Session NI2: Invited MF: MHD, Macro-Stability, Reversed Field Pinch, Z-Pinch

Controlled Healing of NTMs by Fueling Pellets in DIII-D and KSTAR and Impact on ECCD Requirements for Complete NTM Stabilization

DIII-D and KSTAR experiments with high field side deuterium pellet injection show a stabilizing effect of deep fueling on core 2/1 Neoclassical Tearing Mode (NTM) magnetic islands. NTM control is important as 2/1 islands can significantly degrade confinement and lead to plasma termination. DIII-D data and GENE non-linear gyrokinetic turbulence simulations with magnetic islands, presented here, qualitatively support the hypothesis that pellet triggered multi-scale NTM-turbulence interaction can cause islands to shrink. Deep fueling increases local gradients in the island region and concomitant local low-k turbulence in the expected range of the Micro Tearing Mode and Trapped Electron Mode instabilities. This can enhance transport through the island separatrices, reducing the pressure flat spot at the O-point and diminishing the NTM drive. Gyrokinetic simulations with the GENE code qualitatively support causality between increased gradients outside of the island, increased turbulence penetration into the island and reduced NTM drive. In sync with increased local gradients at q$=$2, a Mirnov probe array detects the reduction of the 2/1 magnetic amplitude. This interaction can reduce the required EC current for NTM suppression by 70{\%}, as predicted by the Rutherford equation. These benefits can (i) extend NTM control solutions to operational regimes where the current drive efficiency is low - in particular ITER's planned operation at half magnetic field, where the 2nd harmonic absorption at q$=$2 will have lower current drive efficiency due to 3rd harmonic absorption in the edge, (ii) free up gyrotrons for use elsewhere and (iii) improve the net electricity output of future reactors. Thus NTM healing by pellets may offer substantial benefits for ITER.   

\textbf{A New Explanation of Sawtooth Phenomena in Tokamaks}

The ubiquitous sawtooth phenomena in tokamaks are so-named because the central temperature rises slowly and falls rapidly, similar to the blades of a saw. First discovered in 1974, it has so far eluded a theoretical explanation that is widely accepted and consistent with experimental observations. We propose here a new explanation for sawtooth phenomena in auxiliary heated tokamaks that is motivated by our recent simulations and understanding of ``flux pumping'' in tokamaks$^{\mathrm{1}}$. In this theory, the role of the m$=$1 mode is primarily to generate a central dynamo voltage via a saturated interchange mode. This regulates the central safety factor, q$_{\mathrm{0}}$, to be very near but slightly above unity with very low central magnetic shear. As the temperature and density profiles peak, they abruptly become unstable to centrally localized non-resonant pressure driven ideal MHD modes with poloidal and toroidal mode numbers (m,n) with m$=$n \textgreater 1. It is these higher order modes interacting with each other that cause the sudden crash of the temperature profile, due to rapid E x B convection, not magnetic reconnection. Long time 3D MHD simulations of multiple cycles using M3D-C1 demonstrate this phenomenon, which appears to be consistent with many experimental observations: that q$_{\mathrm{0}}$ changes very little during the crash and is near 1.0; that the crash can be very abrupt and fast, occurring on an ideal MHD time scale; and that rapid impurity penetration can occur during the crash, implying strong convection. This also possibly offers an explanation of how (1,1) impurity snakes can survive many sawtooth oscillations . Important elements of these simulations are that they use high toroidal mode number resolution and that they use inductive current drive, i.e. not purely RF. $^{\mathrm{1}}$Jardin, \textit{et al}, Phys. Rev. Lett. \textbf{21} 215001 (2015), Krebs, \textit{et al}, Phys. Plasmas \textbf{24} 102511 (2017)   

Toroidal modeling of post-disruption runaway beam by MHD instabilities in DIII-D.

Understanding various potential mechanisms for relativistic runaway electrons (REs) mitigation or suppression is crucial, since REs can potentially cause severe material damage in ITER. A recent DIII-D experiment, where \textasciitilde 1 MA level of post-disruption runaway current was achieved, shows that fast-growing magneto-hydrodynamic (MHD) instabilities occur when the plasma edge safety factor drops to around 2, and these large MHD perturbations in turn suppress the runaway beam. The MARS-F stability computations identify these instabilities as resistive kink modes with a mixture of both internal and external eigenmode structures. A new drift orbit model for relativistic test electrons has been developed to study RE confinement in the presence of MHD perturbations. The updated code shows that a fast growing resistive kink instability of \textasciitilde 100 Gauss level induces a significant fraction of RE loss. The RE beam is completely lost as the instability grows up to 1 kG level, consistent with experiment. The key loss mechanism is the prompt drift orbit loss due to radial expansion of RE trajectory in the presence of 3D fields. The 3D field induced loss increases with the perturbation amplitude but decreases with the particle energy, while generally being not sensitive to the initial particle pitch angle. The particle velocity change, due to electric field acceleration/deceleration, small angle scattering, synchrotron radiation and Bremsstrahlung, further perturbs the RE trajectory but plays a minor role in prompt RE loss within microsecond time scale. The RE orbit model will also be applied to study RE confinement with 3D resonant magnetic perturbation fields. The idea of using RMP to excite/amplify MHD modes for RE control will also be exploited.   

Advances in physics understanding of high poloidal beta regime towards steady-state operation of CFETR

Experimental and modeling investigations on EAST and DIII-D show how plasma current profiles, turbulent transport and radiation properties self-consistently evolve toward fusion relevant steady state conditions. Integrated experiments on EAST demonstrate that high $\beta _{\mathrm{P\thinspace }}$(\textasciitilde 2.0), fully non-inductive, moderate bootstrap current fraction (f$_{\mathrm{bs}}$50{\%}) plasmas are maintained over 40 current relaxation times with metal wall, low rotation and small ELMs at high density (n$_{\mathrm{e}}$/n$_{\mathrm{GW}}$\textasciitilde 0.80) and using only RF H{\&}CD. The current density profile was broadened at higher density and higher $\beta_{\mathrm{P}}$ operation, with an increase of f$_{\mathrm{bs}}$, leading to a slightly reversed shear profile, which contributes to the increase in energy confinement, similar to observations on DIII-D. The improved confinement was observed at high $\beta _{\mathrm{P}}$, consistent with lower electron turbulence measurement. The achieved small ELMs facilitate RF power coupling in H-mode phase and reduce divertor sputtering/erosion. Low tungsten concentration was observed at high $\beta_{\mathrm{P\thinspace }}$with a hollow profile in the core region. Reduction of the peak heat flux on the divertor with f$_{\mathrm{rad}}$ up to 40{\%} was compatible with high $\beta_{\mathrm{P}}$ scenario by using active radiation feedback control. Modeling and physics experiments confirmed synergistic effects between ECH and LHW, where ECH enhances heating and current drive from LHW injection, enabling fully non-inductive operation at higher density. On DIII-D, high normalized fusion performance results from a large radius ($\rho $\textasciitilde 0.7) internal transport barrier, observed at high $\beta_{\mathrm{P}}$ (\textgreater 2.0) and high normalized density (n$_{\mathrm{e}}$/n$_{\mathrm{GW}}$\textasciitilde 1.0), and consistent with the effect of Shafranov shift stabilization of turbulence. Excellent confinement in this regime is insensitive to plasma rotation. These results increase confidence in the extrapolation of the high $\beta_{\mathrm{P}}$ regime to steady state scenarios for CFETR.   

Direct measurements of the 3D plasma flow velocity in single-helical-axis RFP plasmas

The first local velocity measurements of helical equilibrium plasmas in the RFP are made to characterize the equilibrium flow profile. In high current, low density MST plasmas, the island associated with the innermost resonant tearing mode can grow and envelop the magnetic axis, resulting in a saturated Single Helical Axis (SHAx) equilibrium. The process by which this self-organized transition occurs is not fully understood. Theory and modeling suggest that viscous dissipation or large flow or magnetic shear might stimulate the transition. Local, toroidally resolved non-axisymmetric velocity measurements are obtained with a CHERS diagnostic while using a resonant magnetic perturbation to control the orientation of the helical plasma. The axisymmetric part of the flow is a rigid-rotor-like poloidal flow and relatively flat toroidal flow. Outside of the core, r/a \textgreater 0.5, the non-axisymmetric flow shows variations of order 10 km/s and more structure than a simple sinusoidal variation matching the helical variation of the magnetic axis. V3FIT ideal MHD 3D equilibrium reconstructions shows magnetic shear with respect to the minor radius (dq/dr) is strengthened in a region outside of the helical magnetic axis due to flux surface compression (ds/dr). The toroidally resolved helical flow shear measured by CHERS is less than the critical shear predicted to mute nonlinear coupling of tearing modes. Flow measurements are compared with preliminary NIMROD simulations of visco-resistive, single-fluid MHD in toroidal and cylindrical geometry with full and limited axial periodicity. Both measurements and toroidal simulations show stronger inboard flows relative to the outboard. In the experiment, the n $=$ 5 component of the poloidal flow is phase shifted by \textasciitilde 0.7 rad from the reconnection-like flow observed in the simulations, possibly due to decoupling of the ion and electron fluids over much of the plasma.   

Sheared flow stabilized Z-pinch plasma production on the FuZE experiment

Sheared-flow stabilization is reigniting interest in Z-pinches for thermonuclear fusion. Recent measurements of steady-state DD neutron production lasting up to 8 $\mu $s, coincident with keV impurity ion temperatures and quiescent MHD activity suggest that thermonuclear plasmas are produced on the FuZE experiment. FuZE studies how a column of axially-flowing plasma with radial velocity shear can be compressed and heated by electrical current. We summarize our understanding of plasma dynamics on FuZE and possible control schemes via tailored gas injection. FuZE consists of a 1 m coaxial plasma accelerator, followed by a 0.5 m assembly region, an extension of the outer electrode past the inner. Gas is supplied from 3 sets of fast valves with independent mass flow rates and delay times to generate diverse axial gas density profiles. The discharge begins with an initial current sheet propagating in a snowplow manner, injecting a slug of plasma into the assembly region where it collapses towards the axis. Maintaining the pinch requires continuous plasma injection that is provided by a second current sheet moving backwards through the neutral gas in the accelerator. Flexible gas injection allows for control of this process. Plasma dynamics is characterized with several diagnostics. A fast video camera films visible light emission. Space-and-time resolved spectroscopy shows the presence of keV-temperature C-V ions with sheared velocity profiles, coincident with neutron production. Correlating time resolved spectroscopy with video reveals key phenomena: the presence of high neutral densities in the initial slug ejected by the snowplow, stagnation of plasma near the endwall, and silicon lines near viewports from plasma impact. Models describing these phenomena, and their implications for the shear-flow stabilized Z-pinch concept, are discussed.