Bulletin of the American Physical Society
57th Annual Meeting of the APS Division of Plasma Physics
Volume 60, Number 19
Monday–Friday, November 16–20, 2015; Savannah, Georgia
Session PI3: MHD and RotationInvited

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Chair: Guoyong Fu, Princeton Plasma Physics Laboratory Room: Oglethorpe Auditorium 
Wednesday, November 18, 2015 2:00PM  2:30PM 
PI3.00001: Collapse of core toroidal angular momentum due to the coupling of rotating magnetic islands in tokamaks Invited Speaker: B.J. Tobias The dynamic, nonlinear evolution of tearing instabilities on DIIID reveals a coupling of rational surfaces that can lead to phaselocking amongst multiple rotating magnetic island chains.\footnote{B. Tobias, et. al, Rev. Sci. Instrum. 85, 11D847 (2014).} This loss of flow shear increases disruptivity, particularly at the low level of rotation expected in ITER. Bifurcation of differential mode frequency and fluid rotation in hybrid scenario discharges has been interpreted by comparison to a recently developed theory of nonlinear mode coupling.\footnote{R. Fitzpatrick, Phys. Plasmas 22, 042514 (2015).} Magnetic islands of different toroidal mode number couple to flatten the toroidal rotation profile, and the resulting phaselocked state is similar to the socalled ``slinky'' mode observed in reversed field pinch devices. Reduction of the edge safety factor increases the momentum transport, easily overwhelming the local torque density available from neutral beam injection. In discharges with $q_{95}\sim$ 4.5, however, the participating modes do not remain phaselocked. In these cases, ECEImaging data have been used to show that the poloidal rotation of the composite, multihelicity structure exceeds that of the measured carbon (and estimated deuterium) fluid flow. The present model of nonlinear 3wave mode coupling does not generate the forces required to drive this rotation. Therefore, flow shear inversion represents a transition from phaselocking to a new regime of convective momentum transport in which additional mechanisms become important. These results highlight the importance of controlling multimode interactions in order to maintain stabilizing flow shear. [Preview Abstract] 
Wednesday, November 18, 2015 2:30PM  3:00PM 
PI3.00002: Effects of the q Profile on Toroidal Rotation in Alcator CMod LHCD Plasmas Invited Speaker: John Rice Changes in the core toroidal rotation velocity profiles following injection of lower hybrid (LH) waves have been documented in Alcator CMod plasmas. Shot by shot scans of LH input power have been performed at fixed magnetic field and electron density for several plasma currents. If the input power is low enough that there are still sawtooth oscillations, the change in the core rotation is in the countercurrent direction, consistent in sign and magnitude with direct momentum input from the LH waves. If the power level is high enough that there are significant changes to the q profile, the change in the toroidal rotation is in the cocurrent direction, consistent with changes in the residual stress through its dependence on the current density profile. The direction of the rotation changes depends on the whether q$_{\mathrm{0}}$ is below or above unity, and seemingly not on the magnetic shear. [Preview Abstract] 
Wednesday, November 18, 2015 3:00PM  3:30PM 
PI3.00003: Torqueconsistent 3D force balance and optimization of nonresonant fields in tokamaks Invited Speaker: JongKyu Park A nonaxisymmetric magnetic perturbation in tokamaks breaks the toroidal symmetry and produces toroidal torque, which is well known as neoclassical toroidal viscosity (NTV) effects. Although NTV torque is second order, it is the firstorder change in the pressure anisotropy that drives currents associated with local torques and thereby modifies the field penetration in force balance. The force operator becomes nonHermitian, but can be directly solved using parallel, toroidal, and radial force balance, leading to a modified EulerLagrange equation. The general perturbed equilibrium code (GPEC), which has been successfully developed to solve the modified EulerLagrange equation, gives the torqueconsistent 3D force balance as well as selfconsistent NTV torque. The selfshielding of the torque becomes apparent in the solutions in high $\beta $, which was implied in recent MARSK applications [1]. Furthermore, the full response matrix including the torque in GPEC provides a new and systematic way of optimizing torque and nonresonant fields. Recently the optimization of 3D fields for torque has been actively studied using the stellarator optimizing tools [2], but the efficiency and accuracy can be greatly improved by directly incorporating the torque response matrix. There are salient features uncovered by response with the torque, as the response can become invisible in amplitudes but only significant in toroidal phase shift. A perturbation in backward helicity [3] is an example, in which NTV can be induced substantially but quietly without measurable response in amplitudes. A number of other GPEC applications will also be discussed, including the multimode responses in high$\beta $ tokamak plasmas and the new nonaxisymmetric control coil (NCC) design in NSTXU. This work was supported by DOE Contract DEAC0209CH11466. \\[4pt] [1] Z. R. Wang, M. Lanctot, Y. Liu, J.K. Park et al., Phys. Rev. Lett. \textbf{114,} 145005 (2015)\\[0pt] [2] S. Lazerson, J.K. Park et al., Plasma Phys. Controlled Fusion, in Press (2015)\\[0pt] [3] J.K. Park, Y. M. Jeon et al., Phys. Rev. Lett. \textbf{111}, 095002 (2013) [Preview Abstract] 
Wednesday, November 18, 2015 3:30PM  4:00PM 
PI3.00004: Effect of Resonant Magnetic Perturbations on 3D equilibria in the MST RFP Invited Speaker: Stefano Munaretto The orientation of 3D, stellaratorlike equilibria in the MST RFP can now be controlled with application of an m $=$ 1 RMP. This has led to greatly improved diagnosis, revealing enhancements in both the central electron temperature and density. Coupled to a recent advance in the V3FIT code, reconstructions of the 3D equilibria have also been dramatically improved. The RMP also inhibits the generation of highenergy \textgreater 20 keV electrons that is otherwise common with the 3D state. This state occurs when the normally broad spectrum of coreresonant m $=$ 1 tearing modes condenses, with the innermost resonant mode growing to large amplitude, reaching $\sim$ 8{\%} of the axisymmetric field strength. This occurs in plasmas of sufficiently large Lundquist number $\sim$ I$_{\mathrm{p}}$T$_{\mathrm{e}}$$^{3/2}$, and the duration of the state is maximized with zero applied Bt (infinite toroidal beta). As the dominant mode grows, eddy current in MST's conducting shell slows the mode's rotation. This leads to locking of the 3D structure, but with an orientation that varies randomly shot to shot, making diagnosis difficult. An m $=$ 1 RMP can now be applied with an array of saddle coils at the vertical insulated cut in the shell. With an amplitude br/B $\sim$ 10{\%} and a tailored temporal waveform, the RMP can force the 3D structure into any desired orientation relative to MST's diagnostics. A recent advance in V3FIT allows calculation of the substantial helical image current flowing in MST's shell, which has in turn allowed selfconsistent utilization of both external and internal (Faraday rotation) measurements of the magnetic field. The ORBIT code predicts reduced stochasticity and improved confinement of highenergy electrons within the 3D structure. The suppression of these electrons by the m $=$ 1 RMP may reflect a change to the central magnetic topology. The generation of these electrons is unaffected by nonresonant perturbations, such as m $=$ 3. Supported by the US DOE. [Preview Abstract] 
Wednesday, November 18, 2015 4:00PM  4:30PM 
PI3.00005: Gyrokinetic Simulation of Lown Tearing Modes Invited Speaker: Yang Chen Direct gyrokinetic simulation of the lown tearing mode in a tokamak plasma has been a great computational challenge, for two reasons. First, lown tearing modes, unlike the microtearing modes, have very small growth rates and very fine mode structure in the tearing layer, which requires a large number of radial grid cells and fine control of numerical dissipation. Second, kinetic electron effects are needed in the tearing layer. Here, we first present linear gyrokinetic simulation of the lown tearing mode in cylindrical geometry. Ions are gyrokinetic and electrons are either drift kinetic or fluid. New field solvers have been developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate lown modes. For the fluid electron model, an eigenmode analysis with finite Larmor radius effects has been developed to study the linear resistive tearing mode. Excellent agreement between eigenmode analysis and initial value gyrokinetic simulation is obtained. The mode growth rate is shown to scale with resistivity as $\eta^{1/3}$, the same as the semicollisional regime in previous kinetic treatments. Simulation of the collisionless and semicollisional tearing mode with drift kinetic electrons has been carried out with GEM's direct splitweight controlvariate algorithm. It is found that a full torus simulation of the m=2, n=1 tearing mode in a present day large tokamak is still difficult with kinetic electrons, but a generalized matching technique can be used to ameliorate the problem. The radial dimension is divided into an external region and the tearing region, with the external region described by a reduced model that gives the boundary condition for the tearing region. The size of the tearing region is small compared with the minor radius, but not arbitrarily small as done in the standard asymptotic matching approach. Gyrokinetic simulation verifies the collisionless tearing mode growth rate with finite electron mass, the semicollisional linear growth rate, as well as the nonlinear scaling of particle trapping frequency with linear growth rate in the collisionless regime. Nonlinear results including collisions show that the mode initially saturates at low amplitude, followed by an algebraic growth period (the Rutherford regime). Current progress on simulating the lown toroidal tearing mode in toroidal geometry will be reported. [Preview Abstract] 
Wednesday, November 18, 2015 4:30PM  5:00PM 
PI3.00006: Quasisteady multiple flux tubes induced by localized current perturbation in toroidal plasma Invited Speaker: Gunsu Yun Quasisteady helical modes with dual, triple, or more flux tubes are easily produced by localized current drive in the core of \textit{sawtoothing} plasma on the KSTAR tokamak [1, 2]. Individual flux tubes have $m/n=1/1$ helicity, corotate around the magnetic axis, and later merge into a single $m=1$ mode. The merged mode eventually crashes with rapid collapse of the core pressure and the next cycle repeats the same pattern, exhibiting sawtoothlike oscillations in the core pressure. The generation mechanism of multiple flux tubes (MFTs) has been studied in two different approaches to understand the observed trend that the number of flux tubes increases as the current drive location moves away from the magnetic axis up to about the magnetic surface of the safety factor $q=1$ at the mode collapse: (1) nonlinear reduced MHD simulation with a localized current source modeling the timevarying interaction between the current source and flux tubes [3] and (2) linear MHD simulation with a prescribed $q$ profile with a radially localized current blip. Both studies show that MFTs can be produced only in plasmas with nearly flat $q$ profile close to unity, \textit{suggesting the collapse of the $m=1$ mode (i.e., sawtooth crash) is complete.} Recent observation of longlived MFTs induced by localized current drive in nonsawtoothing plasma suggests that $q$ profile evolution toward lower$m$ instability is required for the merging and crash of MFTs.\\[4pt] [1] G.S. Yun et al., Phys. Rev. Lett. 109,145003 (2012)\\[0pt] [2] G.H. Choe et al., Nucl. Fusion 55, 013015 (2015)\\[0pt] [3] A. Bierwage et al., Nucl. Fusion 55, 013016 (2015) [Preview Abstract] 
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