Session JO09: Magnetic Confinement: MHD & Control

Live

A numerical study on the influence of plasma viscosity and of the plasma $\beta $ ($=$kinetic pressure/magnetic pressure) parameter on the nonlinear evolution of resistive internal kink modes in tokamak plasmas is presented. A new regime with relatively low viscosity is found, such that sawtooth oscillations spontaneously evolve towards states with stationary $m/n=$1 magnetic islands. It is suggested that the mechanism at work in the limit of small viscosity is related to magnetic flux pumping, which, allied with the nonlinear resistive internal kink dynamics, leads to a stationary helical flow, only weakly dissipated by viscosity and entirely self-consistent with the presence of saturated $m/n=$1 stationary magnetic islands. It is also found that the threshold viscosity value for the onset of the steady state regime increases with increasing $\beta $ values. The newly found regime for a steady-state $m/n=$1 magnetic island may be relevant for the understanding of tokamak experiments, where saturated helical structures such as the density snake and steady-state magnetic islands are sometimes observed in the core plasma region where the safety factor is close to or below unity   

Live

An outstanding problem in sawtooth physics are the observations where $q_0$ stays around $0.7$, which cannot be explained by the Kadomtsev model that predicts a reset to $q_0 = 1$. We present a sawtooth model where the crash is caused by stochastization of a core region through the transition of the magnetic axis into an alternating-hyperbolic X-point when $q_0$ reaches $2/3$, which is within measurement uncertainty of the oft-measured value of $0.7$. This transition is revealed through the identification of the structure of the magnetic field line map around the axis with elements of the Lie group $\mathrm{SL}(2, \mathbb{R})$, which shows several transitions, one of which when $q_0=2/3$. We identify a fast-growing ideal 2/3 mode localized on the axis that appears when $q_0=2/3$ which perturbs the magnetic field such as to drive the transition to the alternating-hyperbolic geometry and stochastization of the core region.   

Live

Motional Stark effect (MSE) data acquired during large fast-ion stabilized sawteeth are critically reexamined. The safety factor at the sawtooth crash changes by $\Delta q\simeq0.15$, much more than any likely errors, indicating that substantial reconnection occurs at these sawtooth crashes. The absolute magnitude of the central safety factor after the crash is less certain: $q_0\simeq0.90$-0.97 with an uncertainty of $\sim0.05$.   

Live

The core plasma in tokamaks is known to exhibit sawtooth oscillations when q-axis drops below unity. In each sawtooth cycle, temperature, density, and current in the core increase gradually, followed by a rapid drop in these quantities. The rapid drop, known as the sawtooth crash, is attributed to magnetic reconnection. We study the sawtooth crash process in three-dimensions using a new fully-kinetic particle-in-cell code called PICTOR. Our self-consistent kinetic simulations reveal that the dynamics at the kinetic scales, which are not resolved by MHD, play a significant role. We find that a) linear growth of large-scale internal kink modes, which precede the crash, is much slower than what is predicted by the MHD, b) turbulence and micro-instabilities are excited within the spatial domain where the safety factor q is less than unity, and their relative strength and nature depend on the radial profile of the safety factor and pressure, and c) the plasma pressure becomes substantially anisotropic during the crash, with distribution functions showing strong non-Maxwellian features.   

Live

High-performance tokamak plasmas are sometimes terminated prematurely by disruptions, one cause of which is operation with an edge safety factor $q_a \leq 2$. In order to better understand plasma behavior near and beyond this stability boundary, and to set the stage for future studies of disruption physics, tokamak discharges are studied with low edge safety factor $0.8 \leq q_a \leq 2.5$ in the Madison Symmetric Torus (MST). The MST has a thick, circular conducting shell which prevents the growth of the external kink instability, but allows the study of internally resonant resistive kink modes. Magnetic equilibria and fluctuations are investigated using a high-spatial-resolution probe spanning roughly the outer half of the minor radius. The effect of density variations on the approach to steady-state is discussed, and internal measurements of sawtooth behavior are presented. Experimental equilibrium reconstructions are used to initiate nonlinear MHD simulations with the NIMROD code, with a Lundquist number, $S \sim 10^5$, similar to that in the experiment. The modeled MHD behavior is compared to that of the experiment, both to help understand the experimental data and to help validate the numerical model.   

Live

General Fusion is developing a fusion reactor based on compression of a self-organized spherical tokamak plasma by a liquid metal liner. To reach conditions for energy production the DT plasma will be compressed from meter to decimeter size in milliseconds. Due to resistivity of the liquid metal, magnetic flux will diffuse from the plasma volume into the liquid during the compression. This soaking of magnetic flux into the wall will be enhanced by flux shearing in the converging quasi-incompressible liquid metal flow. The soaking of poloidal flux in particular has significant consequences for the plasma including decrease of edge q and q shear and degradation of major radius compression. Two-dimensional MHD simulation of plasma compression by a resistive liquid metal liner is used to explore attainment of fusion conditions in the presence of flux diffusion.   

Live

Future reactors, including ITER, will have to withstand severe steady state high heat flux loads on many plasma-facing components (PFCs). Thus, robust, reliable and simplified physics-based RT models for monitoring and effective feedback control strategies for PFC heat load control are mandatory on future fusion reactors. Flux expansion control in the scrape-off layer of a reactor offers the possibility of controlling heat flux and divertor detachment closer to the timescale of the ion equilibration time (\textasciitilde few to 10's of ms) in comparison to the slow response (\textasciitilde 1 s) anticipated for reactor gas valves. A new controller has been developed to make use of the flexible divertor poloidal field coil set of the DIII-D tokamak, and enable precise control of the flux expansion. The design ensures flexibility through a complementary set of orthogonal actuator directions to guarantee minimum effect on existing controlled variables, e.g. radial and vertical position of the X-point. A non-linear free-boundary simulation code (GSevolve) is used to study the closed loop response and to verify the implementation of the algorithm on the DIII-D plasma control system. First results of the experimental commissioning of the new controller during the 2020 DIII-D campaign are presented   

Live

The HIT-SI3 device uses Steady-Inductive Helicity Injection (SIHI) to form and sustain spheromak plasma equilibria. A real-time control system has been developed to control the amplitude, phase, and offset of bulk plasma parameters of the SIHI system. Control software running entirely on a Nvidia Tesla P40 Graphical Processing Unit (GPU) is able to receive digitizer inputs at a sample rate of 10 MS/s and send response patterns to a PWM controller with a control loop period of 12.8 $\mu$s. A three-parameter PID controller is shown to be sufficient to inform the PWM controller to drive the desired oscilltaing plasma waveform, with an oscillating frequency of 15.6 kHz. This control system allows the demonstration of perturbation mode spectrum control in the formation and sustainment of spheromak plasmas on the HIT-SI3 device. Plans for feedback control of the upcoming HIT-SIU injector system will be presented.   

Live

ITER's operational characteristics of high-power long-pulse DT operation present a complex and challenging radiation environment. The nuclear radiation source consists of both the plasma and activated water. Activation of tokamak cooling water results from neutron irradiation of oxygen in water resulting in $^{\mathrm{16}}$N gammas and $^{\mathrm{17}}$N neutrons as reaction products. The need for radiation hardened electronics was established based on a detailed radiation transport and shielding analysis undertaken at Oak Ridge National Laboratory for combined plasma and activated water sources. The analysis demonstrated that it was not possible to implement sufficient shielding (due to space and weight constraints) to moderate neutrons sufficiently to comply with the Total Neutron Flux (TNF) alert threshold of 10$^{\mathrm{-2}}$ n/cm$^{\mathrm{2}}$. Having established mixed gamma and neutron radiation field requirements, a modular solution was devised based on the CERN GigaBit Transceiver (GBT) custom radiation tolerant ASICs initially developed for the LHC ATLIS, CMS and ALICE detectors at CERN.   

Live

Steady state fusion reactor design free from large scale instabilities is one of the main goals in the fusion research community. In magnetically confined fusion devices, transport barriers formation can be characterized by the local reduction of the heat and particle diffusivities. Transport barriers help to make the plasma core hot and dense enough to get fusion power. Removal of these barriers allows profile relaxation through the enhancement of turbulence. E X B shear suppression of the turbulence plays the major role in formation of the internal transport barriers. Control of internal transport barriers in the ITER parameter scenarios is studied. External actuators like NBI power, RF power and Pellets are used to control the profile and the barrier. ~We used a one dimensional five field transport model for this research. We explored the use of a combination of RF heating and pellet injection to control the local gradients and therefore the growth rates and shearing rates for barrier initiation and control in self heated plasmas. Self-heating is found to reduce the amount of external power necessary for the steep profile formation as compared to the case without it. Using RF heating on both electron and ion channels at proper locations, electron channel barriers along with ion channel barriers can be formed and removed demonstrating a control technique. Likewise pellets can also be one of the controlling knobs for those barriers.   

Not Participating

The influence of toroidal plasma rotation on the stability of the resistive wall mode (RWM) is investigated using the AEGIS code for the newly designed China Fusion Engineering Test Reactor (CFETR) 1GW steady-state operating (SSO) scenario. Generally the RWM is found unstable in this scenario, and can be stabilized by uniform toroidal rotation above $1.5\%$ core Alfv\'{e}nic speed. However, the stabilizing effects are not so robust while considering the non-uniform rotation profiles. It is found that the rotation at the plasma edge region affects the RWM the most and the rotation in the core region is less crucial. This is due to the peeling-like mode structure caused by the high current and pressure gradients in the edge pedestal region. By artificially reduce the bootstrap current fraction and pressure gradient in pedestal region in the equilibrium, the amplitude of the internal mode radial eigenfunction becomes much larger relatively and have more interaction with the core rotation. Our study suggests that to keep RWM stable in CFETR 1GW SSO scenario, the edge rotation needs to be maintained at above $1.5\%$ core Alfv\'{e}nic speed, if none of the kinetic stabilization mechanisms for RWM is taken into account.   

Not Participating

Using the in-viscid two-field reduced MHD model, a new analytical theory is developed to unify the Hahm-Kulsrud-Taylor (HKT) linear solution and the Rutherford nonlinear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in Taylor's problem. An integral form of analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford nonlinear solution. In particular, the quasi-linear effect can be described by a single coefficient $K_s$. The HKT linear solution for response can be recovered when the index $K_s\propto S^{8/5} \psi_c^2\rightarrow 0$. On the other hand, the quasi-linear current perturbation plays a key role in the island growth when $K_s\sim1$. Our new analytical solution has also been compared with reduced MHD simulations with agreement.   

Plasma flow evolution in response to resonant magnetic perturbation in a tokamak

Externally applied non-axisymmetric magnetic fields such as error field and resonant magnetic perturbation (RMP) are known to influence the plasma momentum transport and flow evolution through plasma response in a tokamak, whereas the evolution of plasma response itself strongly depends on the plasma flow as well. The nonlinear interaction between the two have been captured in the conventional error field theory with a ``no-slip'' condition, which has been recently extended to allow the ``free-slip'' condition. For comparison with simulations, we solve for the nonlinear plasma response and flow evolution driven by a single-helicity RMP in a tokamak, using the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Good agreement with the extended theory has been achieved for plasma flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the ``no-slip'' condition diminishes as the plasma resistivity approaches zero.   

Steady state toroidal rotation profile in tokamak edge pedestal in presence of resonant magnetic perturbations

Steady state toroidal rotation can significantly influence the transport and stability in tokamak edge pedestal, as well as the edge plasma response to resonant magnetic perturbation (RMP). Neoclassical toroidal viscosity (NTV) torque induced by RMP has been found significant in tokamak edge pedestal due to large diamagnetic drifts [1]. In this work, we calculate the edge steady state toroidal rotation in presence of RMP, based on a coupling scheme developed between the NIMROD and the NTVTOK codes. In presence of the NTV torque alone, toroidal rotation would relax to the neoclassical offset rotation in steady state. In general, other toroidal momentum sources in addition to NTV torque may pull the rotation away from the neoclassical offset rotation. However, as the RMP amplitude increases and the NTV torque dominates, the steady state toroidal rotation would eventually evolve towards the neoclassical offset rotation, which is found peaked at the center of edge pedestal. Of particular interest is a location where the rotation remains unchanged as RMP amplitude increases, which happens to be the natural offset rotation in absence of RMP. \\ $[1]$ X.-T. Yan, P. Zhu, and Y.-W. Sun, Phys. Plasmas 24, 082510 (2017).