N.C. Logan

Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D

DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics (MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidal mode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. These tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. Scans of the applied poloidal spectrum and edge safety factor confirm that low-pressure, n = 1 non-axisymmetric tokamak equilibria are determined by a single, dominant, stable eigenmode. However, at higher beta, near the ideal kink mode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.

Error field detection in DIII-D by magnetic steering of locked modes

Optimal correction coil currents for the n?=?1 intrinsic error field of the DIII-D tokamak are inferred by applying a rotating external magnetic perturbation to steer the phase of a saturated locked mode with poloidal/toroidal mode number m/n?=?2/1. The error field is detected non-disruptively in a single discharge, based on the toroidal torque balance of the resonant surface, which is assumed to be dominated by the balance of resonant electromagnetic torques. This is equivalent to the island being locked at all times to the resonant 2/1 component of the total of the applied and intrinsic error fields, such that the deviation of the locked mode phase from the applied field phase depends on the existing error field. The optimal set of correction coil currents is determined to be those currents which best cancels the torque from the error field, based on fitting of the torque balance model. The toroidal electromagnetic torques are calculated from experimental data using a simplified approach incorporating realistic DIII-D geometry, and including the effect of the plasma response on island torque balance based on the ideal plasma response to external fields. This method of error field detection is demonstrated in DIII-D discharges, and the results are compared with those based on the onset of low-density locked modes in ohmic plasmas. This magnetic steering technique presents an efficient approach to error field detection and is a promising method for ITER, particularly during initial operation when the lack of auxiliary heating systems makes established techniques based on rotation or plasma amplification unsuitable.

The importance of matched poloidal spectra to error field correction in DIII-D

Optimal error field correction (EFC) is thought to be achieved when coupling to the least-stable “dominant” mode of the plasma is nulled at each toroidal mode number (n). The limit of this picture is tested in the DIII-D tokamak by applying superpositions of in- and ex-vessel coil set n = 1 fields calculated to be fully orthogonal to the n = 1 dominant mode. In co-rotating H-mode and low-density Ohmic scenarios, the plasma is found to be, respectively, 7× and 20× less sensitive to the orthogonal field as compared to the in-vessel coil set field. For the scenarios investigated, any geometry of EFC coil can thus recover a strong majority of the detrimental effect introduced by the n = 1 error field. Despite low sensitivity to the orthogonal field, its optimization in H-mode is shown to be consistent with minimizing the neoclassical toroidal viscosity torque and not the higher-order n = 1 mode coupling.

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.

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque

Systematic comparison and numerical benchmarking have been successfully carried out among three different approaches of neoclassical toroidal viscosity (NTV) theory and the corresponding codes: IPEC-PENT is developed based on the combined NTV theory but without geometric simplifications [Park et al., Phys. Rev. Lett. 102, 065002 (2009)]; MARS-Q includes smoothly connected NTV formula [Shaing et al., Nucl. Fusion 50, 025022 (2010)] based on Shaings analytic formulation in various collisionality regimes; MARS-K, originally computing the drift kinetic energy, is upgraded to compute the NTV torque based on the equivalence between drift kinetic energy and NTV torque [J.-K. Park, Phys. Plasma 18, 110702 (2011)]. The derivation and numerical results both indicate that the imaginary part of drift kinetic energy computed by MARS-K is equivalent to the NTV torque in IPEC-PENT. In the benchmark of precession resonance between MARS-Q and MARS-K/IPEC-PENT, the agreement and correlation between the connected NTV formu...

Calculation of neoclassical toroidal viscosity with a particle simulation in the tokamak magnetic braking experiments

Accurate calculation of perturbed distribution function #14;δf and perturbed magnetic fi eld #14;δB is essential to achieve prediction of non-ambipolar transport and neoclassical toroidal viscosity (NTV) in perturbed tokamaks. This paper reports a study of the NTV with a #14;δf particle code (POCA) and improved understanding of magnetic braking in tokamak experiments. POCA calculates the NTV by computing #14;f with guiding-center orbit motion and using #14;B from the ideal perturbed equilibrium code (IPEC). POCA simulations are compared with experimental estimations for NTV, which are measured from angular momentum balance (DIII-D) and toroidal rotational damping rate (NSTX). The calculation shows good agreement in total NTV torque for the DIII-D discharge, where an analytic neoclassical theory also gives a consistent result thanks to relatively large aspect-ratio and slow toroidal rotations. In NSTX discharges, where the aspect-ratio is small and the rotation is fast, the theory only gives a qualitative guide for predicting NTV. However, the POCA simulation largely improves the quantitative NTV prediction for NSTX. It is discussed that a self- consistent calculation of δ#14;B using general perturbed equilibria is eventually necessary since a non-ideal plasma response can change the perturbed eld and thereby the NTV torque.

Measurements of the toroidal torque balance of error field penetration locked modes

Detailed measurements from the DIII-D tokamak of the toroidal dynamics of error field penetration locked modes under the influence of slowly evolving external fields, enable study of the toroidal torques on the mode, including interaction with the intrinsic error field. The error field in these low density Ohmic discharges is well known based on the mode penetration threshold, allowing resonant and non-resonant torque effects to be distinguished. These m/n = 2/1 locked modes are found to be well described by a toroidal torque balance between the resonant interaction with n = 1 error fields, and a viscous torque in the electron diamagnetic drift direction which is observed to scale as the square of the perturbed field due to the island. Fitting to this empirical torque balance allows a time-resolved measurement of the intrinsic error field of the device, providing evidence for a time-dependent error field in DIII-D due to ramping of the Ohmic coil current.

Decoupled recovery of energy and momentum with correction of n = 2 error fields

Experiments applying known n = 2 ‘proxy’ error fields (EFs) find that the rotation braking introduced by the proxy EF cannot be completely alleviated through optimal n = 2 correction with poorly matched poloidal spectra. This imperfect performance recovery demonstrates the importance of correcting multiple components of the n = 2 field spectrum and is in contrast to previous results with n = 1 EFs despite a similar execution. Measured optimal n = 2 proxy EF correction currents are consistent with those required to null dominant mode coupling to the resonant surfaces and minimize the neoclassical toroidal viscosity (NTV) torque, calculated using ideal MHD plasma response computation. Unlike rotation braking, density pumpout can be fully corrected despite poorly matched spectra, indicating density pompous is driven only by a single component proportional to the resonant coupling. Through precise n = 2 spectral control density pumpout and rotation braking can thus be decoupled. Rotation braking with n = 2 fields is also found to be proportional to the level of co-current toroidal rotation, consistent with NTV theory. Furthermore, plasmas with modest counter-current rotation are insensitive to the n = 2 field with neither rotation braking nor density pumpout observed.

Magnetic diagnostics for equilibrium reconstructions in the presence of nonaxisymmetric eddy current distributions in tokamaks (invited).

The lithium tokamak experiment (LTX) is a modest-sized spherical tokamak (R(0)=0.4 m and a=0.26 m) designed to investigate the low-recycling lithium wall operating regime for magnetically confined plasmas. LTX will reach this regime through a lithium-coated shell internal to the vacuum vessel, conformal to the plasma last-closed-flux surface, and heated to 300-400 °C. This structure is highly conductive and not axisymmetric. The three-dimensional nature of the shell causes the eddy currents and magnetic fields to be three-dimensional as well. In order to analyze the plasma equilibrium in the presence of three-dimensional eddy currents, an extensive array of unique magnetic diagnostics has been implemented. Sensors are designed to survive high temperatures and incidental contact with lithium and provide data on toroidal asymmetries as well as full coverage of the poloidal cross-section. The magnetic array has been utilized to determine the effects of nonaxisymmetric eddy currents and to model the start-up phase of LTX. Measurements from the magnetic array, coupled with two-dimensional field component modeling, have allowed a suitable field null and initial plasma current to be produced. For full magnetic reconstructions, a three-dimensional electromagnetic model of the vacuum vessel and shell is under development.

Three-dimensional equilibria and island energy transport due to resonant magnetic perturbation edge localized mode suppression on DIII-D

Experiments in the DIII-D tokamak show that the plasma responds to resonant magnetic perturbations (RMPs) with toroidal mode numbers of n = 2 and n = 3 without field line reconnection, consistent with resistive magnetohydrodynamic predictions, while a strong nonlinear bifurcation is apparent when edge localized modes (ELMs) are suppressed. The magnetic response associated with this bifurcation is localized to the high field side of the machine and exhibits a dominant n = 1 component despite the application of a constant amplitude, slowly toroidally rotating, n = 2 applied field. The n = 1 mode is born locked to the vacuum vessel wall, while the n = 2 mode is entrained to the rotating field. Based on these magnetic response measurements and Thomson scattering measurements of flattening of the electron temperature profile, it is likely that these modes are magnetic island chains near the H-mode pedestal. The reduction in ∇Te occurs near the q = 4 and 5 rational surfaces, suggesting five unique islands are p...