Bulletin of the American Physical Society
51st Annual Meeting of the APS Division of Plasma Physics
Volume 54, Number 15
Monday–Friday, November 2–6, 2009; Atlanta, Georgia
Session NI3: Plasma Rotation and Helical Equilibria |
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Chair: Eric Fredrickson, Princeton Plasma Physics Laboratory Room: Centennial II |
Wednesday, November 4, 2009 9:30AM - 10:00AM |
NI3.00001: Transport Equations In Tokamak Plasmas Invited Speaker: J.D. Callen Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for: neoclassical effects on the parallel Ohm's law (trapped particle effects on resistivity, bootstrap current); fluctuation-induced transport; heating, current-drive and flow sources and sinks; small B field non-axisymmetries; magnetic field transients etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed recently using a kinetic-based framework. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfv\'{e}n waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along field lines, incompressible flows within a flux surface); and ion collisions (damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on the plasma fluid: 7 ambipolar collision-based ones (classical, neoclassical, etc.) and 8 non-ambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients etc.). The plasma toroidal rotation equation [1] results from setting to zero the net radial current induced by the non-ambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the non-ambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The resultant transport equations will be presented and contrasted with the usual ones. \\[4pt] [1] J.D. Callen, A.J. Cole, C.C. Hegna, ``Toroidal Rotation In Tokamak Plasmas,'' to be published in Nuclear Fusion. [Preview Abstract] |
Wednesday, November 4, 2009 10:00AM - 10:30AM |
NI3.00002: Generation and Sustainment of Rotation in Tokamaks Invited Speaker: W.M. Solomon Recent experiments on DIII-D, NSTX and C-Mod have led to new discoveries related to toroidal rotation in tokamaks, including evidence for an effective torque responsible for ``intrinsic rotation" generation and the existence of a strong inward pinch of angular momentum. Measurements on DIII-D using a mix of co- and counter-neutral beam injection show an effective torque in the co-current direction for H-mode plasmas with a profile that is largely localized toward the edge. This shows consistency with theoretical models of non-diffusive momentum transport such as the ``residual stress" driven for example by the turbulent Reynolds stress. New data from DIII-D show that the effective torque is modified by electron cyclotron heating, resulting in a counter torque inside of the deposition radius. Application of lower hybrid heating in C-Mod also modifies the intrinsic rotation, again presumably through modifications to the residual stress. In NSTX, experiments have demonstrated the existence of an inward momentum pinch of up 40 m/s, generally showing quantitative agreement with theoretical predications originating from consideration of low-k turbulence. Similar observations have been obtained on DIII-D and C-Mod, although in some cases the experimental pinch can significantly exceed the theoreticallt expected level. Significant inward pinches will directly affect the peakedness of the rotation profile in plasmas with minimal external torque and an edge drive for the intrinsic rotation. In plasmas with large rotation and strong $E\times B$ shear, ion thermal transport can be reduced to neoclassical levels in DIII-D and NSTX; however, diffusive momentum transport still remains highly anomalous. The common physics of momentum transport between the three devices is under investigation. [Preview Abstract] |
Wednesday, November 4, 2009 10:30AM - 11:00AM |
NI3.00003: Comparison of poloidal velocity measurements to neoclassical theory on NSTX Invited Speaker: R.E. Bell Knowledge of poloidal velocity is required for the determination of the radial electric field, which along with its gradient, is linked to turbulence suppression and transport barrier formation. Pitch-angle measurements from the motional Stark effect require knowledge of the radial electric field to obtain accurate current profiles. Measurements of impurity poloidal flow on conventional tokamaks, that differ an order of magnitude from expected neoclassical values, challenge neoclassical theory as presently formulated. In contrast, recent poloidal velocity measurements from a new diagnostic on NSTX are much more similar to neoclassical predictions from the code NCLASS. The novel NSTX charge exchange recombination spectroscopy diagnostic addresses many atomics physics issues that complicate poloidal velocity measurements, e.g. the collisonal energy dependence of the charge exchange cross section and effects due to ion gyro motion, which lead to pseudo velocities not associated with plasma flow. Uncertainties in atomic physics cross sections that can dominant the relatively small impurity poloidal velocity to be measured are virtually eliminated with a novel viewing geometry. Unique active and passive sets of up/down symmetric views are used to isolate charge exchange emission in the beam volume. Each up/down viewing pair yields an independent line-integrated measurement of poloidal velocity that does not rely on any atomic physics, since gyro orbit effects are small due to low magnetic fields on NSTX. Local profiles can be obtained with an inversion of line-integrated measurements in the beam volume. Comparisons between the measured poloidal velocity and neoclassical predictions and the potential implications will be described. [Preview Abstract] |
Wednesday, November 4, 2009 11:00AM - 11:30AM |
NI3.00004: Three-dimensional shaping of tokamak plasmas Invited Speaker: Michael Zarnstorff Three-dimensional (3-D) shaping of advanced tokamak plasmas is explored to provide resilience against disruptions, eliminate the need for current drive, and stabilize several instabilities without external feedback. The 3-D shaping is constrained to be approximately quasi-axisymmetric, so the orbit and neoclassical properties of the original equilibrium are preserved. Sequences of numerically generated equilibria with $\beta $=4{\%} are studied, parametrically varying the shape and aspect ratio to examine the properties achieved at different levels of shaping, and the impact on coil-set complexity. The base axisymmetric equilibrium has elongation of 1.8, high triangularity, and average aspect ratio $\sim $4. The 3-D shaping has N=3 periodicity in the toroidal direction. It is found that a small distortion, producing a vacuum rotational transform $\iota $=0.05, stabilizes the vertical instability. With vacuum $\iota $=0.1 and a self-consistent bootstrap current, the need for external current drive is eliminated, while keeping the Shafranov shift less than half the minor radius. Above vacuum $\iota $=0.2, the equilibrium remains inside the vacuum vessel even if the plasma pressure and current disappear. Thus, this should be robust against disruptions, similar to experiments on W7-A. For vacuum $\iota $=0.3, the external kink and resistive wall mode are passively stable. With fixed 3-D shape amplitude, variations of the average two-dimensional plasma shape changed the MHD stability thresholds as in axisymmetric tokamaks. Increased aspect ratio systematically reduces the toroidal excursion of a modular coil set that produces the 3-D shaped magnetic field, giving simpler, smoother coils. Other strategies to simplify the coil shapes will be discussed, including saddle coils combined with planar tokamak coils. [Preview Abstract] |
Wednesday, November 4, 2009 11:30AM - 12:00PM |
NI3.00005: Transport barriers in helical equilibria: structural change in the reversed field pinch Invited Speaker: Piero Martin Self-organization of RFX plasmas in single helical axis equilibrium, with $m$=1,$n$=7 helicity, is a structural change for the reversed field pinch (RFP) [Lorenzini et al., Nature Phys 2009 doi:10.1038/nphys1308]. This happens at high plasma current (I$>$1 MA) while axisymmetric boundary conditions are enforced: the helical state has almost conserved magnetic flux surfaces, interpreted as ghost surfaces [Hudson{\&}Breslau PRL 2008], leading to strong core electron transport barriers. Electron temperature Te reaches 1.3keV @1.7MA. Ion temperature Ti is $\sim $(0.5-0.75)Te, consistent with collisional ion heating. The core barrier extends up to $\sim $0.65r/a. Magnetic surfaces quality improves with Lundquist number $S$, thanks to the simultaneous decrease of magnetic chaos and increase of the helical field strength. Helical equilibria are reconstructed by the 3d code VMEC. The (1,7) helicity acts to hold the core safety factor almost flat and below 1/7. The barrier foot coincides with a zero magnetic shear region, where density of rational surfaces is minimum, as in other configurations. Plasma-wall interaction is smoother. Main gas particle confinement time improves in pellet-fuelled plasmas, with record value $\sim $10ms. No core impurity accumulation is evident in Laser Blow Off experiments, which is consistent with numerical simulation results. High current sets a transition also for the edge, where robust Te gradients are observed with a pedestal of $\sim $1keV in $\sim $3cm, possibly due to improved magnetic topology and synergic with core barrier. As persistence and quality of these improved helical states increase with current, the likelihood of achieving steady helical multi-MA RFPs can be inferred. RFX experiments allow a study of the beneficial effects of non-axisymmetric shaping and may provide a platform for a more general validation of theoretical tools developed for stellarators. Moreover, these results are transformational in supporting the RFP as a low-external field, non-disruptive, ohmic approach to fusion, exploiting self-organization and technological simplicity. [Preview Abstract] |
Wednesday, November 4, 2009 12:00PM - 12:30PM |
NI3.00006: Internal Electron Transport Barrier due to Neoclassical Ambipolarity in the HSX Stellarator Invited Speaker: Jeremy Lore Strongly peaked electron temperature profiles are measured in the core of the Helically Symmetric Experiment (HSX) during electron cyclotron heating; with central temperatures of 2.5keV for 100kW of injected power. These measurements, coupled with neoclassical predictions of large ``electron root'' radial electric fields with strong radial shear, are evidence of a neoclassically driven thermal transport barrier. Neoclassical transport is analyzed using the PENTA code [1], in which parallel momentum is conserved. Momentum conservation, including the effects of parallel flow, has long been known to be important in tokamak neoclassical calculations. Conventional stellarators, on the other hand, typically exhibit strong flow damping in all directions on a flux surface, and the parallel flows can be neglected. In this case, the radial electric field is calculated using a simple ambipolarity constraint: setting the ion flux equal to the electron flux. In stellarators with very low effective ripple, such as HSX, parallel flow and momentum conservation are again expected to be important. Large parallel flow measurements ($\sim $20km/s) from the ChERS diagnostic are consistent with reduced damping in the direction of symmetry. In addition to neoclassical transport, a model of Trapped Electron Mode turbulence is used to calculate the turbulent-driven electron thermal diffusivity. The very peaked T$_{e}$ profile is reproduced by predictive transport simulations only when turbulent transport quenching via sheared ExB flow is included [2]. ChERS measurements of the radial electric field profile and comparison to the neoclassical calculations will also be presented.\\[4pt] [1] D.A. Spong, Phys. Plasmas \textbf{12}, 056114 (2005).\\[0pt] [2] W. Guttenfelder, J. Lore, \textit{et. al}, Phys. Rev. Lett. \textbf{101}, 215002 (2008). [Preview Abstract] |
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