Bulletin of the American Physical Society
53rd Annual Meeting of the APS Division of Plasma Physics
Volume 56, Number 16
Monday–Friday, November 14–18, 2011; Salt Lake City, Utah
Session JI2: 3D Equilibrium, Stability and Control |
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Chair: Mike Mauel, Columbia University Room: Ballroom BD |
Tuesday, November 15, 2011 2:00PM - 2:30PM |
JI2.00001: Stabilization of the Resistive Wall Mode and Error Field Reduction by a Rotating Conducting Wall Invited Speaker: The hypothesis that the Resistive Wall Mode (RWM) can be stabilized by high-speed differentially-rotating conducting walls is tested in a linear device. This geometry allows the use of cylindrical solid metal walls, whereas a torus would require a flowing liquid metal. Experiments over the past year have for the first time explored RWM stability with a rotating copper wall capable of achieving speeds ($r \Omega_{w}$) of up to 280 km/h, equivalent to a magnetic Reynolds number ($R_m$) of 5. The main results are: 1) Wall rotation increases the stability window of the RWM, allowing $\approx$ 25\% more plasma current ($I_p$) at $R_m$ = 5 while maintaining MHD stability. 2) Error field reduction below a critical value allows the observation of initial mode rotation, followed by braking, wall-locking, and subsequent faster growth. 3) Locking is found to depend on the direction of wall rotation ($\hat{\Omega}_{w}$) with respect to the intrinsic plasma rotation, with locking to both the static wall (vacuum vessel) and rotating wall observed. Additionally, indirect effects on RWM stability are observed via the effect of wall rotation on device error fields. Wall rotation shields locking error fields, which reduces the braking torque and inhibits mode-locking. The linear superposition of error fields from guide field ($B_z$) solenoid misalignments and current-carrying leads is also shown to break symmetry in $\hat{\Omega}_{w}$, with one direction causing stronger error fields and earlier locking irrespective of plasma flow. Vacuum field measurements further show that rotation decreases the error field penetration time and advects the field to a different orientation, as predicted by theory. Experiments are conducted on the Rotating Wall Machine, a 1.2 m long and 16 cm diameter screw-pinch with $B_z \approx 500$ G, where hollow-cathode injectors are biased to source up to 7 kA of $I_p$, exciting current-driven RWMs. MHD activity is measured through 120 edge $B_{r}$, $B_{\theta}$, $B_z$ probes as well as internal Bdot, Langmuir and Mach probes. RWM eigenfunctions are found to be skewed towards the anode end, likely due to anode-directed axial flows measured to be $\approx$ 6 km/s. Eigenfunctions also illustrate increased helicity at higher $I_p$ and helicity is reversed with $B_z$, while wall counter-rotation is found to reduce mode helicity. [Preview Abstract] |
Tuesday, November 15, 2011 2:30PM - 3:00PM |
JI2.00002: Calculation of Linear Two-Fluid Plasma Response to Applied Non-Axisymmetric Fields Invited Speaker: The development of new numerical tools has allowed for the first time, the calculation of the response of a plasma to applied non-axisymmetric fields using a two-fluid model in diverted toroidal geometry. Reconstructed equilibria from several DIII-D discharges are considered. In addition to two-fluid effects, the model includes Spitzer resistivity using experimental electron temperature profiles, and realistic values of perpendicular viscosity and thermal conductivity. Toroidal rotation of the equilibrium is also included, with the axisymmetric equilibrium self-consistently modified as needed. The computational domain extends across the separatrix and the open field-line region is modeled as a low-temperature plasma. Both screening of applied fields and amplification of resonant modes are observed. Although rotation is found generally to inhibit the penetration of non-axisymmetric fields, it is found that the plasma response is not invariant under a reversal of the toroidal rotation, even within the context of single-fluid resistive magnetohydrodynamics. When two-fluid effects are included, it is found that error field penetration is greatest when the perpendicular flow velocity is small. Even in cases without rotation, time-independent parallel currents are found to exist in boundary layers at mode-rational surfaces. The time-independent response is calculated in two different ways: by evolving the dynamical system to steady-state and by directly solving the inhomogeneous time-independent equations. Calculations are performed using a parallel finite-element code, M3D-C1. [Preview Abstract] |
Tuesday, November 15, 2011 3:00PM - 3:30PM |
JI2.00003: Local and Nonlocal Parallel Heat Transport in General Magnetic Fields Invited Speaker: Transport in magnetized plasmas is a topic of fundamental interest in controlled fusion, space plasmas, and astrophysics. Three issues make this problem particularly challenging: (i) The {\em extreme anisotropy} between the parallel (i.e., along the magnetic field), $\chi_\parallel$, and the perpendicular, $\chi_\perp$, conductivities; (ii) Magnetic {\em field lines chaos} which may preclude the use of magnetic coordinates; and (iii) {\em Nonlocal parallel transport} in the limit of small collisionality. As a result of these challenges, standard finite-difference and finite-element numerical methods face significant limitations. Motivated by the strong anisotropy typically encountered in magnetized plasmas ($\chi_\perp /\chi_\parallel $ may be less than $10^{-10}$ in fusion plasmas) we consider heat transport in the extreme anisotropic regime, $\chi_\perp=0$. To overcome the limitations of previous approaches, we present a novel Lagrangian Green's function method that bypasses the need to discretize and invert the transport operators on a grid.\footnote{D. del-Castillo-Negrete and L. Chacon, Phys. Rev. Lett. {\bf 106} 195004 (2011).} The method allows the integration of the parallel transport equation without perpendicular pollution, preserving the positivity of the temperature field at all times. The method is applicable to local (i.e., diffusive) and non-local (e.g., free streaming) heat flux closures in integrable or chaotic magnetic fields. The method is applied to study: (i) Local and non-local parallel temperature mixing and flattening inside magnetic islands; (ii) Fractal structure of the Devil's staircase temperature profile in the previously inaccessible $\chi_\perp=0$ regime in weakly chaotic fields; (iii) Transport in fully chaotic fields. For the last problem it is shown that, for local and non-local parallel closures, transport is incompatible with the quasilinear diffusion model. In particular, flux-gradient plots show clear evidence of non-diffusive, non-local effective radial transport. [Preview Abstract] |
Tuesday, November 15, 2011 3:30PM - 4:00PM |
JI2.00004: First-order FLR effects on magnetic tearing and relaxation in pinch configurations Invited Speaker: Drift and Hall effects on magnetic tearing, island evolution, and relaxation in pinch configurations are investigated using a non- reduced fluid model with first-order FLR effects. When the tearing-layer width is smaller than the ion sound gyroradius ($\rho_{s}$), cylindrical computations show that kinetic-Alfven- wave (KAW) physics increases linear growth rates relative to resistive MHD. An unexpected result with a uniform pressure profile is a drift effect that reduces the growth rate at intermediate-$\rho_{s}$ values. This drift is present only with warm-ions FLR modeling, and analytics show that it arises from $\nabla B$ and poloidal curvature represented in the Braginskii gyroviscous stress. While the flux-surface average contribution from these drifts are small relative to diamagnetic drifts in tokamaks, they are dominant in pinch profiles. Growth rates and rotation frequencies are derived for a heuristic dispersion relation using the ion-drift effects and a resistive-MHD Ohm's law. This dispersion relation is in agreement with numerical results in the intermediate drift regime before KAW effects are significant. Nonlinear single-helicity computations with experimentally-relevant $\rho_{s}$ values show that the warm-ion gyroviscous effects reduce saturated-island widths. In contrast to diamagnetic drift-tearing, the $\nabla B$ and poloidal curvature profiles are largely unaffected by magnetic islands. The result suggests an increasing tendency to obtain quasi-single helicity in reversed-field pinches with increasing ion temperature. [King et al., Phys.\ Pl.\ 2011] Multihelicity simulations show that both MHD and Hall dynamos contribute to relaxation events. The presence of Hall dynamo implies a fluctuation-induced Maxwell stress, and the simulation results show net transport of parallel momentum. The magnitude of force densities from the Maxwell stress and a competing Reynolds stress, and changes in the parallel-flow profile are within a factor of 1.5 of measurements [Kuritsyn et al., Phys.\ Pl.\ 2009] during a relaxation event in the Madison Symmetric Torus. [Preview Abstract] |
Tuesday, November 15, 2011 4:00PM - 4:30PM |
JI2.00005: High Resolution Detection and Excitation of Resonant Magnetic Perturbations in a Wall-Stabilized Tokamak Invited Speaker: We report the first high-resolution detection of the 3D magnetic response of wall- stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse (HBT- EP) device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations [1]. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of multiple modes without the need to fit either a Fourier or a model-based basis. We have observed the plasma response to be strongly dependent on the edge safety factor, q$_{a}$, and the helicity of the control coil currents. As the amplitude of the applied perturbations increase, the initially linear plasma response becomes nonlinear. We observe the plasma response to saturate and, at the highest levels of applied fields, a major disruption is induced when the applied perturbation is rapidly switched off and the plasma attempts to relax back from the induced asymmetry. Modeling of the response with ideal MHD indicates the strongest multimode response occurs with q$_{a}\sim $3 with the excitation of both n=1 and 2 modes. These predictions are compared with measurements of the plasma response as a function of q$_{a}$ and plasma rotation.\\[4pt] [1] D A Maurer, et al.,~2011 Plasma Phys. Control. Fusion 53 074016 [Preview Abstract] |
Tuesday, November 15, 2011 4:30PM - 5:00PM |
JI2.00006: Tearing Under Stress--The Collusion of 3D Fields and Resistivity in Low Torque H-modes Invited Speaker: New processes have been identified in the interaction of 3-D fields with tearing mode stability in tokamaks that pose challenges for H-modes even at modest $\beta$. These arise from the plasma resistive response at the tearing resonant surface, and an interaction with the natural tearing instability. Sensitivity to 3-D fields is found to depend on proximity to the natural tearing limit on DIII-D and NSTX. An increasing magnetic response develops as normalized $\beta$ rises, even at very modest values $\sim$1.4. The field required to induce modes tends to zero as the tearing limit is approached. The response is enhanced at low rotation, where fields of just 1-2 Gauss induce modes in ITER-like H-modes, well below thresholds in Ohmic plasmas, making ITER error field correction requirements even more stringent. The interpretation is confirmed by modeling with the MARS-F and M3D-C1 codes, which show the usual plasma screening response breaking down at low rotation, introducing a resistive response and further dependencies on $\beta$ and the current profile. Both resonant ($n=1$) and non-resonant ($n=3$) fields lead to modes at similar field amplitudes, and paradoxically, the interaction is found to lead to rotating modes more often in lower torque plasmas. This is attributed to the fields reducing flow shear, and decreasing inherent tearing stability. Thus mode onset can be considered in terms of a torque balance. On this basis new measurements of the main scalings for field thresholds to induce modes have been obtained in torque free H-modes. These have similar dependences to Ohmic plasmas, but with 7 times lower threshold at the ITER baseline $\beta$, and a linear dependence on proximity to the tearing normalized $\beta$ limit ($\sim$2.2 at zero torque). This reinforces the needs to optimize error field correction and torque injection in ITER. [Preview Abstract] |
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