Ideal MHD Modes Research Articles

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part B. safe termination of DEMO plasmas

An optimized plasma current ramp-down strategy is critical for safe and fast termination of plasma discharges in a tokamak demonstration fusion reactor (DEMO), both in planned and emergency scenarios, avoiding plasma disruptions and excessive heat loads to the first wall. Plasma stability limits and machine-specific technical requirements constrain the stable envelope through which the plasma must be navigated. Large amounts of auxiliary heating are required throughout the ramp-down phase, to avoid a radiative collapse in the presence of intrinsic tungsten and seeded xenon impurities, as quantitatively estimated in this work. As the plasma current is reduced, the current density becomes increasingly peaked, reflected by a growing value of the internal inductance ℓi3 , resulting in reduced controllability of the vertical position of the plasma. The feasibility of different plasma current ramp-down rates is tested by applying an automated optimization framework embedding the RAPTOR core transport solver. Optimal time traces for plasma current Ip(t) and plasma elongation κ(t) are proposed, to satisfy an Ip -dependent upper limit on the plasma internal inductance, as obtained from vertical stability studies using the CREATE-NL code, as well as a constraint on the time evolution of q 95, to avoid an ideal MHD mode. A negative current density near the plasma edge is observed in our simulations, even for the most conservative Ip ramp-down rate, indicating significant transient dynamics due to a large resistive time.

Investigation of the dependence of pe,ped on ne,sep in JET H-Mode plasmas using integrated JETTO-MISHKA-FRANTIC simulations

Experimentally, it has been observed in high-confinement (H-Mode) plasmas with Edge Localised Modes (ELMs) on JET that the pressure pedestal (pe,ped) is degraded by approximately a factor of two when there is a change in electron separatrix density, ne,sep, from 1−4×1019m−3. Previous work using the pedestal stability code EUROPED, has been able to predict the degradation of pe,ped but only for ne,sep≤1.5×1019m−3. In this work, we apply a coupled code JETTO-MISHKA-FRANTIC, to self-consistently predict the transport in the pedestal region and neutral source with varying separatrix conditions. The code feeds back on the transport in the pedestal region to achieve profiles that are marginally stable to ideal MHD modes (continuous ELM model in JETTO). When accounting for the change in electron separatrix temperature (Te,sep), ion separatrix temperature (Ti,sep) and the poloidally integrated neutral flux crossing the separatrix (Γsep,neut) as it changes with ne,sep (according to a scan in ne,sep in the edge code EDGE2D-EIRENE), no degradation in pe,ped was observed in JETTO-MISHKA-FRANTIC in contrast to experiment. Instead, an increase in pe,ped with ne,sep was observed which is driven by an increasing density pedestal (ne,ped). Within the presented JETTO-MISHKA-FRANTIC simulations, changing the pedestal width by a factor of two and a half in normalised poloidal flux (ψn) resulted in an approximately 40% degradation in pe,ped for ne,sep=1−3×1019m−3. This change in pedestal width was not supported by experimental data. A scan in the ratio of particle and energy transport in the pedestal (D/χ) was found to have a negligible effect on pe,ped. Qualitative agreement between JETTO-MISHKA-FRANTIC with EUROPED was found when the input density profiles are identical.

A study of the heating and current drive options and confinement requirements to access steady-state plasmas at Q ∼ 5 in ITER and associated operational scenario development

Access to steady-state (SS) plasma scenarios that can be potentially achieved in ITER by the exploitation of the neutral beam (NB) and electron cyclotron (EC) heating and current drive capabilities, including their foreseen upgrades, has been assessed and development of the Q ∼ 5 ITER SS operation (SSO) scenario has been carried out by combining all the necessary physics and engineering components. A set of modelling codes including 0.5D/1.5D transport and source modelling suites (METIS, ASTRA and CORSICA) and ideal MHD stability analysis codes (KINX and MISHKA) are applied to combined analysis and scenario development. Operating the plasma with a moderate density peaking factor (n e0/<n e> ∼ 1.3) for sufficient fusion gain (Q up to 5) at a low density (f GW = 0.6–0.8) and the required current drive efficiency produced an internal inductance (l i(3) ∼ 0.8–0 9) which improves the stability margin for low-n external ideal MHD modes. Based on this first observation, a combined operational space and ideal MHD stability analysis has recently identified Q ∼ 5 ITER SS target plasmas (Polevoi et al 2020 Nucl. Fusion 60 096024), and then the CORSICA scenario modelling suite has been applied to study access to the target plasmas as well as to develop a candidate operation scenario. Ideal MHD stability analysis on the SS plasmas has been performed using DCON embedded in the CORSICA scenario modelling suite. The use of off-axis electron cyclotron current drive (ECCD) with a power level of 20–30 MW from the equatorial and upper launchers was essential for the tailoring of the current profile to maintain ideal MHD stability of SS plasmas in ITER. Upgrading the NBI power from the baseline 33 MW to 49.5 MW provided the necessary current drive capability to allow fully non-inductive Q ∼ 5 operation with an energy confinement enhancement requirement (H 98 ≲ 1.6) similar to that achieved in some experiments in present tokamaks (Petty et al 2020 62nd Annual Meeting of the APS Division of Plasma Physics, Virtual Meeting (USA, 9–13 November 2020); Snyder et al 2019 Nucl. Fusion 59 086017; Solomon et al 2013 Nucl. Fusion 53 093033). The CORSICA simulations of the access to the Q ∼ 5 ITER SS target plasmas show that, provided that the enhancement of the energy confinement (H 98 ∼ 1.5–1.6) is achieved, it is possible for ITER to demonstrate the Q ∼ 5 SSO with NB and EC heating and current drive within the limits of the ITER Central Solenoid (CS)/Poloidal Field (PF) coil systems.

Anisotropy and shaping effects on the stability boundaries of infernal ideal MHD modes in tokamak hybrid plasmas

Anisotropy and some limiting toroidal flow effects on the stability of nearly resonant ideal magnetohydrodynamic modes in hybrid shaped tokamak plasmas are investigated within the ideal MHD infernal mode framework. Such effects are found to alter the plasma magnetic well/hill, which can be interpreted as imparing the average curvature, and the strength of mode coupling. In line with previous results, it is found that better stability properties are achieved through deepening the magnetic well by special cases of uniform toroidal flow and parallel plasma anisotropy. Plasma shaping provides additional modifications to the magnetic well depth, whose global stabilising or destabilising effect depends on the mutual interplay of elongation, triangularity and toroidicity. Further stabilisation is achieved by weakening the mode drive in vertically elongated plasmas.

On the Helical MHD Mode in a Finite-Conductivity Tokamak Plasma

A helical MHD perturbation in a finite-conductivity tokamak plasma has been considered in the straight-cylinder model in a situation where there is no resonance surface q = m/n in plasma. The radial eigenfunction of the helical mode, in addition to the large-scale component described at σ||→ ∞ by the ideal MHD equation, contains a small-scale component localized near the wall and near discontinuities in the radial profiles of the unperturbed quantities. At smooth profiles, the small-scale component is attached to the wall and is smaller in magnitude than the large-scale component. Therefore, beyond a thin near-wall plasma layer, the mode is close to the large-scale ideal MHD mode. The presence of the small-scale component is necessary to satisfy the boundary conditions for the perturbed field on the wall.

Energetic-ion excited internal kink modes with weak magnetic shear in tokamak plasmas**Project supported by the National Natural Science Foundation of China (Grant No. 11261140326).

The energetic particle driven internal kink mode is investigated in this paper for tokamak plasma with weak magnetic shear. With the effect of energetic particles, the internal mode structure in tokamak plasma does not appear as a rigid step-function when safety factor passes through q = 1 rational surface. It is found that even when the rational surface is removed, the mode may be still unstable under the low magnetic shear condition if the energetic particle drive is strong enough; with the low shear region of safety factor profile widening, the mode becomes more unstable with its growth-rate increasing. Furthermore, we find that the existence of the q = 1 rational surface does not have a significant effect on the stability of the plasma if energetic particles are present, which is very different from the scenarios of the ideal-MHD modes.

Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode

The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.

Excitation of flow-stabilized resistive wall mode by coupling with stable eigenmodes in tokamaks.

In a rotating toroidal plasma surrounded by a resistive wall, it is shown that linear MHD instabilities can be excited by couplings between the resistive wall mode (RWM) and stable ideal MHD modes. In particular, it is shown that the RWM can couple not only with stable external kink modes but also with Alfvén eigenmodes that are ordinarily in the stable continuum of a toroidal plasma. The RWM growth rate is shown to peak whenever the Doppler shift caused by the plasma rotation cancels the frequency of an ideal MHD mode, so that the mode appears to have zero frequency in the laboratory frame. At these values of the rotation frequency, the RWM can overcome the stabilizing effects of plasma rotation, continuum damping, and ion Landau damping.

Thick-wall effects on the rotational stabilization of resistive wall modes in tokamaks

This paper is devoted to studying the combined effect of mode rotation and energy dissipation in the resistive wall on plasma stability. The problem is analysed on the basis of the energy approach complementing the standard methods of the traditional MHD theory of plasma stability. The key element that makes our model different from this theory and commonly used thin-wall approaches to the stability analysis of resistive wall modes (RWMs) is the incorporation of the skin effect. In the ideal MHD theory of plasma stability, the skin depth is, formally, zero. In contrast, the conventional thin-wall theory of RWM stability assumes a skin depth much larger than the wall thickness. The presented model considers the intermediate case with a finite skin depth compared with the wall thickness. This covers the modes in between the typical RWMs and the ideal MHD modes when wall resistivity still affects the mode dynamics. It is shown that, in this region, the growth rate of the locked modes must be substantially larger than that calculated in the thin-wall models. On the other hand, the fast RWMs can be completely stabilized by mode rotation above some critical level. Qualitatively, this corresponds to the rotational stabilization observed in the DIII-D tokamak and allowing the plasma operation above the no-wall stability limit (Strait et al 2003 Nucl. Fusion 43 430). This is the main result of this study, which is completely analytical with all dependences explicitly shown. In particular, the dispersion relations for the fast RWMs and the critical frequency of mode rotation necessary for rotational stabilization are expressed through quantities that depend on the plasma parameters or can be experimentally found by magnetic measurements outside the plasma.

Thermal force drift wave

A drift instability of a collisional magnetized plasma, unstable due to the Braginskii thermal force but not requiring any direct dissipation such as resistivity or electron inertia, is examined. Unlike conventional drift-modes, the maximum growth rate of the thermal force drift wave (TFDW) is of order the drift frequency, making for a strongly turbulent nonlinear state. A 3D, magnetized two-fluid code is developed to allow the study of both ideal MHD modes as well as lower frequency drift modes. The governing equations are essentially the ideal MHD equations with the inclusion of Hall and thermal force terms in Ohm’s law. This set of equations is reduced in a finite β, long parallel wavelength, and small but significant Larmor radius ordering and tested for shear Alfven waves, parallel sound waves, and drift modes. The code is employed to recover the TFDW instability, to verify the code against the mode’s analytic linear characteristics, and to study the nonlinear behavior of the TFDW. The TFDW growth is strongly suppressed by parallel thermal conduction and thus this mode is more likely to be observed in low temperature plasmas.

Effect of core pressure gradient just inside the top of the pedestal on the energy loss due to the edge localized mode in JT-60U

The effect of core pressure gradient just inside the top of the pedestal on the energy loss due to type-I edge localized modes (ELMs) is studied. An analysis of the experimental data from JT-60U shows that the ELM energy loss normalized by the pedestal stored energy increases with the pressure gradient inside the top of the pedestal normalized by the pedestal pressure gradient. The dependence of normalized ELM energy loss on the normalized pressure gradient inside the top of the pedestal is similar to that predicted by the integrated code TOPICS-IB. The stability of linear ideal MHD modes is analysed using experimental profiles. It is found that the steep core pressure gradient inside the top of the pedestal broadens the eigenfunction profiles of unstable modes inwards. The TOPICS-IB simulation predicted that this broadening can enhance the ELM energy loss.

MINERVA: Ideal MHD stability code for toroidally rotating tokamak plasmas

A new linear MHD stability code MINERVA is developed for investigating a toroidal rotation effect on the stability of ideal MHD modes in tokamak plasmas. This code solves the Frieman–Rotenberg equation as not only the generalized eigenvalue problem but also the initial value problem. The parallel computing method used in this code realizes the stability analysis of both long and short wavelength MHD modes in short time. The results of some benchmarking tests show the validity of this MINERVA code. The numerical study with MINERVA about the toroidal rotation effect on the edge MHD stability shows that the rotation shear destabilizes the intermediate wavelength modes but stabilizes the short wavelength edge localized MHD modes, though the rotation frequency destabilizes both the long and the short wavelength MHD modes.

MHD stability analysis of small ELM regimes in JET

We have analysed the edge stability of JET discharges with small edge localized modes (ELMs) using the high resolution Thomson scattering system for accurate edge profiles in the equilibrium reconstruction. For the reference plasmas with large Type I ELMs we confirm the results from earlier analyses that the edge stability is limited by intermediate-n peeling–ballooning modes with a relatively large radial extent. The double null configuration needed to replace Type I ELMs by smaller Type II ELMs considerably increases the stability against these modes while the stability against n = ∞ ballooning modes is not affected. When this is combined with high collisionality (which is the other requirement for Type II ELMs), we find that the plasma cannot reach the Type I ELM triggering peeling–ballooning mode stability boundary before it is destabilized by high-n ballooning modes resulting in more benign ELMs. The ELM mitigation by magnetic perturbation causes the edge stability to be limited by pure peeling modes with a narrow radial extent. This explains the smaller ELM size and also why the ELMs are not fully suppressed. The transition from Type I ELMs to Type III ELMs by increasing the edge radiation fully stabilizes the edge plasma against ideal MHD modes. Therefore, the Type III ELMs are due to be triggered by some other mechanism than an ideal MHD instability.

Stable Spheromaks Sustained by Neutral Beam Injection

It is shown that spheromak equilibria, stable at zero-beta but departing from the Taylor state, could be sustained by non-inductive current drive at acceptable power levels. Stability to both ideal MHD and tearing modes is verified using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive and pressure effects could point the way to improved fusion reactors.

Attainment of High Normalized Current by Current Profile Manipulation in the Pegasus Toroidal Experiment

Large stable values of normalized current IN are achievable in spherical tori due to the large gradient of the toroidal field across the plasma. This allows access to high Troyon beta limits. Values of IN > 12 MA/m-T are expected to be stable to ideal MHD modes in the ultra-low-A Pegasus Toroidal Experiment. In previous experiments, the toroidal field utilization (Ip/Itf) was found to be limited roughly to unity by the onset of large-scale low-order tearing modes during the current ramp, which limited IN to roughly 6 MA/m-T. Three techniques have now been developed that allow access to higher values of IN, primarily through modification of the current density profile. The first of these techniques employs a fast rampdown of the low-inductance toroidal field coil to rapidly decrease Itf. The other techniques employ gas-fueled washer stack guns as plasma sources. The second technique uses these guns to provide preionization at low toroidal field, while the third relies on the guns as helicity sources to form ST plasmas non-inductively. Using these techniques, values of Ip/Itf > 2 have been obtained.

Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks

A numerical method for the stability analysis of ideal MHD modes is devised by using a physical model based on the two-dimensional Newcomb equation in combination with the conventional ideal MHD model. The MARG2D code based on this numerical method is able to analyze the stability of ideal MHD modes with a wide range of toroidal mode numbers. The validity of the MARG2D code has been confirmed through benchmarking tests using the DCON code for the low toroidal mode number MHD mode analysis, and tests using the ELITE code for intermediate to high toroidal mode number mode analysis. By using the MARG2D code, the MHD stability property of JT-60SA, the complemental device of ITER, is investigated with a focus on the effect of the plasma shape.

Extension of the Newcomb equation into the vacuum for the stability analysis of tokamak edge plasmas

The formulation for solving numerically the two-dimensional Newcomb equation has been extended to calculate the vacuum energy integral by using a vector potential method. According to this extension, a stability code MARG2D has been adapted, and coded for parallel computing in order to reduce substantially the CPU time. The MARG2D code enables a fast stability analysis of ideal external MHD modes from low to high toroidal mode numbers on the basis of the single physical model, and then the code works as a powerful tool in an integrated simulation where it is combined with transport codes, and also in the analysis of tokamak edge plasma experiments.

Optimization of compact stellarator configuration as fusion devices

Optimization of the stellarator configuration requires tradeoffs among a large number of physics parameters and engineering constraints. An integrated study of compact stellarator power plants, ARIES-CS, aims at examining these tradeoffs and defining key R&amp;D areas. Configurations with a plasma aspect ratio of A⩽6 and excellent quasiaxisymmetry (QA) in both two and three field period versions were developed while reducing α-particle losses to &amp;lt;10%. Stability to linear ideal MHD modes was attained, but at the expense of reduced QA (and increased α-particle losses) and increased complexity of the plasma shape. Recent experimental results indicate, however, that linear MHD stability limits may not be applicable to stellarators. By utilizing a highly efficient shield-only region in strategic areas, the minimum standoff was reduced by ∼30%. This allows a comparable reduction in the machine size. The device configuration, assembly, and maintenance procedures appear to impose severe constraints: three distinct approaches were developed, each applicable to a certain blanket concept and/or stellarator configuration. Modular coils are designed to examine the geometric complexity and to understand the constraints imposed by the maximum allowable field, desirable coil-plasma separation, coil-coil spacing, and other coil parameters. A cost-optimization system code has also been developed and will be utilized to assess the tradeoff among physics and engineering constraints in a self-consistent manner in the final phase of the ARIES-CS study.

The frequently interrupted regime of neoclassical tearing modes (FIR-NTMs): required plasma parameters and possibilities for its active control

The plasma parameters required for the occurrence of (3, 2) FIR-NTMs and thus good confinement properties at high normalized plasma pressure (βN) are investigated. Both on ASDEX Upgrade and on JET it is found that, with remarkable consistency between the devices, for a variety of plasma parameters in conventional current profile scenarios, this regime establishes itself for discharges with sufficient high normalized plasma pressure at mode onset, βN,onset > 2.3. An active triggering of this regime has been achieved by lowering the magnetic shear at the q = 4/3 rational surface. That way an ideal (4, 3) MHD mode is being destabilized, forcing the required three-wave coupling between the (3, 2) NTM, (1, 1) and (4, 3) mode activity.

Solar coronal heating by relaxation events

A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed nanoflares. We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.