Theory Weekly Highlights for January through June 2006
Highlights for June 2006
Construction of the new TGLF transport model (the successor to the GLF23 model) is in its final stage and nearing completion. A preliminary model for the saturated turbulence amplitude has been fit to the database compiled from non-linear GYRO runs. The model is in the form of a generalized mixing length rule that depends only on the linear growth rate, frequency and wavenumber of the most unstable mode. The fluxes of particles and energy are computed by multiplying the saturation rule model by the quasilinear weights found with the new TGLF eigenmode solver. A set of 63 GYRO runs in shifted circle geometry over a range of plasma parameters was used for the fitting of the model. The model achieves an 18% fractional deviation for ion and electron energy fluxes and 32% for the particle flux. The higher fractional deviation for the particle flux is due to the large number of cases near zero particle flux in the database. The model works very well for large particle outflow or pinch.
Stability calculations in support of studies of the fast-ion stabilization of DIII-D discharges with the Porcelli model showed that there are some significant differences from the predictions of the analytic, large aspect ratio, circular cross section Bussac model for the ideal internal kink. For reconstructed equilibria in discharges with large sawteeth, the eigenfunction has approximately the "Top-Hat" structure of the Bussac model where the Porcelli model is applicable. For a discharge with much smaller sawteeth, however, the eigenfunction shape is significantly different. GATO calculations show that the difference in structure of the eigenfunctions is due to the change in the position of the q = 1 surface, r(q=1), rather than to a change in the safety factor q on axis. As r(q = 1) increases the computed eigenmode becomes closer to "Top Hat" model. In addition, both the growth rate and marginal point can be sensitive to removing the wall with little visible change in the mode structure. This, the so-called 'toroidal kink' mode, has been noted in previous studies of model equilibria. For real discharges, the Porcelli model incorporating the Bussac internal kink will need to be extended to account for these deviations.
The linear stability properties of a reconstructed DIII-D discharge equilibrium, unstable to an edge-localized mode, has been studied with the NIMROD code. The poloidal drift frequency ω* for this case is peaked in the edge region where the electron pressure gradient is strongest. The stability analysis consequently included both the Hall and gyroviscous effects.; this was the first time these effects have been included in a calculation for ELMs in a real reconstructed DIII-D discharge. The Lundquist number S was approximately 2x107 and the Prandtl number was 0.1. The linear, single fluid growth rate spectrum with respect to toroidal mode number is peaked around n=10 and drops to marginality near n=20. In contrast, with the Hall and gyroviscous terms included, the peak growth rate is reduced and mode numbers above n=16 are completely stabilized but the low n stability is weakly affected. This is in agreement with the conventional wisdom and with previous calculations for model equilibria. Future studies will include the Hall and gyroviscous effects in the nonlinear calculations as well.
Carlos Estrada-Mila successfully defended his doctoral thesis at UCSD on June 5. The thesis "Gyrokinetic Studies of Particle Transport in Tokamaks" covered the work detailed in several previous highlights (see the Highlights for January 21 2005). and January 6 2006).
Carlos is returning to Colombia where he will be pursuing new adventures.
A new 2D magnetohydrodynamic simulation of pellet ablation in the electrostatic approximation was developed in collaboration with R. Samulyak and T. Lu of BNL. The major conclusion of the study is that in purely hydrodynamic simulations (without the JxB force), changing the heat flux from spherically symmetric 1D to axisymmetric 2D deposition leads to a minor reduction in the ablation rate, contrary to the prevailing expectation of a "factor of 2" reduction. However, in the magnetohydrodynamic simulations with the JxB force included, the magnetic field channels the flow into an extended plasma shield and significantly reduces the ablation rate by a factor of 2 to 3, depending on the time it takes for the heat flux to ramp up as seen by a moving pellet. Fast pellets crossing pedestal regions in ITER would lead to shorter warm-up times, which in turn lead to narrower ablation channels, stronger shielding, and reduced ablation rates.
Numerical 3D turbulence studies show a strong impact of magnetic geometry on the oscillating zonal flows known as geodesic acoustic modes (GAMs), a ubiquitous phenomenon detected five years ago that is prevalent near the tokamak edge. On one hand, changing the Shafranov shift, ellipticity, safety factor, or magnetic shear, individually alter the drive efficiency from Reynolds Stress, Stringer-Winsor force, and finite-Larmor-radius heat flux. On the other hand, geometric effects also couple the GAMs to various parallel sound waves, giving rise to complex interactions. A deep understanding of the experimental GAM amplitudes would open up a novel way to improve tokamak performance, since - at least in the simulations - dramatic reductions in transport are possible by choosing a GAM-optimized configuration.
An EFIT version that incorporates the new DIII-D vacuum vessel and limiter geometry, new magnetic diagnostics in the new lower divertor shelf, and a new more complete magnetic uncertainty matrix has been released to support DIII-D plasma operations. The new magnetic uncertainty algorithms are currently being tested and will be available for general public use in the summer after this testing is completed.
Highlights for May 2006
The latest version of ReviewPlus has been installed at NSTX. ReviewPlus is a generic IDL visualization code developed by the data analysis group for MDSplus signals. Changes were made that were necessary to make the code portable to other sites, in addition to configuration changes specific for NSTX. Feedback from NSTX has been very positive.
Vincent Chan, Lang Lao, and Ron Waltz attended an ITER Simulation Workshop hosted by the Peking University to solicit opinions from international scientists and the Chinese fusion community on how to develop simulation capabilities in China to support ITER.
A 64-bit parallel version of the GCNM solver, called GCNMP, (Globally Convergent Newton Method-parallel) was developed. The solver includes the basic tokamak transport equations as originally developed for the ONETWO code with GLF23 as the primary energy transport vehicle. The modular nature of GCNMP allows it to interact with all transport related physics codes (eg. neutral beam, RF heating and current drive, MHD, etc.). In addition, GCNMP can utilize adaptive grids (variable size and spacing) and a variable number of equations by simply creating state files that include the necessary information. GCNMP is now being tested and will be installed shortly at PPPL and ORNL for use by the NTCC and SWIM projects.
Emily Belli arrived at GA to work as an ORISE Postdoctoral Fellow on developing gyrokinetic-based computational models for studying tokamak edge plasmas.
The validity of the quasilinear (QL) theory for resonant interactions of ions and ICRF waves with realistic magnitude was examined using the Monte-Carlo code ORBIT-RF for an Alcator C-Mod fundamental heating experiment. Preliminary calculations with just the mean QL "kick" turned on and no collisions in ORBIT-RF show that the relative phase between the wave and particle becomes highly stochastic in the resonance region with a wave electric field of 1 KV/m. This value is typical for the power levels used in the experiment. However, the relative change in particle magnetic moment due to the RF kicks remains small. The relative phase is rapidly randomized on a time scale much shorter than the thermal ion slowing down time. The origin of this randomization is that the rapid changes in particle orbit can lead to sampling of different local cyclotron frequencies and parallel wave numbers, which greatly affects the relative phase. These results appear to justify the use of a QL diffusion model.
The formalism for the gyrokinetic implementation of the equilibrium model of Miller et al. has been rederived in detail and extended to up-down asymmetry. In the process, minor errors that appear in the published literature (but had over time been corrected in numerical codes) were also corrected. The possibility of up-down asymmetry of plasma triangularity allows more realistic modeling of experimental tokamak equilibria. The new formulation has been added to GYRO, such that the coding is now fully consistent with the new documentation.
Highlights for April 2006
The new Advanced Imagery Laboratory (AIL) is ready for use as a conference room and as a remote collaboration environment for meetings and experimental operations. This lab is intended to provide a convenient environment for the remote collaboration needs of the DIII-D staff. The lab is equipped with an IP-based H.323 videoconferencing system, an AG node and a VRVS node, as well as an echo-cancellation speakerphone, network connectivity, and cameras. An externally addressable camera is on order. There is also a three front project display system for H.323/AG/VRVS video, a portable computer display, and an additional computer display. The AIL also now houses the 8-tile rear projection system.
Jon Kinsey presented an invited talk on: "Parametric Dependencies of Transport Using Gyrokinetic Simulations Including Kinetic Electrons" at the combined April 2006 APS and Sherwood meetings in Dallas Texas on Sunday April 23.
The theoretical framework used in the ELITE edge stability code has now been extended to include higher order flow shear terms in addition to the terms that dominate for short wavelength modes. The strongly sheared toroidal flows found in the H-mode edge region of tokamaks can impact peeling-ballooning modes thought to be responsible for many types of edge localized modes (ELMs). ELITE can now accurately calculate growth rates with flow shear for mode numbers from 5 to several hundred, and has been successfully benchmarked against both the MARS and CASTOR codes for the long wavelength end of this range. The newly extended ELITE, in conjunction with MARS, is being used to quantify a new model of the Quiescent H-mode, as well as to further explore flow shear effects in ELMing plasmas.
Nonlinear stability analyses of ELMs using equilibrium reconstructions based on DIII-D discharges 113207 and 113317, in the NIMROD code, show well resolved filamentary structures near the plasma edge. Linearly unstable modes are in the range 5 < n < 25. The linear growth rates peak at approximately n=12 for 113317 and n=15 for 113207. Other modes are driven non-linearly, some by two-wave interaction and some by three-wave interaction. The differences in the linear spectrum affect which modes are nonlinearly driven; higher n peaking linear spectrum drives higher mode numbers nonlinearly, and ultimately a larger number of smaller filaments. In the nonlinear regime, the time evolution of the kinetic energy, using a range of toroidal modes (up to ~ 40), show that the fine structure of the filaments increases as the calculation progresses. The penetration depth of the nonlinear mode into the plasma is in reasonable agreement with experiment but the difference between the two cases is too small to make a distinction. In contrast, previous studies of model equilibria under the same computational conditions showed larger losses of temperature and density than expected from experimental data. Toroidal flow shears the structure of the nonlinear mode and limits the extension of the filaments into the vacuum region, while having a smaller effect on the penetration inward. Careful studies of families of equilibria representing the series of times leading to an ELM event are expected to shed more light on the differences between the two discharges and how the theoretical results compare with experiment. These results are contributing to the DOE theory milestone.
Corrections to &delta-W to restabilize the Alfven continuum were implemented and shown to work extremely well in test cases. The Finite Hybrid Element method used in the GATO, ERATO, and KINX ideal MHD codes is well known to numerically destabilize the Alfven continuum slightly; localized continuum modes then converge from the unstable side to the marginal point quadratically with increasing mesh. The technique to restabilize these modes at a finite mesh, first used in the KINX code, was applied to the GATO representation. With the correction, the numerically destabilized continuum modes were shifted to just slightly on the stable side (~ 10-7), leaving the physically unstable modes hardly affected. With this new feature, the need for numerical convergence studies is greatly alleviated and the way is open to use GATO as a true &delta-W code, which should make simple stability determinations much faster. It also is a key prerequisite for using GATO to study the plasma response to exte rnally imposed perturbations.
Highlights for March 2006
A new version, Version 4.0, of the ONETWO transport code was developed that features full integration of the NuBeam NTCC module, as well as the ability to run simpler and faster NFREYA-derived beam calculations for between-shot analysis in DIII-D. In addition, the coupling of ONETWO to TORAY was improved by supplying additional MHD-derived information to TORAY. The current drive calculations were updated to be compatible with the new interface and may result in some, typically less than five percent, changes in ECCD. The NTCC Multi-mode confinement module MM95 was added to ONETWO as well and comparisons with GLF23 are underway.
A general approach to determining the nonlinear plasma response to external nonaxisymmetric perturbations as a constrained 3D equilibrium was formulated. This approach was shown to be closely related to the Almost Ideal MHD (AIMHD) theory proposed previously by Torkil Jensen. However, the specific implementation of AIMHD originally proposed by Jensen ignored the possibility that the profiles may have different functional dependences within different simply connected regions (i.e. within islands). When this is accounted for, it appears that AIMHD can be formulated with reasonable physically valid constraints. New constraints need to be developed that describe the profiles in the new island flux regions. Some ideas on this can be obtained from transport modeling in addition to conservation laws.
A prototype graphical client code for automated input preparation of TRANSP was completed. This new client code, called AutoTRANSP, streamlines the process of preparing TRANSP runs for execution on FusionGrid.
Analysis of DIII-D Hybrid discharges just before onset of a 2/1 tearing mode found that the tearing stability at q = 2 is highly sensitive to qmin approaching unity, as a result of the ideal βN limit rapidly decreasing toward the experimental βN. In approximately a third of DIII-D Hybrid discharges, the high performance phase is terminated by the growth of these large 2/1 tearing modes. The analysis used the experimental equilibria with q0 constrained within the uncertainty of the reconstruction between 0.98 and 1.05. Varying q0 in this range resulted in little or no change in the equilibrium near q=2 or elsewhere. For qmin ~ 1.02 and above, the 2/1 tearing stability is only weakly dependent on βN. However, when qmin =1.01 and below, the 2/1 tearing mode (at q = 2) becomes strongly unstable as the equilibrium approaches the n=1 ideal limit. This suggests that the proximity to the q=1 resonance is critical to the 2/1 tearing mode stability, and is responsible for the onset of the mode. The 2/1 onset could therefore be prevented by a slight increase in qmin.
Electromagnetic fluctuations have been added to the new Trapped Gyro-Landau Fluid (TGLF) equations. Linear stability calculations show good agreement with the gyro-kinetic linear stability code GKS. Magnetic field fluctuations both parallel and perpendicular to the equilibrium field have been added. Except for parallel velocity shear, the TGLF equations now have the same comprehensive physics as the GKS code. TGLF will be made available as a much faster alternative to GKS for linear stability analysis of DIII-D data.
In re-examining the calculation of angular momentum flux in the Pfirsch-Schluter regime, (see July 01 2005 highlight at: http://fusion.gat.com/theory/weekly_highlights/july_2005_highlights.html) it was found that the expression for the flux differs substantially from the previous expression obtained by Hazeltine in 1974. The relevant distribution function was obtained by expansions in basis functions (Burnett functions) in lieu of a variationa l principle. The flux itself was calculated using the adjoint equation method recently employed for the same problem in the banana regime while retaining the poloidal variation of electrostatic potential. The new expression predicts a steady-state electric field at the edge pedestal region that exhibits a well structure that is observed in some experiments. The results are presently being written up for publication.
Highlights for February 2006
A new similarity model to determine the conditions for spark ignition of a liner has been developed. To achieve high fusion energy gain, all inertial fusion concepts rely on igniting and burning a portion of the cold dense fuel or liner by heat deposition from alpha particles released from a centrally ignited hot-spot of relatively much lower mass. The key ingredient in the new model is that the stopping length of the alpha particles incident on the inner liner layer increases with liner temperature. The front velocity and temperature of the liner heating zone scale in time respectively as Vf ~ 1/t(2/5) and T ~ t(2/5). In terms of the fuel burn-up fraction Fb and the product of the radius times the density, ρ*r, of the hot spot, the liner heating zone temperature scales as T ~ [Fb*ρ*r](2/5). As a result, the model predicts that magnetized target hot spots that achieve ignition at much lower ρ*r and Fb than ICF targets, will produce liner temperatures much too low to "fire-up" the liner fuel.
GYRO received an Innovative and Novel Computational Impact on Theory and Experiment (INCITE) award for 400,000 processor-hours on the ORNL National Center for Computational Sciences (NCCS) Cray X1E. The award will support simulations which couple ion-temperature-gradient plus trapped-electron-mode (ITG/TEM) turbulence to electron-temperature-gradient (ETG) turbulence. This award adds to the recent GYRO Users Group NCCS award of 440,000 processor-hours on the X1E.
Preliminary (and tentative) results on coupled ITG/TEM-ETG simulations using a reduced ion-to-electron mass ratio can be found on the GYRO website at http://fusion.gat.com/comp/parallel (see publications).
A second mechanism, in addition to the novel KAW mechanism described earlier (see Oct. 28 highlight at http://fusion.gat.com/theory/weekly_highlights/october_2005_highlights.html is being considered as a candidate for providing the negative central current drive that maintains the axis safety factor q0 > 1 in DIII-D hybrid discharges. The new scheme also relies on the development of a large co-rotating 2/2 sideband excited by the rotating 3/2 island. We propose that the magnetic perturbations due to the 3/2 and 2/2 modes scatter and redistribute the energetic particles. In ONETWO transport code simulations, it is found that the NB-induced current profile depends on the anomalous transport assumed for the energetic ions. The efficiency of the NB current drive depends on the anomalous transport much more strongly than the neutron production rate. This explanation is similar to a previous idea that toroidal Alfven eigenmodes (TAEs) excited by injected energetic beam ions result in a redistribution of the energetic particles at low density. However, in the higher density hybrid discharges considered here, the TAEs are absent but the 3/2 mode with 2/2 sideband plays an analogous role. This mechanism is expected to work in concert with the KAW to control the safety factor profile and maintain its central value above unity in the hybrid discharges.
A GYRO development workshop was held during the week of Jan 16-20 2006. Users from PPPL, ORNL and the University of Texas came to contribute to the development of new standards for experimental profile data, and to refine the TRANSP-GYRO and ONETWO-GYRO interfaces. Much of the machinery for handling experimental profiles in global simulations, and the mapping of experimental data to a given point for local simulations, was logically reorganized and improved. In addition, two days of the meeting were devoted to more general-interest GYRO lectures, which were attended by three graduate students from UCLA as well as more seasoned GYRO users. The final deliverable is the release of a much improved, polished and documented version 5.0.0 of GYRO.
See http://fusion.gat.com/comp/parallel for more details.
Highlights for January 2006
A new collision model for use with the TGLF transport model has been developed. The previous model based on a straightforward moment equation approach to the pitch angle scattering operator did not give accurate results. In the new model, the trapped boundary terms are replaced with simple damping terms. The effective damping rate of these terms is a non-linear function of the ratio of the collision frequency to the electron drift frequency. This model was tested and found to agree very well with the parameter dependence found for GKS runs. Some additional testing is needed but this is looking very encouraging.
Dr. Klaus Hallatschek was awarded the 2005 Rosenbluth Prize in a ceremony at GA on January 26. He subsequently presented a seminar on his work and it's context entitled: "When little whirls make larger whirls, and larger whirls a river ..."
Two new collaborative technologies - SharedAppVNC and Multicursor Window Manager - were installed in the DIII-D control room and demonstrated to physics staff. Multicursor allows multiple users to control the display wall simultaneously from their own stations, as opposed to the display wall console. SharedAppVNC allows users to share selected windows with the display wall or with other users, instead of their entire desktop. Further details are available at: http://shared-app-vnc.sourceforge.net
Both SharedAppVNC and Multicursor Window Manager were developed as part of the National Fusion Collaboratory and will be used in the upcoming DIII-D run campaign to support plasma operations.
John M. Greene received the 2006 AMS Leroy P. Steele Prize, one of the highest distinctions in mathematics. The prize was awarded by the American Mathematical Society on January 13, 2006, in San Antonio, Texas. John shared the prize with three co-authors for their 1974 joint paper: "Korteweg-deVries equation and generalizations. VI. Methods for exact solution", (Commun. Pure and Applied Math., 27, 97, 1974). See the announcement at: http://fusion.gat.com/theory/announcements/John_Greene.pdf
Recent studies of the effects of plasma shaping on the E x B shear quench rule found the quench point varies considerably from the rule γE/γmax = 2.0. In previous shifted circle studies, it was found that the E x B shear quench point was robustly at γE/γmax = 2.0 for both ITG and TEM dominated cases. In the GYRO simulations with kinetic electrons using the Miller equilibrium model for real geometry, however, it was found that less E x B shear is needed to quench the transport for high elongation. The E x B shear quench point also varies with aspect ratio, A, at fixed plasma elongation and triangularity. Here, the quench point follows an offset linear dependence on A with low aspect ratio needing less E x B shear to quench the transport. A power law fit of (γE/γmax)quench ~ A0.65 fits the GYRO results equally well over a range of 2 < A < 4. A summary of the variation in quench point with elongation and aspect ratio can be seen at: http://fusion.gat.com/theory/weekly_highlights/attachments/quench_point.pdf
Paul Garabedian from the Courant Institute of NYU visited from January 5 through 12 to discuss various issues with GA and DIII-D staff on confinement in 3D configurations, with a focus on the issues of alpha confinement in ITER.
In a burning plasma, the alpha-particle population will be localized within the core (r/a < 0.6), whereas turbulence levels are generally weak for r/a < 0.4 and increase towards the edge. GYRO simulations in the vicinity of r/a=0.5, where an overlap of alpha particles with ITG turbulence occurs, indicate that for ITER-like plasmas the turbulent alpha fluxes (both density and energy) can be as strong (per particle) as the turbulent D-T fluxes. This violates the common wisdom that the effects of turbulence on large-gyroradius alphas are averaged out. This research ultimately indicates that in the outer band, 0.4 < r/a < 0.6, alpha particle modeling codes may need to account for profile modification due to interaction with ITG turbulence.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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