Experimental conditions to suppress edge localised modes by magnetic perturbations in the ASDEX Upgrade tokamak

Access conditions for full suppression of Edge Localised Modes (ELMs) by Magnetic Perturbations (MP) in low density high confinement mode (H-mode) plasmas are studied in the ASDEX Upgrade tokamak. The main empirical requirements for full ELM suppression in our experiments are: 1. The poloidal spectrum of the MP must be aligned for best plasma response from weakly stable kink-modes, which amplify the perturbation, 2. The plasma edge density must be below a critical value, $3.3 \times 10^{19}$~m$^{-3}$. The edge collisionality is in the range $\nu^*_i = 0.15-0.42$ (ions) and $\nu^*_e = 0.15-0.25$ (electrons). However, our data does not show that the edge collisionality is the critical parameter that governs access to ELM suppression. 3. The pedestal pressure must be kept sufficiently low to avoid destabilisation of small ELMs. This requirement implies a systematic reduction of pedestal pressure of typically 30\% compared to unmitigated ELMy H-mode in otherwise similar plasmas. 4. The edge safety factor $q_{95}$ lies within a certain window. Within the range probed so far, $q_{95}=3.5-4.2$, one such window, $q_{95}=3.57-3.95$ has been identified. Within the range of plasma rotation encountered so far, no apparent threshold of plasma rotation for ELM suppression is found. This includes cases with large cross field electron flow in the entire pedestal region, for which two-fluid MHD models predict that the resistive plasma response to the applied MP is shielded

Observation of a multimode plasma response and its relationship to density pumpout and edge-localized mode suppression

Density pumpout and edge-localized mode (ELM) suppression by applied n=2 magnetic fields in low-collisionality DIII-D plasmas are shown to be correlated with the magnitude of the plasma response driven on the high-field side (HFS) of the magnetic axis but not the low-field side (LFS) midplane. These distinct responses are a direct measurement of a multimodal magnetic plasma response, with each structure preferentially excited by a different n=2 applied spectrum and preferentially detected on the LFS or HFS. Ideal and resistive magneto-hydrodynamic (MHD) calculations find that the LFS measurement is primarily sensitive to the excitation of stable kink modes, while the HFS measurement is primarily sensitive to resonant currents (whether fully shielding or partially penetrated). The resonant currents are themselves strongly modified by kink excitation, with the optimal applied field pitch for pumpout and ELM suppression significantly differing from equilibrium field alignment.This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Awards No. DE-FC02-04ER54698, No. DE-AC02-09CH11466, No. DE-FG02-04ER54761, No. DE-AC05-06OR23100, No. DE-SC0001961, and No. DE-AC05-00OR22725. S. R. H. was supported by AINSE and ANSTO

Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks

Novel spatial, temporal, and energetically resolved measurements of bremsstrahlung hard-x-ray (HXR) emission from runaway electron (RE) populations in tokamaks reveal nonmonotonic RE distribution functions whose properties depend on the interplay of electric field acceleration with collisional and synchrotron damping. Measurements are consistent with theoretical predictions of momentum-space attractors that accumulate runaway electrons. RE distribution functions are measured to shift to a higher energy when the synchrotron force is reduced by decreasing the toroidal magnetic field strength. Increasing the collisional damping by increasing the electron density (at a fixed magnetic and electric field) reduces the energy of the nonmonotonic feature and reduces the HXR growth rate at all energies. Higher-energy HXR growth rates extrapolate to zero at the expected threshold electric field for RE sustainment, while low-energy REs are anomalously lost. The compilation of HXR emission from different sight lines into the plasma yields energy and pitch-angle-resolved RE distributions and demonstrates increasing pitch-angle and radial gradients with energy.United States. Department of Energy (DE-FC02-04ER54698)United States. Department of Energy (DE-FG02-07ER54917)United States. Department of Energy (DE-AC05-00OR22725)United States. Department of Energy (DE-FC02-99ER54512)United States. Department of Energy (DE-SC0016268

Use of Ar pellet ablation rate to estimate initial runaway electron seed population in DIII-D rapid shutdown experiments

Small (2-3 mm, 0.9-2 Pa • m3) argon pellets are used in the DIII-D tokamak to cause rapid shutdown (disruption) of discharges. The Ar pellet ablation is typically found to be much larger than expected from the thermal plasma electron temperature alone; the additional ablation is interpreted as being due to non-thermal runaway electrons (REs) formed during the pellet-induced temperature collapse. Simple estimates of the RE seed current using the enhanced ablation rate give values of order 1-10 kA, roughly consistent with estimates based on avalanche theory. Analytic estimates of the RE seed current based on the Dreicer formula tend to significantly underestimate it, while estimates based on the hot tail model significantly overestimate it

An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements

The DIII-D tokamak magnetic diagnostic system [E. J. Strait, Rev. Sci. Instrum. 77, 023502 (2006)] has been upgraded to significantly expand the measurement of the plasma response to intrinsic and applied non-axisymmetric "3D" fields. The placement and design of 101 additional sensors allow resolution of toroidal mode numbers 1 ≤ n ≤ 3, and poloidal wavelengths smaller than MARS-F, IPEC, and VMEC magnetohydrodynamic model predictions. Small 3D perturbations, relative to the equilibrium field (10(-5) < δB/B0 < 10(-4)), require sub-millimeter fabrication and installation tolerances. This high precision is achieved using electrical discharge machined components, and alignment techniques employing rotary laser levels and a coordinate measurement machine. A 16-bit data acquisition system is used in conjunction with analog signal-processing to recover non-axisymmetric perturbations. Co-located radial and poloidal field measurements allow up to 14.2 cm spatial resolution of poloidal structures (plasma poloidal circumference is ~500 cm). The function of the new system is verified by comparing the rotating tearing mode structure, measured by 14 BP fluctuation sensors, with that measured by the upgraded B(R) saddle loop sensors after the mode locks to the vessel wall. The result is a nearly identical 2/1 helical eigenstructure in both cases.S. R. Haskey wishes to thank AINSE Ltd. for providing financial assistance

Pedestal bifurcation and resonant field penetration at the threshold of edge-localized mode suppression in the DIII-D tokamak

Rapid bifurcations in the plasma response to slowly varying n=2 magnetic fields are observed as the plasma transitions into and out of edge-localized mode (ELM) suppression. The rapid transition to ELM suppression is characterized by an increase in the toroidal rotation and a reduction in the electron pressure gradient at the top of the pedestal that reduces the perpendicular electron flow there to near zero. These events occur simultaneously with an increase in the inner-wall magnetic response. These observations are consistent with strong resonant field penetration of n=2 fields at the onset of ELM suppression, based on extended MHD simulations using measured plasma profiles. Spontaneous transitions into (and out of) ELM suppression with a static applied n=2 field indicate competing mechanisms of screening and penetration of resonant fields near threshold conditions. Magnetic measurements reveal evidence for the unlocking and rotation of tearinglike structures as the plasma transitions out of ELM suppression.This work is supported by the U.S. Department of Energy under Awards No. DE-FC02-04ER54698, No. DE-AC02-09CH11466, No. DE-FG02-07ER54917, No. DE-FG02-89ER53296, No. DE-FG02-08ER54999, No. DE-FG02-08ER54984, No. DE-AC05-00OR22725, No. DE-FG02-86ER53218, and No. DE-FG02- 92ER54139

Implications of Vertical Stability Control on the SPARC Tokamak

To achieve its performance goals, SPARC plans to operate in equilibrium configurations with a strong elongation of $\kappa_\mathrm{areal}\sim1.75$, destabilizing the $n=0$ vertical instability. However, SPARC also features a relatively thick conducting wall that is designed to withstand disruption forces, leading to lower vertical instability growth rates than usually encountered. In this work, we use the TokSyS framework to survey families of accessible shapes near the SPARC baseline configuration, finding maximum growth rates in the range of $\gamma\lesssim100\,$s$^{-1}$. The addition of steel vertical stability plates has only a modest ($\sim25\%$) effect on reducing the vertical growth rate and almost no effect on the plasma controllability when the full vertical stability system is taken into account, providing flexibility in the plate conductivity in the SPARC design. Analysis of the maximum controllable displacement on SPARC is used to inform the power supply voltage and current limit requirements needed to control an initial vertical displacement of $5\%$ of the minor radius. From the expected spectra of plasma disturbances and diagnostic noise, requirements for filter latency and vertical stability coil heating tolerances are also obtained. Small modifications to the outboard limiter location are suggested to allow for an unmitigated vertical disturbance as large as $5\%$ of the minor radius without allowing the plasma to become limited. Further, investigations with the 3D COMSOL code reveal that strategic inclusion of insulating structures within the VSC supports are needed to maintain sufficient magnetic response. The workflows presented here help to establish a model for the integrated predictive design for future devices by coupling engineering decisions with physics needs

Wide operational windows of edge-localized mode suppression by resonant magnetic perturbations in the DIII-D tokamak

Edge-Localized-Mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor q95) in the DIII-D tokamak. However, wide q95 ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER Similar Shape (ISS) plasmas with n=3 RMPs, the range of q95 for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed q95 windows of ELM suppression and the dependence on plasma density, based on the conditions for resonant field penetration at the top of the pedestal. When the RMP amplitude is close to the threshold for resonant field penetration, only narrow isolated magnetic islands form near the top of the pedestal, leading to narrow q95 windows of ELM suppression. However, as the threshold for field penetration decreases with decreasing density, resonant field penetration can take place over a wider range of q95. For sufficiently low density (penetration threshold) multiple magnetic islands form near the top of the pedestal giving rise to continuous q95 windows of ELM suppression. The model predicts that wide q95 windows of ELM suppression can be achieved at substantially higher pedestal pressure in DIII-D by shifting to higher toroidal mode number (n=4) RMPs

TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial orders for analytic and cross-code test cases