Session BI3: 3D Fields and Effects

ITER Test Blanket Module Error Field Simulation Experiments

Recent experiments at DIII-D used an active-coil mock-up to investigate effects of magnetic error fields similar to those expected from two ferromagnetic Test Blanket Modules (TBMs) in one ITER equatorial port. The largest and most prevalent observed effect was plasma toroidal rotation slowing across the entire radial profile, up to 60\% in H-mode when the mock-up local ripple at the plasma was $\sim$4 times the local ripple expected in front of ITER TBMs. Analysis showed the slowing to be consistent with non-resonant braking by the mock-up field. There was no evidence of strong electromagnetic braking by resonant harmonics. These results are consistent with the near absence of resonant helical harmonics in the TBM field. Global particle and energy confinement in H-mode decreased by $<$20\% for the maximum mock-up ripple, but $<$5\% at the local ripple expected in ITER. These confinement reductions may be linked with the large velocity reductions. TBM field effects were small in L-mode but increased with plasma beta. The L-H power threshold was unaffected within error bars. The mock-up field increased plasma sensitivity to mode locking by a known $n=1$ test field ($n =$ toroidal harmonic number). In H-mode the increased locking sensitivity was from TBM torque slowing plasma rotation. At low beta, locked mode tolerance was fully recovered by re-optimizing the conventional DIII-D ``I-coils" empirical compensation of $n=1$ errors in the presence of the TBM mock-up field. Empirical error compensation in H-mode should be addressed in future experiments. Global loss of injected neutral beam fast ions was within error bars, but 1 MeV fusion triton loss may have increased. The many DIII-D mock-up results provide important benchmarks for models needed to predict effects of TBMs in ITER.   

Measurement and Modeling of 3D Equilibria in DIII-D

A detailed experiment-theory comparison reveals that linear ideal MHD theory gives a quantitative description of the external magnetic plasma response to applied non-axisymmetric fields over a broad range of beta. This result represents a significant step toward the goal of advancing the quantitative understanding of 3-D tokamak equilibria. The comparison also highlights the need to include kinetic effects in the MHD model once beta exceeds 80\% of the kink mode limit without a conducting wall. Above the no-wall limit, the measured rotation dependence of the plasma response reveals evidence of resonances between the plasma perturbation and the trapped particle precession and bounce frequencies, providing the first direct evidence for the effect of kinetic resonances on 3-D equilibria. In these experiments, $n=1$ and $n=3$ magnetic fields were applied over a wide range of plasma parameters and field structures. Internal measurements, derived from toroidally distributed soft x-ray cameras, indicate the plasma perturbation structure is ideal and increases linearly with the applied perturbation strength. Ideal MHD modeling of the response field structure shows the plasma response simultaneously prevents reconnection by screening the applied resonant field at the rational surfaces, and amplifies the applied field components that excite the kink mode. Both effects are important when the applied perturbation has strong resonant components. These results elucidate the role of the plasma response in the measured variations of non-resonant magnetic field torques with plasma parameters, and uncover a dynamic response field in the regime relevant for suppression of edge localized modes by resonant magnetic perturbations.   

Three-dimensional equilibria and transport in RFX-mod: a description using stellarator tools

RFX-mod self-organized Single Helical Axis (SHAx) states, spontaneously obtained at high plasma current up to 2 MA, provide a unique opportunity to advance 3D fusion physics and establish a common knowledge basis in a parameter region not covered by Stellarator and Tokamak. VMEC code was adapted to reversed-field pinch (RFP) to model SHAx equilibria, which have a helical core embedded in an almost axisymmetric boundary. Feedback control of helical magnetic field reinforces persistency of 3D shaping, which also increases with plasma current. The helical region boundary, corresponding to an electron transport barrier with zero magnetic shear, high flow shear and improved confinement, is investigated using numerical codes common to the stellarator community. The experimental electron heat diffusivity ($\approx 10m^2/s$ at the barrier), computed by the ASTRA code in 3D coordinates, decreases with plasma current and corresponding residual chaos reduction. The averaged particle diffusivity $\bar {D}$ over the helical volume, estimated with the Monte-Carlo code ORBIT, is consistent with experiment and increases with collisionality. $\bar {D}$ does not show the $1/\nu $ trend of un-optimized stellarators because of de-trapping mechanisms and the absence of superbananas due to negligible helical ripple in the edge. Furthermore, DKES code is being adapted to RFP for local neoclassical transport computations, including radial electric field, in order to estimate diffusion coefficients in the barrier region for typical RFX-mod temperature and density profiles. No change of impurity transport is found, which is consistent with fully collisional transport, and experimentally with a hollow impurity profile and edge-peaked radiation measurements, as in LHD. Analytical and numerical tools like GS2 indicate that small-scale turbulence contributes to drive anomalous transport in the barrier region. Thermal conductivity estimated from microtearing modes is consistent with experiment.   

Minimizing stellarator turbulent transport by geometric optimization

Up to now, a transport optimized stellarator has meant one optimized to minimize neoclassical transport,\footnote{H.E. Mynick, \textit{Phys. Plasmas} \textbf{13}, 058102 (2006).} while the task of also mitigating turbulent transport, usually the dominant transport channel in such designs, has not been addressed, due to the complexity of plasma turbulence in stellarators. However, with the advent of gyrokinetic codes valid for 3D geometries such as GENE,\footnote{F. Jenko, W. Dorland, M. Kotschenreuther, B.N. Rogers, \textit{Phys. Plasmas} \textbf{7}, 1904 (2000).} and stellarator optimization codes such as STELLOPT,\footnote{A. Reiman, G. Fu, S. Hirshman, L. Ku, et al, \textit{Plasma Phys. Control. Fusion} \textbf{41} B273 (1999).} designing stellarators to also reduce turbulent transport has become a realistic possibility. We have been using GENE to characterize the dependence of turbulent transport on stellarator geometry,\footnote{H.E Mynick, P.A. Xanthopoulos, A.H. Boozer, \textit{Phys.Plasmas} \textbf{16} 110702 (2009).} and to identify key geometric quantities which control the transport level. From the information obtained from these GENE studies, we are developing proxy functions which approximate the level of turbulent transport one may expect in a machine of a given geometry, and have extended STELLOPT to use these in its cost function, obtaining stellarator configurations with turbulent transport levels substantially lower than those in the original designs.   

Core measurements of 3D effects in quasi-single-helicity plasmas in the MST RFP

As the current and temperature of RFP plasmas are increased, a spontaneous and self-organized transition can occur from the normal state involving multiple tearing modes of similar amplitude to a quasi-single-helicity state dominated by a single large mode. This dominant mode results in a 3D helical core plasma resembling a stellarator equilibrium, but with an axisymmetric boundary. We report on measurements of the internal magnetic field structure and confinement changes associated with this self-organized transition in MST plasmas. A unique, multi-chord FIR interferometer-polarimeter allows investigation of the magnetic equilibrium modifications and dynamical behavior of the dominant fluctuation associated with this transition. These measurements are made directly in the plasma core where the dominant mode is resonant. A helical shift in the magnetic axis by up to 10{\%} of the plasma diameter is directly observed. Interferometry reveals a peaked density profile within the 3D helical structure, and the global particle confinement time becomes twice that of standard multi-helicity RFP plasmas. Hard-x-ray emission with photon energies exceeding 100 keV indicates that energetic electrons are also well confined. This suggests that the magnetic field is much less stochastic within the 3D structure, consistent with improved thermal particle confinement. Faraday rotation measurements of the current density and magnetic field fluctuations associated with the dominant mode reveal strong correlation, and the Hall dynamo emf, $\langle \tilde {J}\times \tilde {B}\rangle _{\vert \vert } /n_e e$, is sustained for several ms. This is in sharp contrast to the short-lived (0.1 ms), impulsive dynamo in the sawtoothing multiple helicity state. The Hall dynamo emf reinforces the importance of two-fluid physics in magnetic self-organization.   

3D effects on energetic particle confinement and stability

Understanding the confinement and stability of energetic particle (EP) populations in 3D magnetic configurations is crucial to the future of all toroidal devices. Tokamaks will have weak symmetry-breaking effects from discrete coils, heterogeneous distributions of ferritic materials and non-symmetric (ELM/RWM) control coils, while stellarators and helical RFP states have dominant 3D features by design. Significant EP issues for 3D systems include: modifications of the plasma equilibrium and potential amplification of field errors, asymmetry enhanced EP losses and their impact both on wall heat loads and the confined EP distribution, 3D modifications to the Alfv\'{e}n gap and mode structure, and the stability properties of EP-destabilized Alfv\'{e}n modes. 3D equilibria that resolve localized TBM (test blanket module) asymmetries have now been developed for DIII-D and ITER. Such symmetry breaking leads to enhanced EP losses and focused wall deposition. 3D effects also modify the Alfv\'{e}n spectrum by increasing the number of possibilities for mode coupling and introducing new gap structures, including the helical and mirror gaps, fine scale ripple-induced gaps and continuum crossing gaps. Improved methods have recently been developed for evaluating these modes and their stability, taking into account the large number of coupled modes and finite orbit width effects. Successful Alfv\'{e}n mode identifications have been made for a range of stellarators, including W7-AS, LHD, HSX and TJ-II. A comprehensive understanding of energetic particle physics with 3D effects is a necessary prerequisite for wall protection, plasma control and flexibility and for new diagnostic development possibilities in future ignited systems.