tearing mode in the presence of shear flows

The double tearing mode (DTM) is characterized by two eigen states with antisymmetric or symmetric magnetic island structure, referred to as the even or odd DTM. In this work, we systematically revisit the DTM instabilities in the presence of an antisymmetric shear flow with a focus on eigenmode characteristics as well as the stabilization or destabilization mechanism in a wide parameter region. Both initial value simulation and eigenvalue analysis are performed based on reduced resistive MHD model in slab geometry. A degenerated eigen state is found at a critical flow amplitude vc. The even (or odd) DTM is stabilized (or destabilized) by weak shear flow below vc through the distortion of magnetic islands mainly due to the global effect of shear flow rather than the local flow shear. The distortion can be quantified by the phase angles of the perturbed flux, showing a perfect correspondence to the growth rates. As the shear flow increases above vc, the degenerated eigen state bifurcates into two eigen modes with the same growth rate but opposite propagating direction, resulting in an oscillatory growth of fluctuation energy. It is identified that two eigen modes show the single tearing mode structure due to the Alfvén resonance (AR) occurring on one current sheet. Most importantly, the AR can destabilize the DTMs through enhancing the plasma flow exerting on the remaining island. Meanwhile, the local flow shear plays a remarkable stabilizing role in this region. In addition, the eigenmode characteristic of the electromagnetic Kelvin-Helmholtz instability is also discussed.

EFFECTS OF RESISTIVITY ON MAGNETIZED CORE-COLLAPSE SUPERNOVAE

We studied roles of a turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out 2D-resistive-MHD simulations. The three cases with different initial strengths of magnetic field and rotation are investigated; 1. strongly magnetized rotating core; 2.moderately magnetized rotating core; 3. very strongly magnetized non-rotating core. In each case, both an ideal-MHD model and resistive-MHD models are computed. As a result of computations, each model shows a matter eruption helped by a magnetic acceleration (and also by a centrifugal acceleration in the rotating cases). We found that a resistivity attenuates the explosion in case~1 and 2, while it enhances the explosion in case~3. We also found that in the rotating cases, main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of magnetic field and a winding of poloidal magnetic field-lines by differential rotation, which are somewhat dampened down with the presence of a resistivity. Although the magnetorotational instability seems to occur in the rotating models, it will play only a minor role in a magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matters, $> 2.5$, attained in a ideal-MHD model is reduced to some extent in a resistive model. These results indicate that a resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae.

RADIATION MAGNETOHYDRODYNAMIC SIMULATIONS OF PROTOSTELLAR COLLAPSE: PROTOSTELLAR CORE FORMATION

We report the first three-dimensional radiation magnetohydrodynamic (RMHD) simulations of protostellar collapse with and without Ohmic dissipation.We take into account many physical processes required to study star formation processes, including a realistic equation of state. We follow the evolution from molecular cloud cores until protostellar cores are formed with sufficiently high resolutions without introducing a sink particle. The physical processes involved in the simulations and adopted numerical methods are described in detail.We can calculate only about one year after the formation of the protostellar cores with our direct three-dimensional RMHD simulations because of the extremely short timescale in the deep interior of the formed protostellar cores, but successfully describe the early phase of star formation processes. The thermal evolution and the structure of the first and second (protostellar) cores are consistent with previous one-dimensional simulations using full radiation transfer, but differ considerably from preceding multi-dimensional studies with the barotropic approximation. The protostellar cores evolve virtually spherically symmetric in the ideal MHD models because of efficient angular momentum transport by magnetic fields, but Ohmic dissipation enables the formation of the circumstellar disks in the vicinity of the protostellar cores as in previous MHD studies with the barotropic approximation. The formed disks are still small (less than 0.35 AU) because we simulate only the earliest evolution. We also confirm that two different types of outflows are naturally launched by magnetic fields from the first cores and protostellar cores in the resistive MHD models.

Slow shock formation and structure with sub‐Alfvénic shear flow in magnetic reconnection

Slow shock formation and structure associated with magnetic reconnection are investigated in the presence of sub‐Alfvénic shear flow using a compressible resistive MHD model. It is found for the first time that one or two pairs of the slow shocks are formed in the inflow region away from the reconnection separatrices within compressible resistive MHD. The distributions of the slow shocks depend largely on the plasma beta and the shear flow velocity that lead to the increase of magnetic reconnection rate. One pair of the slow shocks is formed for β = 0.2 and two pairs of the slow shocks are generated for β = 1.0 with the shear flow velocity in the range 0.6 VA to 0.9 VA. For high plasma beta (β = 5.0), there is no slow shock formed outside the reconnection separatrices. The results can be applied to interpret slow shock observations at the dayside magnetopause.

Achieving fast reconnection in resistive MHD models via turbulent means

Abstract. Astrophysical fluids are generally turbulent and this preexisting turbulence must be taken into account for models of magnetic reconnection in astrophysical, solar or heliospheric environments. In addition, reconnection itself induces turbulence which provides an important feedback on the reconnection process. In this paper we discuss both the theoretical model and numerical evidence that magnetic reconnection becomes fast in the approximation of resistive MHD. We consider the relation between the Lazarian and Vishniac turbulent reconnection theory and Lapenta's numerical experiments testifying of the spontaneous onset of turbulent reconnection in systems which are initially laminar.

Summary of Papers on ECRH Experiments

The presentations on ECRH experiments presented in EC-17 are summarized. Real time control, feedback control One of the hot topics of ECRH experiment discussed in this workshop was real time control or feed back control fully utilizing local controllability and fast time response of the ECRH system. The real time system for MHD activity control in the FTU tokamak is presented by C. Sozzi, where the several hardware and control argolism for the feedback control of MHD activities (sawtooth, NTM) are implemented and initial test was successfully executed. Related series of papers on FTU are presented by E. Alessi, C. Galperti and A. Moro. ELM control or pacing as well as the suppression of the MHD instabilities is also a hot topic of ECRH experiment and outstanding experimental results in TCV are presented by F. Ferici and M. Lauret. Utilizing newly installed real-time antenna control system with flexible digital real time control system, sawtooth pacing, ELM pacing, NTM suppression are demonstrated. J. Lohr also reported a fine control scheme developed and executed in DIII-D using the plasma control system (PCS) and field program gate array (FPGA) witch are connected also to ECRH system allowing fast control of the injection angle and gyrotron output power. These capabilities are utilized to control plasma instabilities and secure operation of the gyrotrons as well. New fast steerable launcher and ”NTM feedback suite” (equilibrium, density profile, ray tracing, correlation analysis, mirror control) are implemented in ASDEX U are also presented in the talk of J. Stober. Feedforward test of the system were already done and waiting for the feedback control demonstration. ECH and ECCD effects on NTMs stabilization by ECRH is also investigated for JT-60SA tokamak and presented by C. Sozzi. ECRH system upgrades and demonstration of its potential In the presentations of the application of ECRH on the DIII-D Tokamak, R. Prater thoroughly reviewed potential of ECRH in the investigation of the tokamak operation and indicated the upgrading scenario of the ECRH system in the DIII-D. Topics included are the electron heating effects related to the study of plasma rotation and H-mode threshold power, Te profile control for validation of the NBCD model or RWM control , modeling ITER startup and rampdown, modifying the temperature gradient for studying the transition, trapped electron mode, and QH-mode. ECCD was applied to drive currents in the plasma in ITER demonstration steady-state discharges for radially distributed current drive in support of fully noninductive operation at high beta, control of neoclassical tearing modes for experiments on resistive wall modes in low rotation, high beta discharges, for neoclassical tearing a e-mail: kubo@lhd.nifs.ac.jp EPJ Web of Conferences DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2012 , epjconf 201232 / 020 (2012) 02 32 0 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 01 01 Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20123202001 EPJ Web of Conferences mode control using oblique electron cyclotron emission as a diagnostic to determine robustly the optimum location of the ECCD, studies of the validation of resistive MHD models and development of model-based current profile control. In accordance to the increasingly important role of the ECRH, it is reported that the ECRH system is proposed to be upgrade to total injection power up to 12 MW. In ASDEX U, J. Stober reported undergoing upgrade of multi frequency system (140/105 GHz) and injected power reached 3.9 MW at 140 GHz and 2.1 MW at 105 GHz. Such enhanced ECRH power was used for several physics studies such as H-mode optimization. In relation to the system upgrades, monitoring the stray radiation in the vacuum vessel is also an important issue and M. Schubert discussed the Sniffer probes and large area bolometer detectors. J. H. Jeong reported the successful commissioning of 170 GHz, 1MW ECH& CD system in KSTAR. High power long pulse injection experiments are expected to start soon. Detailed Physics Study

Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

FreeFem++ is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma in the context of the ITER project. First we consider the Grad-Shafranov equation, which is derived from the static ideal MHD equations assuming axisymetry. Some of the properties of the equation and its analytical solutions are discussed. Second we discretize a reduced resistive MHD model which admits solutions of the Grad-Shafranov equation as stationary solutions. Then the physical stability of these stationary solutions is investigated through numerical experiments and the numerical stability of the algorithm is discussed.

Conservative numerical methods for a two-temperature resistive MHD model with self-generated magnetic field term

We propose numerical methods on Cartesian meshes for solving the 2-D axisymmetric two-temperature resistivive magnetohydrodynamics equations with self-generated magnetic eld and Braginskii's (1) closures. These rely on a splitting of the complete system in several subsystems ac- cording to the nature of the underlying mathematical operator. The hyperbolic part is solved using conservative high-order dimensionally split Lagrange-remap schemes whereas semi-implicit diusion operators have been developed for the thermal and resistive conduction equations. Source terms are treated explictly. Numerical results on the deceleration phase of an ICF implosion test problem are proposed, a benchmark which was initially proposed in (2). R esum