Resistive Magnetohydrodynamic Model Research Articles

3D Multi‐Fluid MHD Simulation of the Early Time Behavior and Cross‐Field Propagation of an Artificial Plasma Cloud in the Bottom Side Ionosphere

AbstractThe relative motion of an artificial plasma stream in an ambient plasma background transverse to the geomagnetic field produces a polarization current and an drift in the direction of the injected photoionized neutral cloud. The polarization current couples the ion cloud momentum to the ambient plasma causing the stream to brake or “skid” before coming to rest. A multi‐fluid five‐moment resistive magnetohydrodynamic (MHD) model has been previously developed and is used in this study to simulate an artificial barium cloud released at 8 km/s in the lower ionosphere transverse to the magnetic field. The MHD model’s governing equations are used to derive 2D analytical solutions to the equations of motion that capture oscillatory behavior relating the cloud ion cyclotron frequency, artificial and ambient plasma density, initial release velocity, and photoionization rate. The analytical solutions are compared to the MHD results for time t < 1 s and previous 1D momentum coupling models. It is shown that motion in the cloud release direction is consistent with previous models while motion in the polarization direction is consistent with numerical results.

Numerical model of restrikes in gliding arc discharges

Abstract Direct current (DC) electric arcs are of particular interest because they can produce large volumes of thermal plasmas with controlled energy deposition. When such discharges are applied in a gas flow, convection displaces the top of the arc downstream while the arc roots remain attached to the electrodes, thus increasing the length of the arc over time. However, this growth is limited by a restrike phenomenon, which starts from streamers appearing in high electric field regions and shortcutting the long, stretched electric arc. From a numerical point of view, DC arcs can be efficiently simulated with a resistive magneto-hydrodynamics (MHD) model, with numerical requirements in terms of spatial and temporal discretization that are compatible with classic fluid dynamics and combustion simulations. However, arc restrikes rely on the propagation of streamer discharges that are highly non-neutral phenomena, whereas classical MHD assumes neutrality. To tackle this problem, we propose in this paper a model of restrike that can be used in an MHD approach. After describing the ideas of the model, we perform a parametric study of the input parameters to examine its influence on the discharge dynamics.

The virtual element method for the 3D resistive magnetohydrodynamic model

We present a four-field virtual element discretization for the time-dependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity assumptions, which is validated by some numerical tests.

Experimental characterization and modelling of the resistive wall mode response in a reversed field pinch

Model-based control algorithms have potential advantages for resistive wall mode (RWM) feedback control. In this study, a physics model of the RWM response to externally applied perturbation fields is validated against experiments in a reversed field pinch (RFP). The experimental characterization of the RWM plasma response is performed in the EXTRAP T2R device by the excitation of nonaxisymmetric perturbation magnetic fields utilizing an external array of saddle coils for RWM control. The modelling and experimental validation is carried out with an extended sensor array, resolving a wider spectrum of RWM compared to earlier studies, covering the relevant poloidal and toroidal modes for this high aspect ratio RFP device. In addition to the nonresonant unstable modes, which are the primary target of RWM feedback control, this spectrum also includes a wide range of resonant modes. The validated resistive magnetohydrodynamics (MHD) model includes the passive stabilization effect on these modes from intrinsic plasma rotation. The inclusion of resistivity and plasma rotation in the present model provides a substantially better agreement between modelled and experimental growth rates than that observed in earlier studies using the ideal MHD model. The present model provides a realistic description of the plasma response for both nonresonant and resonant modes, which is both relatively simple and compatible with the computing capabilities and latency limitations encountered in practical implementations of model-based control algorithms.

The impact of radial electric fields and plasma rotation on intermittence in TJ-II

This work explores the impact of an imposed radial electric field on the intermittence parameter in magnetically confined plasmas. The intermittence is sensitive to both the magnetic configuration (dominant helical modes or low order rational surfaces) and to poloidal flows or radial electric fields. This behaviour was verified both in numerical turbulence calculations using a resistive magnetohydrodynamic model, and using Langmuir probe data obtained in experiments at the TJ-II stellarator. It is shown that the intermittence parameter can be used to detect when the local plasma rotation velocity, with respect to the laboratory frame of reference, is minimum.

Topology of 2D turbulent structures based on intermittence in the TJ-II stellarator

This work estimates the degree of turbulent intermittence of the plasma potential measured by a heavy ion beam probe in the core plasma region of the TJ-II stellarator. It is shown that the intermittence varies in a significant way with the plasma state (ion or electron root). In addition, radial minima of the intermittence are found to be associated with the location of topological structures of the flow associated with some important low-order rational surfaces. The local pressure gradient was also estimated, and a clear correlation was found between the steepening of the pressure gradient and the deepening of the minima of the intermittence, suggesting that the minima are associated with pressure gradient driven modes. By estimating the rotation velocity of the plasma from the measured plasma potential, it was possible to make a rough reconstruction of the two-dimensional radial–poloidal map of intermittence, thus clarifying the topological structure of the intermittence. The experimental results were put into context by comparing with simulations performed using a resistive magneto-hydrodynamic turbulence model.

The virtual element method for resistive magnetohydrodynamics

We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method include great flexibility of polygonal meshes and automatic divergence-free constraint on the magnetic flux field. In this work, we rigorously prove the well-posedness of the method and the solenoidal nature of the discrete magnetic flux field. We also derive stability energy estimates. The design of the method includes three choices for the construction of the nodal mass matrix and criteria to more alternatives. This approach is novel in the VEM literature and allows us to preserve a commuting diagram property. We present a set of numerical experiments that independently validate theoretical results. The numerical experiments include the convergence rate study, energy estimates and verification of the divergence-free condition on the magnetic flux field. All these numerical experiments have been performed on triangular, perturbed quadrilateral and Voronoi meshes. Finally, we demonstrate the development of the VEM method on a numerical model for Hartmann flows as well as in the case of magnetic reconnection.

Numerical Simulation on the Formation and Pinching Plasma in X-pinch Wires on 2-D Geometry

This paper deals with the computational work to characterize the formation and pinching of a plasma in an X-pinch configuration. A resistive magnetohydrodynamic model of a single fluid and two temperature is adopted assuming a hollow conical structure in the (r,z) domain. The model includes the thermodynamic parameter of tungsten from the corrected Thomas-Fermi EOS(equation of state), determining the average ionization charge, pressure, and internal energy. The transport coefficients, resistivity and thermal conductivity, are obtained by the corrected Lee & More model and a simple radiation loss rate by recombination process is considered in the simulation. The simulation demonstrated the formation of a core-corona plasma and intense compression process near the central region which agrees with the experimental observation in the X-pinch device at Seoul National University. In addition, it confirmed the increase in radiation loss rate with the density and temperature of the core plasma. Keywords: X-pinch, Magnetohydrodynamics, Exploding Wires Keywords: 엑스핀치, ìžê¸°ìœ ì²´ì—­í•™, ì„¸ì„ í­ë°œ

The localization of low order rational surfaces based on the intermittence parameter in the TJ-II stellarator

This work intends to show that the multifractal concept of intermittence can be fruitfully applied to the identification of the radial location of low order rational surfaces inside a magnetically confined plasma. To do so, we make use of Langmuir probe data from a set of experiments in which the rotational transform was scanned dynamically in the TJ-II stellarator. It is shown that up to five rational surfaces can be identified from the data, which is a first in plasma physics, to the best of our knowledge. The effect of the radial electric field on intermittence was also studied using a specific subset of experiments in which the electron density was raised on a shot by shot basis. The observations are contrasted with results from numerical calculations using a resistive magneto-hydrodynamic model to facilitate interpretation.

ELM control optimization for various ITER scenarios based on linear and quasi-linear figures of merit

For the purpose of better understanding type-I edge localized mode (ELM) control in ITER with resonant magnetic perturbation (RMP) fields, the plasma response to RMP is computed by a resistive full magneto-hydrodynamic model in toroidal geometry. Five scenarios designed for ITER are considered, ranging from the pre-nuclear to nuclear phases. The plasma response to RMP is quantified by the plasma surface displacement near the X-point of the divertor plasma and at the outboard mid-plane. The optimal coil configurations between two high-Q deuterium-tritium (DT) scenarios (at the same plasma current of 15 MA and the same magnetic field of 5.3 T but different fusion gains, Q = 5 and 10) are predicted to be similar. For the other ITER scenarios with similar edge safety factor q95 ∼ 3 to that of the baseline scenario, the optimal coil phasing is also similar. The optimization results are different for a half-current full-field (7.5 MA/5.3 T) scenario, largely due to the difference in q95. The RMP coil currents are also optimized to tailor the core vs edge toroidal torques exerted by the 3D RMP fields on the plasma column. Torque optimization, with various objective functions proposed in the study, is useful for minimizing the side effects of RMP on the plasma core flow in ITER, while still maintaining the ELM control capability. Full utilization of three rows of ELM control coils in ITER is found to be essential to ensure both flexibility and robustness of ELM control, in terms of both linear and quasi-linear plasma responses.

Spatial scales and locality of magnetic helicity

Context. Magnetic helicity is approximately conserved in resistive magnetohydrodynamic models. It quantifies the entanglement of the magnetic field within the plasma. The transport and removal of helicity is crucial in both dynamo development in the solar interior and active region evolution in the solar corona. This transport typically leads to highly inhomogeneous distributions of entanglement. Aims. There exists no consistent systematic means of decomposing helicity over varying spatial scales and in localised regions. Spectral helicity decompositions can be used in periodic domains and is fruitful for the analysis of homogeneous phenomena. This paper aims to develop methods for analysing the evolution of magnetic field topology in non-homogeneous systems. Methods. The method of multi-resolution wavelet decomposition is applied to the magnetic field. It is demonstrated how this decomposition can further be applied to various quantities associated with magnetic helicity, including the field line helicity. We use a geometrical definition of helicity, which allows these quantities to be calculated for fields with arbitrary boundary conditions. Results. It is shown that the multi-resolution decomposition of helicity has the crucial property of local additivity. We demonstrate a general linear energy-topology conservation law, which significantly generalises the two-point correlation decomposition used in the analysis of homogeneous turbulence and periodic fields. The localisation property of the wavelet representation is shown to characterise inhomogeneous distributions, which a Fourier representation cannot. Using an analytic representation of a resistive braided field relaxation, we demonstrate a clear correlation between the variations in energy at various length scales and the variations in helicity at the same spatial scales. Its application to helicity flows in a surface flux transport model show how various contributions to the global helicity input from active region field evolution and polar field development are naturally separated by this representation. Conclusions. The multi-resolution wavelet decomposition can be used to analyse the evolution of helicity in magnetic fields in a manner which is consistently additive. This method has the advantage over more established spectral methods in that it clearly characterises the inhomogeneous nature of helicity flows where spectral methods cannot. Further, its applicability in aperiodic models significantly increases the range of potential applications.

Suppression and saturation of error field-driven tearing mode for different magnetic shears in rotating plasmas

Effects of the equilibrium plasma flow on the error field-driven tearing mode are investigated in a two-dimensional resistive magnetohydrodynamics model. It is found that nonlinear suppression of the tearing mode is dominated by the interaction between the magnetic island and the error field rather than the local flow shear on rational surfaces. For a small magnetic shear case, a modest rigid flow can counteract the driving effect of the error field on the mode in the early nonlinear growth stage and transform the error field-driven mode to a general tearing mode. For a large magnetic shear case, after a fast linear growth, the tearing mode will enter a saturated process quickly before the locked mode occurs, and the mode saturation level is reduced due to the magnetic island and error field pushing each other. The threshold flow strength and its scaling analysis for the saturated modes are also given in this paper.

Numerical study of linear plasma dynamics in a spherical tokamak

The magnetohydrodynamic equilibrium is the starting point to study macro- instabilities in a confined plasma; for the particular case, where the system is axially symmetric, the static and stationary equilibrium is due by the Grad-Shafranov equation. We present the equilibrium state for a toroidal plasma confined by a spherical Tokamak with aspect ratio A ∼1.6, total plasma current 1.3 MA and beta parameter β ∼0.35. The Grad-Shafranov equation is solved numerically in a rectangular region of the poloidal plane, using the finite differences method under a successive over-relaxation scheme. Profiles of poloidal magnetic flux, pressure, safety factor and magnetic field are presented. Subsequently, by using the resistive magnetohydrodynamic model, said equilibrium is subjected to perturbations in the velocity to study the dynamics of the plasma in the linear regime. The plasma dynamics simulation is carried out under a fourth order finite difference scheme for the spatial derivatives and implementing the Runge-Kutta algorithm as a temporal integrator. The results show that the perturbations are located in the plasma outer edge; however, some poloidal modes move toward the central zone around the magnetic axis.

Influence of 3D plasmoid dynamics on the transition from collisional to kinetic reconnection

Within the resistive magnetohydrodynamic model, high-Lundquist number reconnection layers are unstable to the plasmoid instability, leading to a turbulent evolution where the reconnection rate can be independent of the underlying resistivity. However, the physical relevance of these results remains questionable for many applications. First, the reconnection electric field is often well above the runaway limit, implying that collisional resistivity is invalid. Furthermore, both theory and simulations suggest that plasmoid formation may rapidly induce a transition to kinetic scales, due to the formation of thin current sheets. Here, this problem is studied for the first time using a first-principles kinetic simulation with a Fokker-Planck collision operator in 3D. The low-β reconnecting current layer thins rapidly due to Joule heating before the onset of the oblique plasmoid instability. Linear growth rates for standard (ky = 0) tearing modes agree with semicollisional boundary layer theory, but the angular spectrum of oblique (|ky|>0) modes is significantly narrower than predicted. In the nonlinear regime, flux-ropes formed by the instability undergo complex interactions as they are advected and rotated by the reconnection outflow jets, leading to a turbulent state with stochastic magnetic field. In a manner similar to previous 2D results, super-Dreicer fields induce a transition to kinetic reconnection in thin current layers that form between flux-ropes. These results may be testable within new laboratory experiments.

The Radial Propagation of Heat in Strongly Driven Non-Equilibrium Fusion Plasmas.

Heat transport is studied in strongly heated fusion plasmas, far from thermodynamic equilibrium. The radial propagation of perturbations is studied using a technique based on the transfer entropy. Three different magnetic confinement devices are studied, and similar results are obtained. “Minor transport barriers” are detected that tend to form near rational magnetic surfaces, thought to be associated with zonal flows. Occasionally, heat transport “jumps” over these barriers, and this “jumping” behavior seems to increase in intensity when the heating power is raised, suggesting an explanation for the ubiquitous phenomenon of “power degradation” observed in magnetically confined plasmas. Reinterpreting the analysis results in terms of a continuous time random walk, “fast” and “slow” transport channels can be discerned. The cited results can partially be understood in the framework of a resistive Magneto-HydroDynamic model. The picture that emerges shows that plasma self-organization and competing transport mechanisms are essential ingredients for a fuller understanding of heat transport in fusion plasmas.

Applicability of transfer entropy for the calculation of effective diffusivity in heat transport

A method has been proposed to study heat transport in magnetically confinement plasmas, based on the transfer entropy (TE). In this work, we study this method by introducing perturbations in simulations made using a resistive Magneto-HydroDynamic model. The evolution of radial heat transport is monitored using the TE, and these results are used to compute an effective heat diffusivity. This effective diffusivity is then compared to estimates from other methods. The analysis is applied to several numerical simulations and in various radial ranges. It is shown that the transfer entropy is a suitable technique to analyze heat transport and evaluate an effective diffusivity in fusion plasmas.

Study of radial heat transport in W7-X using the transfer entropy

In this work, we analyze data obtained using the electron cyclotron emission radiometer at the Wendelstein 7-X stellarator using a relatively new technique: the transfer entropy. Thus, we detect the propagation of information and find that it occurs in a stepwise fashion: we observe both ‘trapping zones’ and radial ‘jumps’, when the information is apparently skipping over intermediate positions. Using scans of the rotational transform, we observe that the ‘trapping zones’ appear to be associated with rational surfaces. Power scan experiments show that these ‘jumps’ increase in importance when power is increased, thus enhancing the effective diffusivity. The observations are interpreted in terms of a resistive magneto-hydrodynamic model, which displays behavior similar to the experimental results. The ‘trapping zones’ are explained in terms of zonal flows associated with rational surfaces, while the ‘jumps’ are ascribed to mode coupling effects, i.e. the transmission of turbulent energy via the magnetic field.

A plasma–vacuum interface tracking algorithm for magnetohydrodynamic simulations of coaxial plasma accelerators

The resistive Magneto-hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. For problems involving the plasma with an open boundary to very low pressure/vacuum regions, the continuum assumption is no longer valid in the entire domain of interest. For example, this is seen in a plasma accelerator where a dense plasma expands into a vacuum background. A common practice to deal with this issue is to assign small values of density and pressure to the vacuum regions and proceed to solve the continuum based MHD equations throughout the domain. We show that this approach fails to produce solutions consistent with the physics of the problem and can give rise to unacceptable artifacts such as spurious shocks. We develop a plasma–vacuum interface tracking approach to mitigate this problem. The plasma–vacuum interface is tracked in a physically consistent manner and the MHD equations are solved only in the regions that contain the plasma. The interface tracking is achieved using a face-flux formulation derived from the theoretical solution to a 1D free expansion problem. Coupled with a threshold based approach, the interface tracking is implemented for both explicit and implicit time stepping frameworks on generalized unstructured grids. Simulations of magnetized thermal plasma jets expanding into a vacuum background indicate plume profiles devoid of the unphysical shock obtained using the small background density approach. In the context of resistive MHD simulations, the interface tracking approach overcomes the numerical stiffness induced by specifying a large background resistivity in the vacuum regions, resulting in significant wall-clock time gains.

Ideal and Resistive Magnetohydrodynamic Two-Dimensional Simulation of the Kelvin-Helmholtz Instability in the Context of Adaptive Multiresolution Analysis

This work is concerned with the numerical simulation of the Kelvin-Helmholtz instability using a two-dimensional resistive magnetohydrodynamics model in the context of adaptive multiresolution approach. The Kelvin-Helmholtz instabilities are caused by a velocity shear and normally expected in a layer between two fluids with different velocities. Due to its complexity, this kind of problem is a well-known test for numerical schemes and it is important for the verification of the developed code. The aim of this paper is to compare our solution with the solution of the well known astrophysics FLASH code to verify our code in respect to this reference.

Shock formation and structure in magnetic reconnection with a streaming flow

The features of magnetic reconnection with a streaming flow have been investigated on the basis of compressible resistive magnetohydrodynamic (MHD) model. The super-Alfvenic streaming flow largely enhances magnetic reconnection. The maximum reconnection rate is almost four times larger with super-Alfvenic streaming flow than sub-Alfvénic streaming flow. In the nonlinear stage, it is found that there is a pair of shocks observed in the inflow region, which are manifested to be slow shocks for sub-Alfvénic streaming flow, and fast shocks for super-Alfvénic streaming flow. The quasi-period oscillation of reconnection rates in the decaying phase for super-Alfvénic streaming flow is resulted from the different drifting velocities of the shock and the X point.