Session TO4: ITER and MFE Physics

Transport Stiffness of TGLF and Its Impact on ITER

The TGLF Gyro-Landau-Fluid transport model has been successful in reproducing the observed density and temperature profiles in a wide variety of tokamak discharges from DIII-D, JET and TFTR. Recently, it was shown that the predicted fusion gain for ITER using TGLF is somewhat more pessimistic than previous GLF23 results due to finite aspect ratio effects that are only present in TGLF. A key ingredient in the TGLF predictions of ITER is profile stiffness. A consequence of the stiff core transport is that the fusion gain scales like $\beta_{ped}$ and like $1/P_{aux}$ at fixed $\beta_{ped}$. Since stiff core transport has an important role in our ITER predictions we seek to quantify the stiffness of TGLF. Stiffness ($S$) is defined as the ratio of the incremental energy diffusivity to the power balance energy diffusivity. To date, we find $S \sim 10$ is typical in the plasma core and drops to less than 3 in the near edge region. The electron and ion stiffness is examined in recent DIII-D experiments and in previous L- and H-mode similarity discharges.   

H-mode ITER Scenario Modeling

The TSC and PTRANSP codes are used in modeling ITER 15 MA H-mode discharges from ramp-up through flat-top. The simulations, in which the temperatures, toroidal angular frequency and currents are evolved, are carried out using the PTRANSP code starting with initial profiles and equilibria obtained from TSC code studies. The goal of these whole-device ITER simulations is to identify physical processes that critically impact fusion performance in ITER scenarios. The ITER 15MA H-mode simulation results are compared with ITER hybrid 12.5MA results [1]. The PTRANSP code includes a wide range of options for predictive simulations using different theory-based transport models, prescribed boundary equilibrium solvers, as well as sophisticated computations of heating, momentum and particle sources. The time evolution of temperature, toroidal angular frequency, current density profiles and fusion power production predicted using the new MMM v7.1 transport model are compared with those predicted using the GLF23 transport model. \\[4pt] [1] Self-Consistent Simulations of Plasma Scenarios with Fixed Boundary Equilibria, T. Rafiq, et al., Final Report for ITER Task Agreement C19TD38FU.   

Understanding first-principles RMP physics to obtain predictive ELM control capability in ITER

A significant new first-principles understanding in RMP penetration and pedestal response has been obtained in the kinetic particle code XGC0 in realistic diverted magnetic field geometry (cf., invited talk by G. Park at this meeting). Results are validated against DIII-D pedestal experiments, including n, T, Er, toroidal plasma flow, and the electron perpendicular flow profiles simulataneously. It appears that one of the key elements is the magnetic field stochasticity, modified by plasma response: The result is consistent with the experimental observation that ``the vacuum Chirikov$>$1 in the whole edge'' is only a necessary condition for ELM control. When the edge plasma is in the so-called ``ELM suppression q- window,'' the magnetic field stochasticity changes abruptly to connect the pedestal top to the material wall. Otherwise, there is a disconnect due to the plasma suppression of the resonant magnetic field. Dependence on the edge collisionality is being investigated. Implication of these new findings to ITER RMP coil design will be discussed. Plans for a more decisive first-prinicples investigation will be presented, including the different inter-device results on DIII-D, ASDEX- U, MAST, and NSTX.   

Analytical Model of Electron Thermal Effects on Interferometry-Polarimetry Measurements in Burning Plasmas

The increasing accuracy of interferometric/polarimetric (I/P) diagnostics requires increasingly precise theoretical models for correctly interpreting experimental data. This is especially important for next step fusion devices like ITER and DEMO where various interferometric techniques will be used for direct real time feedback control of device operations with time resolution $\le $ 1 msec. This determines the high accuracy ($\sim $1{\%}) required for line-averaged I/P measurements in ITER. To address this issue we developed an iterative analytical technique designed to analyze electron thermal effects on the I/P measurements. This approach yields simple analytic expressions for fast real time feedback corrections when slowly operating ray tracing codes are not effective. Our previous linear in $\tau $ = T$_{e }$/m$_{e}$c$^{2}<<$1 calculations predicted (10-30){\%} thermal corrections for the interferometric phase, Faraday rotation and Cotton-Mouton effect at T$_{e }$= 30 keV. This lowest order approach is insufficient for 1{\%} accuracy required by the ITER diagnostic specifications. We report here improved analytic model that includes quadratic terms in $\tau $ and new possibilities for advanced I/P measurements in plasma. *This work is supported by the U. S. DOE and NSF.   

ELM control using n=1 RMP in KSTAR

In the 3rd campaign of KSTAR experiments, the first H-mode discharges were successfully obtained by using NBI and ECRH. The pre-installed versatile in-vessel control coil system can be easily configured to provide a n=1 non-axisymmetric magnetic perturbation. Therefore one of major goals in the 4th campaign was dedicated to investigate ELM control by using n=1 resonant magnetic perturbations. Preliminary vacuum analysis for ELM control based on the H-mode discharges from the 3rd campaign show a possibility of ELM mitigation, by applying n=1 resonant magnetic perturbation with even parity. However a further analysis based on H-mode discharges expected in the 4th campaign shows an apparent possibility of ELM suppression rather than mitigation, by controlling q95. According to this preliminary analysis, RMP power supplies, for tentative use, have been prepared and examined showing maximum currents of 1.8 kA per turns. In this presentation, we introduce preliminary experimental results of ELM control by using this n=1 resonant magnetic perturbations.   

Resistive Wall Modes Identification and Control in RFX-mod low qedge tokamak discharges

In this work the MHD stability of RFX mode tokamak discharges with q$_{edge}<$3 will be studied. The target plasma scenario is characterized by a plasma current 100kA$<$Ip$<$150kA, a Greenwald density fraction included between 0.5 and 1 and a minimum q$_{edge}$=1.7 value. The operation in this regime is limited by the onset of a slowly rotating m=2 n=1 kink mode, which eventually locks to the wall and induces a disruption. The mode growth rates have been characterized with regard to the main plasma parameters and have been compared with predictions by the linear MHD code MARS-F, and the 3D finite elements code CARMA, permitting a full Resistive Wall Mode identification. The stability of the mode in the vicinity of the unstable operational space has been studied using MHD spectroscopy on the (2/1) mode. A good discharge behaviour with q$_{edge}<$2 has been routinely obtained using the RFX-mod MHD active control system, which is capable of fully stabilizing the mode acting on the radial magnetic field at the plasma edge.   

3D Equilibrium Reconstruction of Plasmas with Islands and Stochastic Regions

Recent advances in computational speed and simulation codes have allowed the reconstruction of 3D fields with islands and stochastic regions from experimental data. The ability to reconstruct axisymmetric equilibria from various diagnostic measurements has become a cornerstone of data analysis in tokamaks. However, these codes cannot treat the 3D fields produced by RMP's or helical equilibrium structures present in modern Tokamaks. Building upon work to fit VMEC equilibria to W7AS measurements, the reconstruction effort was applied to the Large Helical Device (LHD). The PIES code relaxes the nested flux surface constraint of the VMEC reconstruction found with the PIES code. This allows for the presence of magnetic islands and stochastic regions. This allows for discussions of the effect of such features on magnetic diagnostics. Work is underway to fit PIES equilibria to measurements in DIIID.   

Theory of external geodesic acoustic mode excitation

It is extremely appealing to externally excite geodesic acoustic modes in a tokamak, either for diagnostic purposes, since the GAM frequency is dependent on the ion and electron temperature and the flux surface shapes, or, provided sufficiently large amplitude is achievable, to artificially reduce the turbulent transport due to the GAM shearing rate. As for symmetry, it should be possible to generate GAMs by applying an external magnetic field at the GAM frequency with a $(m,n)=(2,0)$ component to the plasma column. (In principle, this could be done at present, e.g., in DIII-D with the RWM stabilization coils [I-coils]). The action of external currents on the flux surfaces of the plasma has been studied analytically and with a novel dynamic equilibrium code. The results exhibit several control knobs to influence the drive effectivity and aid in designing a GAM drive antenna. The magnetic drive is possible because a GAM localized at a flux surface exhibits a small ($O(\rho^*)$), intrinsically nonlocal magnetic perturbation of large radial range ($\sim$ minor radius) neglected in most turbulence codes. The response of the turbulent plasma to the external driving has been studied using nonlocal NLET code runs including scenarios of complete local turbulence suppression.   

Gyrokinetic particle simulations of reversed shear Alfv\'en eigenmode in DIII-D tokamak

Simulations of reversed shear Alfv\'en eigenmode (RSAE) in DIII-D discharge 142111 near $750 \mathrm{ms}$ have been successfully performed using the global gyrokinetic toroidal code (GTC). The background plasma pressure raises the mode frequency due to the elevation of the Alfv\'en continuum by the geodesic compressibility. The non-perturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory due to the breaking of radial symmetry, in qualitative agreement with XHMGC and TAEFL simulations and recent 2D imaging of RSAE mode structure in DIII- D tokamak. Various RSAE damping mechanisms are identified and measured in the simulations. The mode structure, frequency, and growth rate obtained from GTC simulations are close to those given by GYRO and TAEFL simulations. The frequency up-chirping of the RSAE and the mode transition from RSAE to toroidal Alfv\'en eigenmode (TAE) are revealed to be close to the experimental results when scanning $q_{\min}$ values in our simulations. Study of nonlinear effects of the RSAE is in progress.   

Energy absorption due to spatial resonance of Alfven waves at continuum tip

We investigate the response of tokamak plasma to an external driving source. An impedance-like function depending on the driving frequency that is growing at a small rate, is calculated and interpreted with different source profiles. Special attention is devoted to the case where driving frequency approaches that of the TAE continuum tip. The calculation can be applied to the estimation of TAE damping rate by analytically continuing the inverse of the impedance function to the lower half plane. The root of the analytic continuation corresponds to the existence of a quasi-mode, from which the damping rate can be found.   

Nonlinear development of Magnetic Islands by Symmetry Breaking in Fast Interchange-Drift Modes

We investigate the multi-scale nonlinear dynamics of a linearly stable/unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island. Examples from ITG and ETG driven turbulence are given.   

Simulation of pellet ablation in DIII-D tokamak

We investigated by numerical simulations the effect of various physical parameters on the pellet ablation rate in a tokamak. In particular, we did benchmark simulations against exprimental data from DIII-D tokamak pellet launches. As a model for the tumbling pellet, the anisotropic heating of pellet was averaged over the pellet surface so that the pellet remains spherical as it ablates. The rotation of the pellet due to the distribution of electrostatic potential was included in the simulations. DIII-D plasma temperature profile was used, while the plasma density was assumed to have a linear ramp in the pedestal region. The pellet lifetime and density profiles reproduced by simulations have been compared to the experimental measurements. The mechanisms for the striation in the ablation cloud have also been studied numerically.   

Evaluation of plasma torque by RF waves in a tokamak using a combined Full-wave code and bounce-averaged Fokker-Plank code

RF power injection with an asymmetric wave spectrum relative to the static magnetic field direction is a significant source of torque in a tokamak. In order to investigate the ion toroidal rotation and neoclassical radial pinch generated by the RF wave, it is necessary to first compute the torque density on a flux surface. We propose theoretically that there exist two equivalent methods to evaluate the momentum source term, and apply each method to the case of Lower hybrid wave injection in the Alcator C-Mod device. One method is to use the electric field and the susceptibility in a full-wave code (TORLH), and the other is to use the distribution function and Kennel-Engelmann quasilinear diffusion coefficient in a bounce-averaged Fokker-Plank Code (CQL3D). For self-consistency between the electron distribution function and RF electric field, the Fokker-Plank code is iterated with the wave code. Both methods were found to yield the same result with acceptable error. Furthermore the effective parallel refractive index of the RF waves was deduced from the relation between the torque and the power deposition.   

Evolution of the periodicity of magnetic orbits around the magnetic axes during a Sawtooth crash

In this talk/poster, we present some initial research into the evolution of the periodicity of magnetic orbits around the magnetic axes during a Sawtooth crash. In the Kadomtsev sawtooth model, the magnetic axis shifts and merges with the q=1 surface, and is replaced by a magnetic island formed by the reconnection. We have been able to observe the evolution of the periodicity of magnetic orbits around both the old and new axes during this process. During the sawtooth, which magnetic axis should be considered the ``true'' axis is ambiguous; thus, the traditional definition of the safety factor becomes ill-defined. We consider the evolution of q and p, where p and q are the ratio of the toroidal to poloidal transits around the two axes. Generally, p and q are not equal during the sawtooth process. The magnetic fields during the instability are calculated using the extended-MHD code M3D-C1. The periodicity of the magnetic orbits are dynamically illustrated using new field-line tracing capabilities implemented in the visualization software VisIt.   

Improvement of the Gyocenter-Gauge (G-Gauge) algorithm

The gyrocenter-gauge (g-gauge) algorithm was improved to simulate rf waves propagating in the three-dimensional sheared magnetic field. The conventional local gyro-center coordinate system $(X,Y,Z,\mu,\theta,u)$ is constructed on the local magnetic field. When particle travel in a sheared magnetic field, the coordinates of particles must be transformed between different local coordinate systems. To avoid these transformation, a new geometric approach is developed to construct a global Cartesian gyro-center coordinate system $(X,Y,Z,v_{x},v_{y},v_{z})$, where $(X,Y,Z)$ is the coordinate of the gyro-center, and $(v_{x},v_{y},v_{z})$ is the velocity of particle. In the g-gauge theory, the perturbation of distribution function, is obtained from the Lie derivative of gyro-center distribution function F along the perturbing vector field G. The evolution of the first order perturbed distribution contains a term $L_{\tau}L_{G}F=L_{\left[\tau,G\right]}F$ , where $\tau$ is the Hamilton vector field of unperturbed world-line of particles. It is proved that vector field $\left[\tau,G\right]$ may be directly solved from the electromagnetic fields. In the improved algorithm, $L_{G}F$ is calculated by integrating along the unperturbed world-line. The improved g-gauge algorithm has been successfully applied to study the propagation and evolution of rf waves in three-dimensional inhomogeneous magnetic field.