J.W. Berkery

Advances in global MHD mode stabilization research on NSTX

Stabilizing modes that limit plasma beta and reduce their deleterious effect on plasma rotation are key goals for the efficient operation of a fusion reactor. Passive stabilization and active control of global kink/ballooning modes and resistive wall modes (RWMs) have been demonstrated on NSTX and research is now advancing towards understanding the stabilization physics and reliably maintaining the high beta plasma for confident extrapolation to ITER and a fusion component test facility based on the spherical torus. Active n = 1 control experiments with an expanded sensor set, combined with low levels of n = 3 field phased to reduce error fields, reduced resonant field amplification and maintained plasma rotation, exceeded normalized beta = 6 and produced record discharge durations limited by magnet system constraints. Details of the observed RWM dynamics during active control show the mode being converted to a rotating kink that stabilizes or saturates and may lead to tearing modes. Discharges with rotation reduced by n = 3 magnetic braking suffer beta collapse at normalized beta = 4.2 approaching the no-wall limit, while normalized beta greater than 5.5 has been reached in these plasmas with n = 1 active control, in agreement with the single-mode RWM theory. Advanced state-space control algorithms proposed for RWM control in ITER theoretically yield significant stabilization improvements. Values of relative phase between the measured n = 1 mode and the applied correction field that experimentally produce stability/instability agree with RWM control modelling. Experimental mode destabilization occurs over a large range of plasma rotation, challenging the notion of a simple scalar critical rotation speed defining marginal stability. Stability calculations including kinetic modifications to the ideal MHD theory are applied to marginally stable experimental equilibria. Plasma rotation and collisionality variations are examined in the calculations. Intermediate rotation levels are less stable, consistent with experimental observations. Trapped ion resonances play a key role in this result. Recent experiments have demonstrated magnetic braking by non-resonant n = 2 fields. The observed rotation damping profile is broader than found for n = 3 fields. Increased ion temperature in the region of maximum braking torque increases the observed rate of rotation damping, consistent with the theory of neoclassical toroidal viscosity at low collisionality.

The role of kinetic effects, including plasma rotation and energetic particles, in resistive wall mode stability

particles, in resistive wall mode stability J.W. Berkery1, S.A. Sabbagh1, R. Betti2, B. Hu2, R.E. Bell3, S.P. Gerhardt3, J. Manickam3, and M. Podesta3 1Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA 2Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA 3Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA

Progress in understanding error-field physics in NSTX spherical torus plasmas

The low-aspect ratio, low magnetic field and wide range of plasma beta of NSTX plasmas provide new insight into the origins and effects of magnetic field errors. An extensive array of magnetic sensors has been used to analyse error fields, to measure error-field amplification and to detect resistive wall modes (RWMs) in real time. The measured normalized error-field threshold for the onset of locked modes shows a linear scaling with plasma density, a weak to inverse dependence on toroidal field and a positive scaling with magnetic shear. These results extrapolate to a favourable error-field threshold for ITER. For these low-beta locked-mode plasmas, perturbed equilibrium calculations find that the plasma response must be included to explain the empirically determined optimal correction of NSTX error fields. In high-beta NSTX plasmas exceeding the n = 1 no-wall stability limit where the RWM is stabilized by plasma rotation, active suppression of n = 1 amplified error fields and the correction of recently discovered intrinsic n = 3 error fields have led to sustained high rotation and record durations free of low-frequency core MHD activity. For sustained rotational stabilization of the n = 1 RWM, both the rotation threshold and the magnitude of the amplification are important. At fixed normalized dissipation, kinetic damping models predict rotation thresholds for RWM stabilization to scale nearly linearly with particle orbit frequency. Studies for NSTX find that orbit frequencies computed in general geometry can deviate significantly from those computed in the high-aspect ratio and circular plasma cross-section limit, and these differences can strongly influence the predicted RWM stability. The measured and predicted RWM stability is found to be very sensitive to the E × B rotation profile near the plasma edge, and the measured critical rotation for the RWM is approximately a factor of two higher than predicted by the MARS-F code using the semi-kinetic damping model.

KSTAR equilibrium operating space and projected stabilization at high normalized beta

Along with an expanded evaluation of the equilibrium operating space of the Korea Superconducting Tokamak Advanced Research, KSTAR, experimental equilibria of the most recent plasma discharges were reconstructed using the EFIT code. In near-circular plasmas created in 2009, equilibria reached a stored energy of 54kJ with a maximum plasma current of 0.34MA. Highly shaped plasmas with near double-null configuration in 2010 achieved H-mode with clear edge localized mode (ELM) activity, and transiently reached a stored energy of up to 257kJ, elongation of 1.96 and normalized beta of 1.3. The plasma current reached 0.7MA. Projecting active and passive stabilization of global MHD instabilities for operation above the ideal no-wall beta limit using the designed control hardware was also considered. Kinetic modification of the ideal MHD n = 1 stability criterion was computed by the MISK code on KSTAR theoretical equilibria with a plasma current of 2MA, internal inductance of 0.7 and normalizedbetaof4.0withsimpledensity,temperatureandrotationprofiles. Thesteepedgepressuregradientofthis equilibrium resulted in the need for significant plasma toroidal rotation to allow thermal particle kinetic resonances to stabilize the resistive wall mode (RWM). The impact of various materials and electrical connections of the passive stabilizing plates on RWM growth rates was analysed, and copper plates reduced the RWM passive growth rate by a factor of 15 compared with stainless steel plates at a normalized beta of 4.4. Computations of active RWM control using the VALEN code showed that the n = 1 mode can be stabilized at normalized beta near the ideal wall limit via control fields produced by the midplane in-vessel control coils (IVCCs) with as low as 0.83kW control power using ideal control system assumptions. The ELM mitigation potential of the IVCC, examined by evaluating the vacuum island overlap created by resonant magnetic perturbations, was analysed using the TRIP3D code. Using a combinationofallIVCCswithdominant n = 2fieldandupper/lowercoilsinanevenparityconfiguration,aChirikov parameter near unity at normalized poloidal flux 0.83, an empirically determined condition for ELM mitigation in DIII-D, was generated in theoretical high-beta equilibria. Chirikov profile optimization was addressed in terms of coil parity and safety factor profile. (Some figures in this article are in colour only in the electronic version)

Investigation of multiple roots of the resistive wall mode dispersion relation, including kinetic effects

The resistive wall mode instability in tokamak plasmas has a complex frequency which can be determined by a dispersion relation that is cubic, in general, leading to three distinct roots. A simplified model of the dispersion relation, including kinetic effects, is presented and used to explore the behavior of these roots. By changing the plasma rotation frequency, it is shown that one root has a slow mode rotation frequency (less than the inverse wall time) while the other two rotate more quickly, one leading and one lagging the plasma rotation frequency. When realistic experimental parameters from the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] are used, however, only one slow rotating, near-marginal stability root is found, consistent with present experiments and more detailed calculations with the MISK code [B. Hu et al., Phys. Plasmas 12, 057301 (2005)]. Electron collisionality acts to stabilize one of the rotating roots, while ion collisionality can stabilize the ...

Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry

This paper presents a calculation of neoclassical toroidal viscous torque independent of large-aspect-ratio expansions across kinetic regimes. The Perturbed Equilibrium Nonambipolar Transport (PENT) code was developed for this purpose, and is compared to previous combined regime models as well as regime specific limits and a drift kinetic δf guiding center code. It is shown that retaining general expressions, without circular large-aspect-ratio or other orbit approximations, can be important at experimentally relevant aspect ratio and shaping. The superbanana plateau, a kinetic resonance effect recently recognized for its relevance to ITER, is recovered by the PENT calculations and shown to require highly accurate treatment of geometric effects.

Laser Discharge Initiation for Gas-fed Pulsed Plasma Thrusters

A method of discharge initiation at an undervoltage by a laser-induced pulse of electrons from a photocathode is presented. The intended application is to produce spatially uniform current sheet initiation in gas-fed pulsed plasma thrusters. The effect is explained by a space charge buildup which can increase the electric field of the gap. A theoretical model was developed and showed that an increase of the charge multiplication coefficient to a level above unity will produce a current rise to breakdown. Attempts to use an ultraviolet light pulse to create a photocurrent spike were unsuccessful probably due to inadequate surface preparation of the photocathode. Infared laser pulses, however, did lead to current production which lead to breakdown from a 15% undervoltage in argon.

Investigation of MHD instabilities and control in KSTAR preparing for high beta operation

Initial H-mode operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) is expanded to higher normalized beta and lower plasma internal inductance moving towards design target operation. As a key supporting device for ITER, an important goal for KSTAR is to produce physics understanding of MHD instabilities at long pulse with steady-state profiles, at high normalized beta, and over a wide range of plasma rotation profiles. An advance from initial plasma operation is a significant increase in plasma stored energy and normalized beta, with Wtot = 340 kJ, βN = 1.9, which is 75% of the level required to reach the computed ideal n = 1 no-wall stability limit. The internal inductance was lowered to 0.9 at sustained H-mode duration up to 5 s. In ohmically heated plasmas, the plasma current reached 1 MA with prolonged pulse length up to 12 s. Rotating MHD modes are observed in the device with perturbations having tearing rather than ideal parity. Modes with m/n = 3/2 are triggered during the H-mode phase but are relatively weak and do not substantially reduce Wtot. In contrast, 2/1 modes to date only appear when the plasma rotation profiles are lowered after H–L back-transition. Subsequent 2/1 mode locking creates a repetitive collapse of βN by more than 50%. Onset behaviour suggests the 3/2 mode is close to being neoclassically unstable. A correlation between the 2/1 mode amplitude and local rotation shear from an x-ray imaging crystal spectrometer suggests that the rotation shear at the mode rational surface is stabilizing. As a method to access the ITER-relevant low plasma rotation regime, plasma rotation alteration by n = 1, 2 applied fields and associated neoclassical toroidal viscosity (NTV) induced torque is presently investigated. The net rotation profile change measured by a charge exchange recombination diagnostic with proper compensation of plasma boundary movement shows initial evidence of non-resonant rotation damping by the n = 1, 2 applied field configurations. The result addresses perspective on access to low rotation regimes for MHD instability studies applicable to ITER. Computation of active RWM control using the VALEN-3D code examines control performance using midplane locked mode detection sensors. The LM sensors are found to be strongly affected by mode and control coil-induced vessel current, and consequently lead to limited control performance theoretically.

Magnetic Surface Visualizations in the Columbia Non-Neutral Torus

Visualizations of magnetic surfaces are a valuable diagnostic in the Columbia Non-neutral Torus (CNT). The CNT is a compact stellarator, which is currently being used to study non-neutral plasmas confined on magnetic surfaces. The full 3-D shapes of magnetic surfaces created by CNTs simple four circular coil geometry are readily visualized by using an electron beam and neutral gas. These visualizations are useful for probe alignment and the confirmation of the magnetic surface topology, and they were necessary for the recent installation of a conducting boundary conforming to the last closed magnetic surface.

The effect of an anisotropic pressure of thermal particles on resistive wall mode stability

The effect of an anisotropic pressure of thermal particles on resistive wall mode stability in tokamak fusion plasmas is derived through kinetic theory and assessed through calculation with the MISK code [B. Hu et al., Phys. Plasmas 12, 0 57301 (2005)]. The fluid anisotropy is treated as a small perturbation on the plasma equilibrium and modeled with a bi-Maxwellian distribution function. A complete stability treatment without an assumption of high frequency mode rotation leads to anisotropic kinetic terms in the dispersion relation in addition to anisotropy corrections to the fluid terms. With the density and the average pressure kept constant, when thermal particles have a higher temperature perpendicular to the magnetic field than parallel, the fluid pressure-driven ballooning destabilization term is reduced. Additionally, the stabilizing kinetic effects of the trapped thermal ions can be enhanced. Together these two effects can lead to a modest increase in resistive wall mode stability.