Session GO4: RF, Stellarators, Stability

Nonlinear Simulations of Trapped Electron Mode Turbulence in Low Magnetic Shear Stellarators

Optimized stellarators, like the Helically Symmetric eXperiment (HSX), often operate with small global magnetic shear to avoid low-order rational surfaces and magnetic islands. Nonlinear, flux-tube gyrokinetic simulations of density-gradient-driven Trapped Electron Mode (TEM) turbulence in HSX shows two distinct spectral fluctuation regions: long-wavelength slab-like TEMs localized by global magnetic shear that extend along field lines and short-wavelength TEMs localized by local magnetic shear to a single helical bad curvature region. The slab-like TEMs require computational domains significantly larger than one poloidal turn and are computationally expensive, making turbulent optimization studies challenging. A computationally more efficient, zero-average-magnetic-shear approximation is shown to sufficiently describe the relevant nonlinear physics and replicate finite-shear computations, and can be exploited in quasilinear models based on linear gyrokinetics as a feasible optimization tool. TEM quasilinear heat fluxes are computed with the zero-shear approximation and compared to experimentally-relevant nonlinear gyrokinetic TEM heat fluxes for HSX.   

Calculations of neoclassical impurity transport in stellarators

The new stellarator Wendelstein 7-X has finished the first operational campaign and is restarting operation in the summer 2017. To demonstrate that the stellarator concept is a viable candidate for a fusion reactor and to allow for long pulse lengths of $\sim$~30~min, i.e. ``quasi-stationary'' operation, it will be important to avoid central impurity accumulation typically governed by the radial neoclassical transport. The SFINCS code [Landreman et al. {\em Phys. Plasmas} {\bf 21} (2014) 042503] has been developed to calculate neoclassical quantities such as the radial collisional transport and the ambipolar radial electric field in 3D magnetic configurations. SFINCS is a cutting-edge numerical tool which combines several important features: the ability to model an arbitrary number of kinetic plasma species, the full linearized Fokker-Planck collision operator for all species, and the ability to calculate and account for the variation of the electrostatic potential on flux surfaces. In the present work we use SFINCS to study neoclassical impurity transport in stellarators. We explore how flux-surface potential variations affect the radial particle transport, and how the radial electric field is modified by non-trace impurities and flux-surface potential variations.   

Bayesian modelling of multiple diagnostics at Wendelstein 7-X using the Minerva framework

Wendelstein 7-X (W7-X) is a large scale optimised stellarator designed for steady-state operation with fusion reactor relevant conditions. Consistent inference of physics parameters and their associated uncertainties requires the capability to handle the complexity of the entire system, including physics models of multiple diagnostics. A Bayesian model has been developed in the Minerva framework to infer electron temperature and density profiles from multiple diagnostics in a consistent way. Here, the physics models predict the data of multiple diagnostics in a joint Bayesian analysis. The electron temperature and density profiles are modelled by Gaussian processes with hyperparameters. Markov chain Monte Carlo methods explore the full posterior of electron temperature and density profiles as well as possible combinations of hyperparameters and calibration factors. This results in a profile inference with proper uncertainties reflecting both statistical error and the automatic calibration for diagnostics.   

Minerva neural network based surrogate model for real time inference of ion temperature profiles at Wendelstein 7-X

Artificial neural networks (ANNs) can reduce the computation time required for the application of Bayesian inference on large amounts of data by several orders of magnitude, making real-time analysis possible and, at the same time, providing a reliable alternative to more conventional inversion routines. The large scale fusion experiment Wendelstein 7-X (W7-X) requires tens of diagnostics for plasma parameter measurements and is using the Minerva Bayesian modelling framework as its main inference engine, which can handle joint inference in complex systems made of several physics models. Conventional inversion routines are applied to measured data to infer the posterior distribution of the free parameters of the models implemented in the framework. We have trained ANNs on a training set made of samples from the prior distribution of the free parameters and the corresponding data calculated with the forward model, so that the trained ANNs constitute a surrogate model of the physics model. The ANNs have been then applied to 2D images measured by an X-ray spectrometer, representing the spectral emission from plasma impurities measured along a fan of lines of sight covering a major fraction of the plasma cross-section, for the inference of ion temperature profiles and then compared with the conventional inversion routines, showing that they constitute a robust and reliable alternative for real time plasma parameter inference.   

Abstract Withdrawn

The influence of electron cyclotron current drive on the m/n$=$2/1 resistive tearing mode is investigated using gyrokinetic simulations in HL-2A and DIII-D configurations. The resistive tearing mode (RTM) evolution is calculated with a finite mass electron model, and the rf current source is obtained from the ray-tracing code and the Fokker-Planck code. The resistive tearing modes are shown to be stabilized completely by a continuous 1MW 68GHz X2-mode in HL-2A tokamak. While the (2/1) tearing mode in the DIII-D tokamak is only eased with the 1MW 110GHz X2-mode due to the inadequate power input. The ion kinetic effect on the resistive tearing mode stabilization is also demonstrated. It is shown, both in HL-2A and DIII-D, that the existence of ion can reduce the island width as well as the growth rate, hence enhance the resistive tearing mode stabilization with electron cyclotron wave injection.   

Coherent current-carrying filaments during nonlinear reconnecting ELMs and VDEs

We have examined plasmoid-mediated reconnection in a spherical tokamak using global nonlinear three-dimensional resistive MHD simulations with NIMROD. We have shown that physical current sheets/layers develop near the edge as a peeling component of ELMs or during vertical displacement events (associated with the scrape-off layer currents -- halo currents), can become unstable to nonaxisymmetric 3-D current-sheet instabilities (peeling- or tearing-like) and nonlinearly form edge coherent current-carrying filaments. Time-evolving edge current sheets with reconnecting nature in NSTX and NSTX-U configurations are identified. [F. Ebrahimi, Phys. Plasmas 23, 120705 (2016); 24, 056119 (2017)] In the case of peeling-like edge localized modes, the longstanding problem of quasiperiodic ELMs cycles is explained through the relaxation of edge current via direct numerical calculations of reconnecting emf terms. For the VDEs during disruption, we show that as the plasma is vertically displaced, edge halo current sheet becomes MHD unstable and forms coherent edge current filament structures, which would eventually bleed into the walls. Our model explains some essential asymmetric physics relevant to the experimental observations. Supported by DOE grants DE-SC0010565, DE-AC02-09CH11466.   

Simulation of the electromagnetic wall response to plasma wall-touching kink and vertical modes with application to ITER

Realistic simulations of electric current excitation in three-dimensional vessel structures by the plasma touching the walls are necessary to understand plasma disruptions in tokamak. In large tokamaks like ITER, the wall-touching kink modes cause large sideway forces on the vacuum vessel determined by the sharing of asymmetric electric current between the plasma and the wall. Our model covers both eddy currents, excited inductively by vertical modes, and source/sink currents due to current sharing between the plasma and the thin conducting wall. The developed finite element approach calculates the electromagnetic wall response to perturbation of magnetic fields and to current sharing between the plasma and the wall. The current density entering/exiting the wall surface from the plasma and the time derivative of the magnetic vector potential of the plasma are the input values. The magnetic field and the vector potential from the wall currents are returned as output. Our model has been checked against analytical examples of a multiply-connected domain of a real ITER wall.   

Controlling runaway vortex via externally injected high-frequency electromagnetic waves

One way of mitigating runaway damage of the plasma-facing components in a tokamak fusion reactor is by limiting the runaway electron energy under a few MeV, while not necessarily reducing the runaway current appreciably. Here we describe a physics mechanism by which such momentum space engineering of the runaway distribution can be facilitated by externally injected high-frequency electromagnetic waves such as the whistler waves. The drastic impact that wave-induced scattering can have on the runaway energy distribution is fundamentally the result of its ability to control the runaway vortex in the momentum space. The runaway vortex, which is a local circulation of runaways in momentum space, is the outcome of the competition between Coulomb collisions, synchrotron radiation damping, and runaway acceleration by parallel electric field. By introducing a wave that resonantly interacts with runaways at a particular range of energy that is mildly relativistic, the enhanced scattering would reshape the vortex by cutting off the part that is highly relativistic. The efficiency of resonant scattering accentuates the requirement that the wave amplitude can be small so the power requirement from external wave injection is practical for the mitigation scheme.   

Stability limits in rotation and $\beta$ with energetic ion, two fluid, and resistive wall effects

The non-ideal magnetohydrodynamic (MHD) stability of a tokamak configuration that is driven unstable to the $m/n=2/1$ mode by increasing pressure is studied in a reduced model that includes many of the key physics components driving the instability: two fluid responses in various regimes at the resonant surface, a drift-kinetic slowing down distribution of trapped energetic ions, variations in the magnetic shear, plasma rotation and a resistive wall. The changes in stability are examined as the rotation varies across the Hall, Semi-Collisional and Inertial regimes, and compared with recent experiments on DIII-D for rotational limits. The energetic ion contribution to the perturbed pressure is included in the model, where energetic ions damp and stabilize the mode when orbiting in significant positive shear, and drive the mode unstable in reversed shear regions. The effect of rotation is included in the drift-kinetic ion model, where it modifies this effect. The equilibria are stable for low $\beta$ and the marginal stability values in $\beta$ and rotation are computed. The impact of the rotation in both the plasma layer responses, and the energetic ion response, must be taken into account to interpret the experimental results.   

Simulation of Double Tearing Modes with plasmoids in High Lundquist Number Regim

A conservative perturbed MHD model [1] and a flux vector splitting (FVS) based high order of accuracy finite difference method [2] was applied to investigate the nonlinear evolution of double tearing modes(DTM) in 2D geometry with Lundquist number higher than 1.0e$+$4. With high spatial resolution approach, the results show the existence of multiple plasmoids generation. The effects of current sheets separation and guiding field upon secondary islands are investigated [2]. It is also find [3] that while the symmetry is well preserved during the simulation, a new quasi-stationary state with two pairs of islands can form after the explosive stage. For larger distance between rational surfaces two fast reconnections during one evolution can take place. Recently work, the numerical capability is extended to cylindrical geometry and validation during the linear and nonlinear DTM simulation in helical symmetry are performed. 1.J. Ma et al, Comunn. Comput. Phys. 21(5), 1429 (2017). 2.W. Guo et al, Phys. Plasmas 24, 032115 (2017). 3.J. Ma, et al Nucl. Fusion, (2017) Accepted.   

Simulations and Theory of nonlinear interchange/tearing instabilities in the SOL edge of toroidal plasmas

Numerical simulations of a reduced theoretical model for the interchange/tearing instabilities are presented for the turbulence generated by the steep gradients in scrape-off-layer (SOL) edge plasmas. Plasma near the Last Closed Flux Surface (LCFS) and into the scrape-off layer (SOL), are characterized by open magnetic field lines that terminate on the divertor plates. Theoretical and numerical modeling is presented - which includes the current diffusivity – which gives the turbulent transport from the pedestal into SOL. The simulations give a low-level saturated current profile in the SOL region with a current density jump across the LCFS. The nonlinear numerical simulations show that the interchange modes evolve into complex structures with a tearing mode/reconnection component that releases both pressure and current gradient energy components. These complex energy releases are consistent with earlier simulations on the current-interchange tearing modes in Zheng and Furukawa [Phys. Plasmas 2010, 2013]. The applicability of the model to the tokamak edge stability and ELM studies is discussed.   

The X-point effects on the peeling-ballooning stability conditions

Due to the X-point singularity the safety factor tends to infinity as the last closed flux surface is approached. The usual numerical treatment of X-point singularity is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point included. This type of treatments have been used to make the peeling-ballooning stability diagram. We found that the mode types, peel or ballooning, can vary depending on how much the edge portion is cut off. When the cutting-off leads the edge safety factor ($q_a$) to become close to a mode rational number, the peeling modes dominate; otherwise the ballooning type of modes prevail. The stability condition for peeling modes with $q_a$ being close to a rational number is much stringent than that for ballooning type of modes. Because $q_a$ tends to infinite near the separatrix, the mode rational surfaces are concentrated in the plasma region and thus the peeling modes are basically excluded. This extrapolation indicates that the stability boundary for high edge current, which is related to the peeling modes, need to be reexamined to take into account the X-point effects.