Session BI2: Disruptions and Stability

The influence of an ITER-like wall on disruptions at JET

Disruptions are a key issue for tokamaks such as ITER because the fast release of the high thermal and magnetic energies will result in large forces and heat loads. Hence, finding methods to avoid them or mitigate their impact is vital. The recent replacement of carbon tiles with a metallic ITER-like wall (ILW) has greatly increased the significance of disruptions for JET operations. This paper summarizes how the metallic wall influenced the disruption physics itself and its influence on the causes of disruptions. Tolerable heat loads on the ILW are reduced compared to the carbon wall because of the potential for melting. This is exacerbated by the fact that with the ILW, significantly less energy is radiated during the disruption and thus more energy is conducted to the wall. The lower radiation and thus higher temperatures also slow down the current decay, yielding larger vessel forces. Mitigation by massive gas injection had to be applied routinely in order to safely operate JET with the new wall. The start of operations with the ILW showed a marked rise in the average disruption rate from 3.4{\%} to 10{\%}, although in the last 2 weeks, H-mode operations with only 3.3{\%} disruptions was achieved. The increased disruption rate can be attributed to the influence of the new wall on plasma operation and control, requiring adjustments of the established carbon-wall scenarios. A detailed survey of disruption causes will be presented, showing the improvements made to avoid various disruption classes, but also indicating those disruption types responsible for the enhanced disruption rate. The latter can be mainly attributed to disruptions due to too high core radiation but also due to density control issues and error field locked modes. Detailed technical and physics understanding of disruption causes is essential for devising optimum strategies to avoid or mitigate these events.   

Understanding the Physics of Thermal Quench Mitigatio

This work presents results obtained on DIII-D on thermal quench (TQ) mitigation by massive impurity injection showing that the delivery speed of the particles has a critical effect on the early assimilation of injected impurities in the discharge thus the radiation/conduction balance (which can be improved from 20\%-40\% up to 90\% by massive particle injection) during the TQ: a delivery faster than the TQ timescale ($\sim$1 ms on DIII-D) is critical to an efficient TQ mitigation as shown by the comparisons between injection methods as well as mitigated vertical displacement events experiments. TQ mitigation will be required on ITER in the early phase of a disruption when most of the thermal energy of the plasma ($\sim$350 MJ on ITER) is lost, inflicting damaging heat loads to the walls of the device. TQ mitigation relies on increasing the balance radiation/conduction to protect the plasma facing components. Injecting impurities through gas or pellet injection has proven an efficient mitigation method on present devices but the extrapolation of thermal quench duration, radiation efficiency, and impurity assimilation to ITER is challenging. But it can generate radiation asymmetries that could induce local melting of the wall on ITER. Strong poloidal flows have been observed during TQ mitigation by impurity injection. These flows that appear not to be driven by $E\times B$ suggest that injecting at different poloidal locations may improve the radiation symmetry. Results enabled by the new multiple locations massive gas puff system designed to study radiation symmetry during the TQ are also presented. They are compared to results obtained on C-Mod with a different poloidal/toroidal configuration ($\sim$1/1 on DIII-D, 1/2 on C-Mod) since modeling with the NIMROD code shows that the toroidal asymmetry may be affected by the phase of a strong 1/1 mode with respect to the impurity injection.   

ITPA Joint Experiment to Measure Threshold E-fields and Densities for Runaway Electron Onset and Suppression

Recent results from an ITPA joint experiment to study the onset, growth, and decay of relativistic electrons (REs) indicate that energy loss mechanisms other than collisional damping may play a dominant role in the dynamics of the RE population. Understanding the physics of RE growth and mitigation is motivated by the theoretical prediction that disruptions of full-current ITER discharges could generate $\sim $10 MA of REs (10-20 MeV) through an avalanche growth process [M. Rosenbluth, S. Putvinski, Nucl Fusion 37 (1997) 1355]. A necessary condition for avalanche growth is that the Coulomb acceleration due to the toroidal electric field has to be at least high enough to counter the collisional drag on background electrons, i.e. E\textgreater E$_{\mathrm{c}}$, where E$_{\mathrm{c}}$ is the critical E-field derived in [J. Connor, R. Hastie, Nucl Fusion 15 (1975) 415]. E$_{\mathrm{c}}$ scales linearly with electron density, n$_{\mathrm{e}}$, so one way to suppress avalanche growth is to quickly raise n$_{\mathrm{e}}$ sufficiently high, but this is problematic on ITER. However, if there are other energy loss mechanisms in addition to collisions, then the actual threshold E-field will be greater than E$_{\mathrm{c}}$, i.e. REs become more difficult to generate and sustain due to the additional loss mechanism(s). Due to the importance of E$_{\mathrm{c}}$ to the issue of REs in ITER, the ITPA MHD group is conducting a joint experiment to measure the threshold E-field on a number of tokamaks under steady-state, low Z$_{\mathrm{eff}}$ conditions in which V$_{\mathrm{loop}}$, n$_{\mathrm{e}}$, and REs can be well-diagnosed, and compared to theory. The analysis must take into account the RE growth time, which can be comparable to the discharge timescale. Data from DIII-D, C-Mod, TEXTOR, and FTU have been obtained so far, and the consensus to date is that the threshold E-field is significantly higher than E$_{\mathrm{c}}$, or conversely, the n$_{\mathrm{e}}$ required to damp REs is significantly less than predicted, suggesting that other loss mechanisms are involved. Implications for RE mitigation in ITER will be discussed.   

Plasma Disruption Avoidance and Mitigation using Strong Non-Axisymmetric Shaping with Stellarator Fields

The avoidance and mitigation of major disruptions remains a critical challenge for ITER and future burning tokamak plasmas. Early stellarator experiments with toroidal plasma current were found to operate without disruptions if the vacuum rotational transform produced by external coils was greater than a threshold value of $\raisebox{-.7ex}{$\mathchar'26$} \mkern-8mu \iota_{\mathrm{vac}}(a) \ge 0.14\,$[1]. Strong 3-D shaping produced by externally generated rotational transform is also observed to suppress disruptive phenomena of current-carrying discharges in the Compact Toroidal Hybrid (CTH), with the amount of $\raisebox{-.7ex}{$\mathchar'26$} \mkern-8mu \iota_{\mathrm{vac}}(a)$ required for suppression dependent upon the disruption scenario. Current-driven disruptions are deliberately generated in CTH by (1) raising the plasma density, (2) operating at low edge safety factor $q(a)$, or (3) by not compensating against the vertical instability of plasmas with high elongation. While the density limit is found to agree with the empirical Greenwald limit at low edge vacuum transform ($\raisebox{-.7ex}{$\mathchar'26$} \mkern-8mu \iota_{\mathrm{vac}}(a) = 0.04$), the experimental densities exceed this limit by up to a factor of three as the vacuum transform is raised to $\raisebox{-.7ex}{$\mathchar'26$} \mkern-8mu \iota_{\mathrm{vac}}(a) = 0.25$. Low-$q$ disruptions near $q(a) = 2$ are observed at low vacuum transform but no longer occur when the vacuum transform is raised above $\raisebox{-.7ex}{$\mathchar'26$} \mkern-8mu \iota_{\mathrm{vac}}(a) > 0.07$, even though $q(a)$ falls below a value of 2. Passive suppression of the vertical instability of elongated plasmas is observed with the addition of external transform, and the amount required is in agreement with an analytic calculation of marginal stability in current-carrying stellarators\,[2].\\[4pt] Work supported by U.S.~Department of Energy Grant No. DE-FG02-00ER54610\\[4pt] [1] W~VII-A Team, Nucl. Fusion \textbf{20}, 1093 (1980).\\[0pt] [2] G.~Y.~Fu, Phys. Plasmas \textbf{7}, 1079 (2000).   

Rotation and kinetic resonance effects on the spherical tokamak ideal-wall limit

Achieving plasma pressures above the no-wall kink stability limit is an important requirement for advanced operating scenarios in conventional and spherical tokamak plasmas. Previous comparisons between MISK and MARS code calculations and NSTX experiments have shown the resonances between particle motion and plasma rotation can have a strong stabilizing effect on the resistive wall mode (RWM). However, comparatively little effort has been placed on understanding possible kinetic modifications of the ``plasma mode,'' i.e. the mode that is unstable above the ideal-wall limit. For the first time, plasma mode stability has been systematically investigated for rapidly-rotating and high-beta spherical tokamak plasmas obtained in the NSTX device using the MARS-K linear kinetic MHD stability code. The MARS-K code includes the effects of rotation and dissipation self-consistently, and calculations indicate that as the toroidal rotation is increased to experimental values in the absence of kinetic dissipation, an n$=$1 plasma mode is destabilized by a combination of rotation shear (Kelvin-Helmholtz-like drive) and plasma pressure gradient. The identification of rotation-shear-driven instabilities is not possible with the MISK code which uses a perturbative approach based on non-rotating ideal MHD. Plasma mode stability can also be modified by kinetic dissipation, and precession-resonance damping can provide plasma mode stability at high rotation, but only for small plasma-wall gap. Importantly, the inclusion of all drift-kinetic resonances (precession, bounce, and transit) can further increase plasma mode stability and improve agreement between predicted stability limits and experimentally measured stability thresholds. Overall, these results indicate that rotation and kinetic resonance effects are important for determining the effective ideal-wall limit in rapidly-rotating high-beta plasmas.   

Self-consistent modelling of energetic particle effects on RWM: anisotropy and finite orbit width

The resistive wall mode (RWM) is a macroscopic instability that can severely limit the achievable plasma pressure, and hence the eventual fusion power production, in present and future tokamak devices. Therefore, understanding the physics associated with this instability, and learning how to control it, is of critical importance in future devices such as ITER, in particular in the so called advanced tokamak scenarios. During recent years, it has been realized that kinetic effects, due to the mode resonance with drift motions of both thermal and energetic particles (EPs), can play a crucial role in stabilizing/destabilizing the RWM. The mode physics in such cases are well described by the MHD-kinetic hybrid approach. This contribution reports the recent new developments in the RWM theory, based on a non-perturbative, or self-consistent, approach for numerical modelling of the RWM stability in the presence of energetic particles. Two important aspects of the EPs effects are examined: (i) the anisotropy of the equilibrium distribution in the phase space, in particular along the particle pitch angle; and (ii) the finite orbit width (FOW) effect of EPs on the mode stability. Both effects have been studied within the so called perturbative approach. In particular, it has been found from a recent study, Ref. [1] below, that for the target plasma as envisaged in the ITER 9MA scenario, the RWM is fully stabilized by the kinetic effects from thermal and energetic particles. The FOW of EPs plays an essential role in the mode damping. Given the fact that the perturbative approach often overestimates the kinetic damping, as compared to the non-perturbative approach (see e.g. Ref. [2] below), it is of great interest to understand how the FOW affects the mode stability following a non-perturbative formulation. Such formulations have recently been developed, incorporated into the MARS-K code, and will be presented in this talk. Simulation results will be reported for full toroidal plasmas such as those designed for the ITER 9MA steady state scenarios. \\[4pt] [1] I.T. Chapman, et al., Phys. Plasmas 19, 052502 (2012).\\[0pt] [2] Y.Q. Liu, Nucl. Fusion 50, 095008 (2010)