MHD Stability Research Articles

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma

A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixed-boundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q(ψ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixed-boundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixed-boundary instabilities, an M × M plasma response matrix WP, with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added to a vacuum response matrix WV to form a total response matrix WT. The existence of negative eigenvalues of WT indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.

The effect of plasma beta on high-n ballooning stability at low magnetic shear

An explanation of the observed improvement in H-mode pedestal characteristics with increasing core plasma pressure or poloidal beta, , as observed in MAST and JET, is sought in terms of the impact of the Shafranov shift, , on ideal ballooning MHD stability. To illustrate this succinctly, a self-consistent treatment of the low magnetic shear region of the ‘’ stability diagram is presented using the large aspect ratio Shafranov equilibrium, but enhancing both and so that they compete with each other. The method of averaging, valid at low s, is used to simplify the calculation and demonstrates how , , plasma shaping and ‘average favourable curvature’ all contribute to stability.

Flow-Induced New Channels of Energy Exchange in Multi-Scale Plasma Dynamics - Revisiting Perturbative Hybrid Kinetic-MHD Theory.

It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.

Linear MHD stability analysis of post-disruption plasmas in ITER

Most of the plasma current can be replaced by a runaway electron (RE) current during plasma disruptions in ITER. In this case the post-disruption plasma current profile is likely to be more peaked than the pre-disruption profile. The MHD activity of such plasma will affect the runaway electron generation and confinement and the dynamics of the plasma position evolution (Vertical Displacement Event), limiting the timeframe for runaway electrons and disruption mitigation. In the present paper, we evaluate the influence of the possible RE seed current parameters on the onset of the MHD instabilities. By varying the RE seed current profile, we search for subsequent plasma evolutions with the highest and the lowest MHD activity. This information can be applied to a development of desirable ITER disruption scenario.

ELM behaviour and linear MHD stability of edge ECRH heated ASDEX Upgrade plasmas

In order to test the peeling–ballooning ELM model, ECRH heating was applied to the edge of ASDEX Upgrade type-I ELMy H-mode plasmas to alter the pedestal pressure and current density profiles. The discharges were analysed with respect to ideal MHD stability. While the ELM frequency increased and the pedestal gradients relaxed with edge ECRH, the MHD stability boundary did not change. The results indicate that the peeling–ballooning model is insufficient to fully explain the triggering of ELM instabilities in the presence of edge ECRH heating.

Three-Dimensional Numerical Analysis of Shear Flow Effects on MHD Stability in LHD Plasmas

Three-Dimensional Numerical Analysis of Shear Flow Effects on MHD Stability in LHD Plasmas

Linear MHD Stability Analysis of Post-Disruption Plasmas in ITER

Linear MHD Stability Analysis of Post-Disruption Plasmas in ITER

Tokamak elongation – how much is too much? Part 2. Numerical results

The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Scaling relations of maximum achievable elongation (${\it\kappa}_{max}$) versus inverse aspect ratio (${\it\varepsilon}$) are obtained numerically for various values of poloidal beta (${\it\beta}_{p}$), wall radius $(b/a)$ and feedback capability parameter (${\it\gamma}{\it\tau}_{w}$) in ranges near the reference values. It is also shown that each value of ${\it\kappa}_{max}$ occurs at a corresponding value of optimized triangularity (${\it\delta}$), whose scaling is also determined as a function of ${\it\varepsilon}$. The results show that the theoretical predictions of ${\it\kappa}_{max}$ are slightly higher than experimental observations for high performance discharges, as measured by high average pressure. The theoretical ${\it\delta}$ values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only $n=0$ MHD stability, but also $n\geqslant 1$ MHD modes described by ${\it\beta}_{N}$ in the Troyon limit and transport as characterized by ${\it\tau}_{E}$. Operation away from the $n=0$ MHD optimum may still lead to higher performance if there are more than compensatory gains in ${\it\beta}_{N}$ and ${\it\tau}_{E}$. Unfortunately, while the empirical scaling of ${\it\beta}_{N}$ and ${\it\tau}_{E}$ with the elongation (${\it\kappa}$) has been determined, the dependence on ${\it\delta}$ has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma–vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number $n=1$ distortions when the edge bootstrap current is large and higher $n$ corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch–Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch–Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

Special Issue on the 19th Workshop on MHD Stability Control

Special Issue on the 19th Workshop on MHD Stability Control

Overview of transport and MHD stability study: focusing on the impact of magnetic field topology in the Large Helical Device

The progress in the understanding of the physics and the concurrent parameter extension in the large helical device since the last IAEA-FEC, in 2012 (Kaneko O et al 2013 Nucl. Fusion 53 095024), is reviewed. Plasma with high ion and electron temperatures (Ti(0) ∼ Te(0) ∼ 6 keV) with simultaneous ion and electron internal transport barriers is obtained by controlling recycling and heating deposition. A sign flip of the nondiffusive term of impurity/momentum transport (residual stress and convection flow) is observed, which is associated with the formation of a transport barrier. The impact of the topology of three-dimensional magnetic fields (stochastic magnetic fields and magnetic islands) on heat momentum, particle/impurity transport and magnetohydrodynamic stability is also discussed. In the steady state operation, a 48 min discharge with a line-averaged electron density of 1 × 1019 m−3 and with high electron and ion temperatures (Ti(0) ∼ Te(0) ∼ 2 keV), resulting in 3.36 GJ of input energy, is achieved.

Modeling the effect of anisotropic pressure on tokamak plasmas normal modes and continuum using fluid approaches

Extending the ideal MHD stability code MISHKA, a new code, MISHKA-A, is developed to study the impact of pressure anisotropy on plasma stability. Based on full anisotropic equilibrium and geometry, the code can provide normal mode analysis with three fluid closure models: the single adiabatic model (SA), the double adiabatic model (CGL) and the incompressible model. A study on the plasma continuous spectrum shows that in low beta, large aspect ratio plasma, the main impact of anisotropy lies in the modification of the BAE gap and the sound frequency, if the q profile is conserved. The SA model preserves the BAE gap structure as ideal MHD, while in CGL the lowest frequency branch does not touch zero frequency at the resonant flux surface where m + nq = 0, inducing a gap at very low frequency. Also, the BAE gap frequency with bi-Maxwellian distribution in both model becomes higher if with a q profile dependency. As a benchmark of the code, we study the m/n = 1/1 internal kink mode. Numerical calculation of the marginal stability boundary with bi-Maxwellian distribution shows a good agreement with the generalized incompressible Bussac criterion (Mikhailovskii 1983 Sov. J. Plasma Phys. 9 190): the mode is stabilized(destabilized) if ().

Recent Progress in Studies of Plasma Heating and Stabilization in Axisymmetric Magnetic Mirrors in Novosibirsk

Axisymmetric magnetic mirrors are capable of confining high-β plasma and, at the same time, enable provision of higher magnetic field in the confinement region compared to non-axisymmetric systems. These advantages and their technical simplicity make them rather attractive as high-flux volumetric neutron sources, fission-fusion hybrids, and in the longer term as pure fusion reactors. The specific issues that still have to be further studied are plasma MHD stability at plasma parameters relevant to fusion applications, too-high plasma end losses, and the relatively low electron temperatures obtained so far in the experiments. These main physics issues were successfully addressed in the recent experiments in the GDT and GOL-3 devices in Novosibirsk. The review concludes with an update of the experimental results from both experimental devices and a discussion about the limiting factors in the current experiments. Specifically, we report on an almost twofold increase of the electron temperature with application of ECR heating, which was obtained in the experiments on the GDT device, and control of plasma rotation profile by injection of an electron beam at the end of the device, which was demonstrated in the GOL-3 device.

Active and passive kink mode studies in a tokamak with a movable ferromagnetic walla)

High-resolution active and passive kink mode studies are conducted in a tokamak with an adjustable ferromagnetic wall near the plasma surface. Ferritic tiles made from 5.6 mm thick Hiperco® 50 alloy have been mounted on the plasma-facing side of half of the in-vessel movable wall segments in the High Beta Tokamak-Extended Pulse device [D. A. Maurer et al., Plasma Phys. Controlled Fusion 53, 074016 (2011)] in order to explore ferritic resistive wall mode stability. Low-activation ferritic steels are a candidate for structural components of a fusion reactor, and these experiments examine MHD stability of plasmas with nearby ferromagnetic material. Plasma-wall separation for alternating ferritic and non-ferritic wall segments is adjusted between discharges without opening the vacuum vessel. Amplification of applied resonant magnetic perturbations and plasma disruptivity are observed to increase when the ferromagnetic wall is close to plasma surface instead of the standard stainless steel wall. Rapidly rotating m/n=3/1 external kink modes have higher growth rates with the nearby ferritic wall. Feedback suppression of kinks is still as effective as before the installation of ferritic material in vessel, in spite of increased mode growth rates.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

An approach to the integrated modelling of plasma regimes in the projected neutron source DEMO-FNS based on different codes is developed. The consistency check of the steady-state regime is carried out, namely, the possibility of the plasma current ramp-up, acceptance of growth rates of MHD modes in the steady-state regime, heat loads to the wall and divertor plates and neutron yield value. The following codes are employed for the integrated modelling. ASTRA transport code for calculation of plasma parameters in the steady-state regime, NUBEAM Monte Carlo code for NBI incorporated into the ASTRA code, DINA free boundary equilibrium and evolution code, SPIDER free boundary equilibrium and equilibrium reconstruction code, KINX ideal MHD stability code, TOKSTAB rigid shift vertical stability code, edge and divertor plasma B2SOLPS5.2 code and Semi-analytic Hybrid Model (SHM) code for self-consistent description of the core, edge and divertor plasmas based on the experimental scaling laws. The consistent steady-state regime for the DEMO-FNS plasma and the plasma current ramp-up scenario are developed using the integrated modelling approach. Passive copper coils are suggested to reduce the plasma vertical instability growth rate to below ∼30 s−1.The outer divertor operation in the ‘high-recycling’ regime is numerically demonstrated with a maximal heat flux density of 7–9 MW m−2 that is technically acceptable.

Simulation of plasma current ramp-up with reduced magnetic flux consumption in JT-60SA

Current ramp-up with reduced central solenoid (CS) flux consumption in JT-60SA has been investigated using an integrated modeling code suite (TOPICS) with a turbulent model (CDBM). The plasma current can be ramped-up from 0.6 MA to 2.1 MA with no additional CS flux consumption if the plasma current is overdriven by neutral-beam-driven and bootstrap current. A time duration required for the current ramp-up without CS flux consumption becomes as long as 150 s in the scenario we have examined. In order to achieve a current overdrive condition from 0.6 MA, the current drive by a lower energy neutral beam (85 keV) is effective. A higher energy neutral beam (500 keV) cannot be used in this early phase with a low central electron density (~2 × 1019 m−3) due to large shine through loss, while it can be effectively used in the later phase. Therefore, the main current driver should be switched from the lower energy neutral beam to the higher energy neutral beam during the current ramp-up phase. As a result of an intensive auxiliary heating, plasma beta (the ratio of the plasma pressure to the magnetic pressure) becomes high. Ideal MHD instabilities of such high beta plasmas have been investigated using a linear ideal MHD stability analysis code (MARG2D). External kink modes which might affect the core plasma can be stabilized during the current ramp-up if there is a perfectly conducting wall at the location of the stabilizing plate and the vacuum vessel of JT-60SA and the plasma has a broader pressure profile with the H-mode pedestal and the internal transport barrier.

MHD stability of the ITER pedestal and SOL plasma and its influence on the heat flux width

MHD stability of ITER plasmas has been analyzed for QDT=10 edge and SOL plasma conditions, showing that the SOL plasma is MHD stable down to pressure gradient scale lengths of λp∼1mm, but that MHD pedestal plasma stability can limit λp to values of 5–8mm just inside the separatrix. Modelling of the corresponding plasma conditions with the SOLPS code shows that heat flux widths λq∼1.2–1.5mm can be obtained which are compatible with λp∼5–8mm. This is due to the fact that the ITER divertor plasma enters the high recycling regime at low values of separatrix densities (∼4.0×1018m−3), which leads to the appearance of a region with reversed flow near the separatrix, modifying plasma transport and leading to high SOL density gradient scale lengths and divertor plasma pressures near the separatrix.

Characterization of peeling modes in a low aspect ratio tokamak

Peeling modes are observed at the plasma edge in the Pegasus Toroidal Experiment under conditions of high edge current density (Jedge ∼ 0.1 MA m−2) and low magnetic field (B ∼ 0.1 T) present at near-unity aspect ratio. Their macroscopic properties are measured using external Mirnov coil arrays, Langmuir probes and high-speed visible imaging. The modest edge parameters and short pulse lengths of Pegasus discharges permit direct measurement of the internal magnetic field structure with an insertable array of Hall-effect sensors, providing the current profile and its temporal evolution. Peeling modes generate coherent, edge-localized electromagnetic activity with low toroidal mode numbers n ⩽ 3 and high poloidal mode numbers, in agreement with theoretical expectations of a low-n external kink structure. Coherent MHD fluctuation amplitudes are found to be strongly dependent on the experimentally measured Jedge/B peeling instability drive, consistent with theory. Peeling modes nonlinearly generate ELM-like, field-aligned filamentary structures that detach from the edge and propagate radially outward. The KFIT equilibrium code is extended with an Akima spline profile parameterization and an improved model for induced toroidal wall current estimation to obtain a reconstruction during peeling activity with its current profile constrained by internal Hall measurements. It is used to test the analytic peeling stability criterion and numerically evaluate ideal MHD stability. Both approaches predict instability, in agreement with experiment, with the latter identifying an unstable external kink.

Controlling tokamak geometry with three-dimensional magnetic perturbations

It is shown that small externally applied magnetic perturbations can significantly alter important geometric properties of magnetic flux surfaces in tokamaks. Through 3D shaping, experimentally relevant perturbation levels are large enough to influence turbulent transport and MHD stability in the pedestal region. It is shown that the dominant pitch-resonant flux surface deformations are primarily induced by non-resonant 3D fields, particularly in the presence of significant axisymmetric shaping. The spectral content of the applied 3D field can be used to control these effects.

Edge-localized-modes in tokamaks

Edge-localized-modes (ELMs) are a ubiquitous feature of H-mode in tokamaks. When gradients in the H-mode transport barrier grow to exceed the MHD stability limit the ELM instability grows explosively, rapidly transporting energy and particles onto open field lines and material surfaces. Though ELMs provide additional particle and impurity transport through the H-mode transport barrier, enabling steady operation, the resulting heat flux transients to plasma facing surfaces project to large amplitude in future low collisionality burning plasma tokamaks. Measurements of the ELM heat flux deposition onto material surfaces in the divertor and main chamber indicate significant broadening compared to inter-ELM heat flux, with a timescale for energy deposition that is consistent with sonic ion flow and numerical simulation. Comprehensive ELM simulation is highlighting the important physics processes of ELM transport including parallel transport due to magnetic reconnection and turbulence resulting from collapse of the H-mode transport barrier. Encouraging prospects for ELM control and/or suppression in future tokamaks include intrinsic modes of ELM free operation, ELM triggering with frequent small pellet injection and the application of 3D magnetic fields.