3D Non-linear MHD Research Articles

Interpretative 3D MHD modelling of deuterium SPI into a JET H-mode plasma

The pre-thermal quench (pre-TQ) dynamics of a pure deuterium ( D2 ) shattered pellet injection (SPI) into a 3MA / 7MJ JET H-mode plasma is studied via 3D non-linear MHD modelling with the JOREK code. The interpretative modelling captures the overall evolution of the measured density and radiated power. The simulations also identify the importance of the drifts of ablation plasmoids towards the tokamak low field side (LFS) and the impurities in the background plasma in fragment penetration, assimilation, radiative cooling and MHD activity in D2 SPI experiments. It is found that plasmoid drifts lead to an about 70% reduction of the central line-integrated density (compared to a simulation without drifts) in the JET D2 SPI discharge considered. Impurities that pre-exist before the SPI as well as those from possible impurity influxes related to the SPI are shown to dominate the radiation in the considered discharge. With inputs from JOREK simulations, modelling with the Lagrangian particle-based pellet code PELOTON reproduces the deviation of the SPI fragments in the direction of the major radius as observed by the fast camera. This confirms the role of rocket effects and plasmoid drifts in the considered discharge and reinforces the validity of the JOREK modelling. The limited core density rise due to plasmoid drifts and the strong radiative cooling and MHD activity with impurities (depending on their species and concentration) could limit the effectiveness of LFS D2 SPI in runaway electron avoidance and are worth considering in the design of the ITER disruption mitigation system.

Viscosity impact on 3D non-linear MHD simulations of RFP fusion plasmas

Several studies pointed out the joint role of resistivity η and viscosity ν in determining the dynamics and the emergence of helical regimes of reversed-field pinch (RFP) plasmas. In this framework, the self-consistent time evolution of the η and ν coefficients still lacks of a fully satisfying modeling, being constrained by many approximations. In this work, the hypothesis of a flat viscosity profile is relaxed: A viscosity profile inspired by the Braginskii perpendicular viscosity is implemented in the code. This choice is motivated by the fact that the magnetohydrodynamics field instabilities relevant for the RFP configuration dynamics (resistive-kink/tearing modes) are active in the direction perpendicular to the magnetic field. Such a non-monotonous profile causes a localized damping of plasma flow in the regions, where the viscosity is stronger, close to the plasma edge. This results in the reduction of the flow shear, in turn allowing the enhancement of edge magnetic field modes amplitude. The impact on the magnetic topology and on connection length to the wall is also analyzed.

On the origin of the plasma current spike during a tokamak disruption and its relation with magnetic stochasticity

A JOREK 3D non-linear MHD simulation of a disruption triggered by an argon massive gas injection in JET, which quantitatively reproduces the plasma current () spike (Nardon et al 2021 Plasma Phys. Control. Fusion 63 115006), is analyzed in order to investigate the origin of the spike and its relation with magnetic stochasticity. The spike is associated to a current density (j φ ) profile relaxation which appears to result from Shear Alfvén Wave (SAW) propagation along stochastic field lines, as proposed by Boozer (2019 Plasma Phys. Control. Fusion 61 024002; 2020 Phys. Plasmas 27 102305), possibly complemented by a macroscopic E×B flow structure. Using axisymmetric JOREK simulations involving a mean field Ohm’s law, we verify that the level of hyper-resistivity associated to SAWs is consistent with the prediction made in (Boozer 2019 Plasma Phys. Control. Fusion 61 024002; Boozer 2020 Phys. Plasmas 27 102305), which connects the spike with the level of stochasticity. The relaxation comprises two main phases, the first one corresponding to a fast (0.1 ms) and almost complete j φ flattening in the q < 2 region, while the second one is longer (0.5 ms) and corresponds to a more gradual, global and incomplete j φ flattening. During the first phase, strong E×B flows develop that play a key role in mixing impurities into the core.

Radiation asymmetry and MHD destabilization during the thermal quench after impurity shattered pellet injection

The radiation response and the MHD destabilization during the thermal quench after a mixed species shattered pellet injection with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the n = 0 global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The thermal quench (TQ) is triggered as the fragments arrive on the q = 1 or q = 2 surface depending on the exact q profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than 1 ms. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases.

Scattering of ion cyclotron range of frequency waves by filaments and ELMs

The scattering of ion cyclotron range of frequency (ICRF) waves by filaments and ELMs has been comprehensively studied via modeling. The influence of filaments on the propagation of ICRF waves is studied by building a 2D COMSOL model which solves the wave equation. It is benchmarked against the Mie scattering theoretical model. Cases either with perfect matching layer boundary condition or with poloidal periodic boundary condition are considered. Parameter scans, including the filament density, the filament radius, the number of filaments as well as the distance between filaments, are performed. Then, the influence of ELMs on the propagation of ICRF waves in realistic geometry is studied by importing density distributions calculated by 3D non-linear MHD code JOREK into the 3D antenna code RAPLICASOL. The evolution of density and wave fields during an ELM is analyzed for cases with a low and high scrape-off layer density, respectively. Both the COMSOL simulation and the realistic simulation with JOREK and RAPLICASOL show that the wave fields and Poynting flux can be significantly and globally modified by the ELM filaments. Due to the mutual influence of many density filaments, radially elongated and poloidally distributed stripe structures of the wave fields develop, leading to poloidally inhomogeneous wave fields. Furthermore, the influence of ELMs on the antenna power and antenna coupling resistance is investigated with experimental results in ASDEX Upgrade.

3D non-linear MHD simulation of the MHD response and density increase as a result of shattered pellet injection

The MHD response and the penetration of a deuterium shattered pellet into a JET plasma is investigated via the non-linear reduced MHD code JOREK with the neutral gas shielding (NGS) ablation model. The dominant MHD destabilizing mechanism by the injection is identified as the local helical cooling at each rational surface, as opposed to the global current profile contraction. Thus the injected fragments destabilize each rational surface as they pass through them. The injection penetration is found to be much better compared to MGI, with the convective transport caused by core MHD instabilities (e.g. 1/1 kink) contributing significantly to the core penetration. Moreover, the injection with realistic JET SPI system configurations is simulated in order to provide some insights into future operations, and the impact on the total assimilation and penetration depth of varying injection parameters such as the injection velocity or fineness of shattering is assessed. Further, the effect of changing the target equilibrium temperature or q profile on the assimilation and penetration is also investigated. Such analysis will form the basis of further investigation into a desirable configuration for the future SPI system in ITER.

Electron acceleration in a JET disruption simulation

Runaways are suprathermal electrons having sufficiently high energy to be continuously accelerated up to tens of MeV by a driving electric field (Connor and Hastie 1975 Nucl. Fusion 15 415). Highly energetic runaway electron (RE) beams capable of damaging the tokamak first wall can be observed after a plasma disruption (Reux et al 2015 Nucl. Fusion 55 129501). Therefore, it is of primary importance to fully understand their generation mechanisms in order to design mitigation systems able to guarantee safe tokamak operations. In a previous work, Sommariva et al (2018 Nucl. Fusion 58), a test particle tracker was introduced in the JOREK 3D non-linear MHD code and used for studying the electron confinement during a simulated JET-like disruption. It was found in Sommariva et al (2018 Nucl. Fusion 58) that relativistic electrons are not completely deconfined by the stochastic magnetic field taking place during the disruption thermal quench (TQ). This is due to the reformation of closed magnetic surfaces at the beginning of the current quench (CQ). This result was obtained neglecting the inductive electric field in order to avoid the unrealistic particle acceleration which otherwise would have happened due to the absence of collision effects. The present paper extends (Sommariva et al 2018 Nucl. Fusion 58) analysing test electron dynamics in the same simulated JET-like disruption using the complete electric field. For doing so, a simplified collision model is introduced in the particle tracker guiding center equations. We show that electrons at thermal energies can become RE during or promptly after the TQ due to a combination of three phenomena: a first REs acceleration during the TQ due to the presence of a complex MHD-induced electric field, particle reconfinement caused by the fast reformation of closed magnetic surfaces after the TQ and a secondary acceleration induced by the CQ electric field.

Test particles dynamics in the JOREK 3D non-linear MHD code and application to electron transport in a disruption simulation

In order to contribute to the understanding of runaway electron generation mechanisms during tokamak disruptions, a test particle tracker is introduced in the JOREK 3D non-linear MHD code, able to compute both full and guiding center relativistic orbits. Tests of the module show good conservation of the invariants of motion and consistency between full orbit and guiding center solutions. A first application is presented where test electron confinement properties are investigated in a massive gas injection-triggered disruption simulation in JET-like geometry. It is found that electron populations initialised before the thermal quench (TQ) are typically not fully deconfined in spite of the global stochasticity of the magnetic field during the TQ. The fraction of ‘survivors’ decreases from a few tens down to a few tenths of percent as the electron energy varies from 1 keV to 10 MeV. The underlying mechanism for electron ‘survival’ is the prompt reformation of closed magnetic surfaces at the plasma core and, to a smaller extent, the subsequent reappearance of a magnetic surface at the edge. It is also found that electrons are less deconfined at 10 MeV than at 1 MeV, which appears consistent with a phase averaging effect due to orbit shifts at high energy.

Progress in understanding disruptions triggered by massive gas injection via 3D non-linear MHD modelling with JOREK

3D non-linear MHD simulations of a D2 massive gas injection (MGI) triggered disruption in JET with the JOREK code provide results which are qualitatively consistent with experimental observations and shed light on the physics at play. In particular, it is observed that the gas destabilizes a large m/n = 2/1 tearing mode, with the island O-point coinciding with the gas deposition region, by enhancing the plasma resistivity via cooling. When the 2/1 island gets so large that its inner side reaches the q = 3/2 surface, a 3/2 tearing mode grows. Simulations suggest that this is due to a steepening of the current profile right inside q = 3/2. Magnetic field stochastization over a large fraction of the minor radius as well as the growth of higher n modes ensue rapidly, leading to the thermal quench (TQ). The role of the 1/1 internal kink mode is discussed. An Ip spike at the TQ is obtained in the simulations but with a smaller amplitude than in the experiment. Possible reasons are discussed.

Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D

In the Quiescent H-mode (QH-mode) regime, the edge harmonic oscillation (EHO), thought to be a saturated kink-peeling mode (KPM) driven unstable by current and rotation, is found in experiment to provide sufficient stationary edge particle transport to avoid the periodic expulsion of particles and energy by edge localized modes (ELMs). In this paper, both linear and nonlinear MHD modelling of QH-mode plasmas from the DIII-D tokamak have been investigated to understand the mechanism leading to the appearance of the EHO in QH-mode plasmas. For the first time nonlinear MHD simulations with low-n modes both with ideal wall and resistive wall boundary conditions have been carried out with the 3D non-linear MHD code JOREK. The results show, in agreement with the original conjectures, that in the non-linear phase, kink peeling modes are the main unstable modes in QH-mode plasmas of DIII-D and that the kink-peeling modes saturate non-linearly leading to a 3D stationary state. The characteristics of the kink-peeling modes, in terms of mode structure and associated decrease of the edge plasma density associated with them, are in good agreement with experimental measurements of the EHO in DIII-D. The effect of plasma resistivity, the role of plasma parallel rotation as well as the effect of the conductivity of the vacuum vessel wall on the destabilization and saturation of kink-peeling modes have been evaluated for experimental QH-mode plasma conditions in DIII-D.

Overview of the RFX-mod contribution to the international Fusion Science Program

The RFX-mod device is operated both as a reversed field pinch (RFP), where advanced regimes featuring helical shape develop, and as a tokamak. Due to its flexibility, RFX-mod is contributing to the solution of key issues in the roadmap to ITER and DEMO, including MHD instability control, internal transport barriers, edge transport and turbulence, isotopic effect, high density limit and three-dimensional (3D) non-linear MHD modelling. This paper reports recent advancements in the understanding of the self-organized helical states, featuring a strong electron transport barrier, in the RFP configuration; the physical mechanism driving the residual transport at the barrier has been investigated. Following the first experiments with deuterium as the filling gas, new results concerning the isotope effect in the RFP are discussed. Studies on the high density limit show that in the RFP it is related to a toroidal particle accumulation due to the onset of a convective cell. In the tokamak configuration, q(a) regimes down to q(a) = 1.2 have been pioneered, with (2,1) tearing mode (TM) mitigated and (2,1) resistive wall mode (RWM) stabilized: the control of such modes can be obtained both by poloidal and radial sensors. Progress has been made in the avoidance of disruptions due to the (2,1) TM by applying q(a) control, and on the general issue of error field control. The effect of externally applied 3D fields on plasma flow and edge turbulence, sawtooth control and runaway electron decorrelation has been analysed. The experimental program is supported by substantial theoretical activity: 3D non-linear visco-resistive MHD and non-local transport modelling have been advanced; RWMs have been studied by a toroidal MHD kinetic hybrid stability code.

Wall-touching kink mode calculations with the M3D code

This paper seeks to address a controversy regarding the applicability of the 3D nonlinear extended MHD code M3D [W. Park et al., Phys. Plasmas 6, 1796 (1999)] and similar codes to calculations of the electromagnetic interaction of a disrupting tokamak plasma with the surrounding vessel structures. M3D is applied to a simple test problem involving an external kink mode in an ideal cylindrical plasma, used also by the Disruption Simulation Code (DSC) as a model case for illustrating the nature of transient vessel currents during a major disruption. While comparison of the results with those of the DSC is complicated by effects arising from the higher dimensionality and complexity of M3D, we verify that M3D is capable of reproducing both the correct saturation behavior of the free boundary kink and the “Hiro” currents arising when the kink interacts with a conducting tile surface interior to the ideal wall.

Three-dimensional non-linear magnetohydrodynamic modeling of massive gas injection triggered disruptions in JET

JOREK 3D non-linear MHD simulations of a D2 Massive Gas Injection (MGI) triggered disruption in JET are presented and compared in detail to experimental data. The MGI creates an overdensity that rapidly expands in the direction parallel to the magnetic field. It also causes the growth of magnetic islands (m/n=2/1 and 3/2 mainly) and seeds the 1/1 internal kink mode. O-points of all island chains (including 1/1) are located in front of the MGI, consistently with experimental observations. A burst of MHD activity and a peak in plasma current take place at the same time as in the experiment. However, the magnitude of these two effects is much smaller than in the experiment. The simulated radiation is also much below the experimental level. As a consequence, the thermal quench is not fully reproduced. Directions for progress are identified. Radiation from impurities is a good candidate.

Numerical verification of Orbit and Nemato codes for magnetic topology diagnosis

We present the results of a benchmark study involving the Orbit and Nemato codes. The two codes have been used to compare magnetic structure in a reversed-field pinch (RFP), where conserved magnetic structures/islands appear both in the core (dominated by m = 1 modes) and in the edge (dominated by m = 0 modes). As input, a snapshot of a 3D nonlinear MHD visco-resistive simulation (produced by the SpeCyl code) has been used. The first test is given by the reconstruction via Poincaré surface of section plot of an island generated by a single mode. In this case, the magnetic field topology corresponds to a time-independent Hamiltonian and shows conserved flux-surfaces used as a reference. Both codes successfully yield field lines which follow the same flux surfaces, in both the m = 1 and m = 0 cases. The benchmark between the codes has then been extended to a more complex configuration with chaotic magnetic field, using as input a fully 3D multiple mode RFP condition, characterized by the typical chain of edge magnetic islands providing a transport barrier. Finally, a quantitative benchmark has been performed, using the same 3D input, by estimating the correlation length of the magnetic field line in a bounded stochastic domain. The conclusion is that both codes yield consistent Poincaré plot structure on one hand, and very good quantitative agreement in correlation length estimate. This gives confidence to the application of both codes to magnetic topology in the RFX-mod device, for which they are used routinely, as well as for a generic fusion device.

MAGNETO-ACOUSTIC WAVES IN SUNSPOTS: FIRST RESULTS FROM A NEW THREE-DIMENSIONAL NONLINEAR MAGNETOHYDRODYNAMIC CODE

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional non-linear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here we present the first results of such modeling. We have developed a 3D non-linear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-dimensional mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfv\'en wave, by calculation of the wave energy fluxes. Our main findings are the following: (1) the conversion from acoustic to the Alfv\'en mode is only observed if the the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cut-off effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level beta=1; (3) waves with frequencies above the cut-off propagate field-aligned to the chromosphere and their power becomes dominating over that of evanescent 5-minute oscillations, in agreement with observations.

HOW DOES RADIO AGN FEEDBACK FEED BACK?

Radio AGN feedback is often assumed to work, but detailed physical models of this process are not well developed. This paper examines a possible path for radio AGN feedback to heat the gas in and around galaxies and perhaps suppress star formation. Nearby radio AGN are almost all FR-I radio galaxies, and it is argued that such outflows become decelerated and fully turbulent in their early stages. A 3D non-linear MHD turbulence calculation is made to determine the time required for this outflowing turbulent energy to be converted into heat. Using radio and x-ray observations of nearby FR-I AGN for normalization results in a time for the onset of heating of about 100 million years. This is comparable to the gas cooling times in and around galaxies, and the resulting location of heat deposition is consistent with FR-I outflows.

3D RESISTIVE MHD SIMULATIONS OF MAGNETIC RECONNECTION AND THE TEARING MODE INSTABILITY IN CURRENT SHEETS

Magnetic reconnection plays a critical role in many astrophysical processes where high energy emission is observed, e.g. particle acceleration, relativistic accretion powered outflows, pulsar winds and probably in dissipation of Poynting flux in GRBs. The magnetic field acts as a reservoir of energy and can dissipate its energy to thermal and kinetic energy via the tearing mode instability. We have performed 3D nonlinear MHD simulations of the tearing mode instability in a current sheet. Results from a temporal stability analysis in both the linear regime and weakly nonlinear (Rutherford) regime are compared to the numerical simulations. We observe magnetic island formation, island merging and oscillation once the instability has saturated. The growth in the linear regime is exponential in agreement with linear theory. In the second, Rutherford regime the island width grows linearly with time. We find that thermal energy produced in the current sheet strongly dominates the kinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law for the power spectral density which suggests that the tearing mode vortices play a role in setting up an energy cascade.

Three‐dimensional Magnetohydrodynamic Wave Behavior in Active Regions: Individual Loop Density Structure

We present the numerical results from a three-dimensional (3D) nonlinear MHD simulation of wave activity in an idealized active region in which individual, realistic loop density structure is included. The active region is modeled by an initially force-free, dipole magnetic configuration with gravitationally stratified density and contains a loop with a higher density than its surroundings. This study represents an extension to the model of Ofman & Thompson. As found in their work, we see that fast wave propagation is distorted by the Alfven speed profile and that the wave propagation generates field line oscillations, which are rapidly damped. We find that the addition of a high-density loop significantly changes the behavior inside that loop, specifically in that the loop can support trapped waves. We also find that the impact of the fast wave impulsively excites both horizontal and vertical loop oscillations. From a parametric study of the oscillations, we find that the amplitude of the oscillations decreases with increasing density contrast, whereas the period and damping time increase. This is one of the key results presented here: that individual loop density structure can influence the damping rate, and specifically that the damping time increases with increasing density contrast. All these results were compared with an additional study performed on a straight coronal loop with similar parameters. Through comparison with the straight loop, we find that the damping mechanism in our curved loop is wave leakage due to curvature. The work performed here highlights the importance of including individual loop density structure in the modeling of active regions and illustrates the need for obtaining accurate density measurements for coronal seismology.

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.

Developments of the culham 3D nonlinear MHD code

The structure of the 3D plasma simulation code NONLIN is outlined, together with a review of previous results. A new toroidal version, TORUS, is being used to study the behaviour of the internal sawtooth oscillation at high beta, and preliminary results are given. The conversion of NONLIN to run on the ICL Distributed Array Processor (DAP) is described, and it is shown that a very high performance is achieved.