Theory Weekly Highlights for July through December 2002
Highlights for December 2002
Preliminary experimental measurements presented by G.L Schmidt of PPPL at the 2002 APS meeting, for deuterium pellets injected into the JET tokamak, were found to be in good agreement with scaling predictions from the pellet ablation model developed at GA. In this model, the large-R drift of pellet ablation material depends strongly on the initial pressure of the ionized portion of the cloud where the ablation flow is predominately parallel to the magnetic field, while moving as a whole along with the pellet. The higher the pressure the larger the drift distance in the large-R direction. Measurements of the cloud density using Stark broadening techniques for deuterium pellets injected into JET from the high-field-side show that the cloud density, and thus distance that the pellet penetrated into the plasma, increases with time. The measured densities fit quite well with the theoretical predictions for the initial cloud pressure and density n0 as a function of local plasma temperature T, density n and pellet radius, confirming the scaling n0 ~ n*T1.5. The agreement can be seen at JET Pellet Cloud Comparison
A new two-dimensional linear ideal stability code, SCOTS, capable of handling the entire plasma, including open flux lines, was developed previously in collaboration with the University of Manchester Institute of Science and Technology and the Royal Observatory of Belgium. This code is now being used to study the eigenfunctions and map the ideal stability boundaries by varying the open flux and closed flux currents for helicity injected spheromaks and spherical tokamaks. For a given coaxial helicity drive, which drives the closed flux current, the stability boundary for the n=1 open flux kink mode determines the maximum closed flux current attainable in helicity injected experiments, since the instability is typically low amplitude and weakly nonlinear, and helicity injected discharges have previously been shown to remain in the vicinity of the n=1 linear stability boundary. The calculated n=1 stability boundary then determines the total toroidal current from coaxial helicity injection as a function of injected current. This provides an extremely useful tool for predicting the performance of helicity injection in experiments such as HIT-II, NSTX and SSPX. In particular, recent work to include open flux currents in reconstructed NSTX discharge equilibria will provide a good comparison to experiment. The code can also answer questions about the effect of open flux or divertor currents on stability in conventional tokamaks such as DIII-D and JET.
Highlights for November 2002
As part of a collaboration with the Hefei Institute of Plasma Physics in China, the EFIT and the ONETWO equilibrium reconstruction and transport codes were applied to analyze long pulse enhanced confinement discharges in the HT-7 superconducting tokamak. Long pulse, limited H-mode discharges with ITB were produced in HT-7 by combining LHCD and IBW. Transport analyses using ONETWO show that ion transport approaches the neoclassical level inside the ITB region. Analyses using the GKS gyro kinetic stability code indicate that ITG modes are unstable inside the ITB region. The results suggest that the enhanced ion confinement may be due the stabilization of the ITB turbulence by the pondermotive force from IBW.
Dylan Brennan and Jeff Candy gave invited presentations at the 44th Division of Plasma Physics APS Meeting in Orlando. Brennan discussed the new model for resistive tearing stability, based on increasing delta-prime as a discharge approaches an ideal stability limit. Candy presented the recent continuum global gyrokinetic GYRO code developments and comparisons with DIII-D experiments obtained using the code.
In addition to accurately predicting the onset conditions, island evolution modeling for DIII-D Tearing Mode experiments has qualitatively reproduced a previously puzzling, but routinely observed, feature in the evolution of spontaneous NTMs, namely a lull in the growth of the island. Initially, the linearly unstable island saturates at a size determined by the polarization cutoff. However, as _ increases and the ideal limit is approached, _' increases sharply and the island begins to grow rapidly. Subsequently, finite island effects slow the growth. This is the "lull" phase. Once the island has grown sufficiently large, however, the island undergoes the transition to the usual NTM state and the growth rate increases rapidly again. Several features in the modeling are critical to reproducing this behavior. For the early phase, the parameters in the island evolution equation need to be accurately calculated from the equilibrium reconstruction, _ needs to be ramped at the same rate as is observed in the experiment to obtain the correct time dependent behavior of _'. Also crucial is the use of a polarization model that removes the unphysically large polarization of the usual theory for vanishingly small islands. Otherwise, the onset and lull cannot be reproduced.
The renormalized GLF23 and Multi-Mode (MM95) core transport models have been used together with scalings for the H-mode pedestal height to predict the profiles in H-mode discharges. Using a recently developed power dependent pedestal scaling along with the GLF23 model, an RMS error of 20% in the core stored energy is obtained for 47 H-mode discharges from DIII-D, JET, and C-Mod. In combined core and pedestal modeling of ITER, FIRE, and IGNITOR the power dependence of the pedestal height is found to be a critical issue. Results obtained using the GLF23 and MM95 core models, along with the power dependent pedestal model, are more optimistic than the results obtained using MHD limit (power independent) pedestal scalings. These results were recently presented at the IAEA Fusion Energy conference in Lyon, France.
Highlights for October 2002
Good agreement was found between the dependence of the observed pedestal height on pedestal width and other control parameters such as plasma shape and density, in discharges from the DIII-D pedestal database, with the predicted trends of the stability boundaries calculated with ELITE for a series of model equilibria. This agreement suggests that the DIII-D pedestal is limited by peeling-ballooning stability. It also shows that the model equilibria are sufficiently accurate that this technique can be used to estimate trends in pedestal height as a function of pedestal width and control parameters in both present and future experiments.
Vincent Chan, Ron Waltz, Jon Kinsey, Philip Snyder, Lang Lao, Ming Chu, and Rip Perkins represented our group at the IAEA meeting in Lyon, France. Snyder gave an oral presentation on "ELMs and Constraints on the H-Mode Pedestal: A Model Based on Peeling-Ballooning Modes". Waltz, Kinsey, Lao, Chu, and Perkins had poster presentations describing the GYRO gyrokinetic turbulence simulations, GLF23 simulations for ITER, FIRE, and IGNITOR, our ITER modeling work, resistive wall and feedback modeling, and Current Hole theory. Snyder and Lao also attended the ITPA pedestal meeting in Garching, Germany and highlighted our edge modeling work.
The ECCD module developed by Y.R. Lin Liu has been implemented in the TORAY-GA ray tracing code. The previous version of TORAY-GA, used R. Cohen's original implementation of the ECCD model and the user needed to manually replace this by the Lin Liu ECCD module in order to use it. In principle, the Lin Liu model is both simpler and superior to the original Cohen model, though in practice, the differences are typically of the order of 10%. The user can now choose either model for the ECCD calculations in the input file "toray.in", with the new Lin Liu model as the default if none is specified. The new model also has the capability to include collisionality corrections. These are still to be implemented but in the meantime, the new version of TORAY is expected to be released publicly soon.
The US Fusion Grid is now being used to perform scientific data analysis at DIII-D. Developed under the auspices of the National Fusion Collaboratory Project , the Fusion Grid presently consists of MDSplus and SQL data servers at C-Mod and DIII-D, and the TRANSP code located on a linux cluster at PPPL. This computational grid is now being used by scientists at DIII-D for the TRANSP analysis that is being presented at the IAEA and APS/DPP meetings. To tie into the Fusion Grid, new tools were created at DIII-D to allow for preparation of TRANSP input data as well as invoking the TRANSP computation. The advantages to this mode of operation are a greatly improved data analysis throughput rate combined with instant access to the latest version of TRANSP.
A theoretical framework is being developed to solve the coupled, steady-state heat diffusion and Grad - Shafranov equilibrium equations simultaneously, in order to find self-consistent pressure and safety factor profiles for what may be considered as an ultimate vision of a steady-state tokamak reactor. In this framework, the plasma current arises almost entirely from the pressure gradient via the bootstrap mechanism, and the pressure gradient, in turn, is determined by heat conduction with a thermal diffusivity that depends on the poloidal field associated with the plasma current. Under circumstances where the confinement improves with increasing negative shear, a solvability condition for the self-consistent profiles can arise. This may call into question the feasibility of such a fully steady state, tokamak fusion reactor.
Highlights for September 2002
In a new analysis of pellet cloud drift dynamics, it was found that the effect of toroidicity becomes increasingly important as the cloudlet elongates with time. With toroidicity, different segments of the cloudlet start drifting on different flux tubes and the differential slippage causes the cloudlet to fragmentize in a rather orderly fashion; beginning with the outermost fluid cells, the cells are sequentially shed, one by one. The remaining cells, being fairly well aligned within a common magnetic flux tube at any given moment, continue to drift coherently in the large-R direction until the next end cell is shed. The mass shedding model was incorporated into our PRL code (Pressure Relaxation Lagrangian), which obtains the mass deposition profile in the plasma. This can then serve as the source profile in any tokamak transport code. A preliminary comparison was made to the experimental profile from DIII-D shot *98796 and good agreement was found. The comparison can be seen at Comparison.pdf
NIMROD simulations of DIII-D discharges, completed in collaboration with SAIC, and which capture the nonlinear extended MHD dynamics of the NTM seeding by sawteeth and spontaneous NTM generation have been made publicly available via MDS+. These results are now being analyzed with advanced 3D visualization tools using the SCIRun package developed in collaboration with the University of Utah.
Full-physics simulations on the global gyrokinetic code GYRO have been speeded up enormously. Previously, full-physics runs (which are 20 times more expensive than state-of-the-art ITG runs) with trapped and passing electrons, finite-beta, real geometry, profile variation and ExB shear, etc., required five 24hr restarts on 128 processors of SEABORG at NERSC. This resulted in a formidable 7 to 10 day job turn-around. The recent computational advances enable scaling well beyond 128 processors so that these jobs can now be done in a single 24hr run on 512 processors. This is close to the same job turn-around time obtained for the reduced-physics ITG runs of a year ago. The new full physics GYRO runs can now be done in production mode but this will require a large increase in the MPP time available to us; otherwise, a full production schedule will exhaust our upcoming yearly NERSC allocation in as little as three months.
A complete set of transport equations for the plasma and the electromagnetic field have been obtained in the cylindrical limit that is appropriate for large aspect ratio flux surfaces of arbitrary shapes. Novel algorithms are proposed for solving the problem of plasma transport with concurrent change of flux surface geometry. Besides presenting a most comprehensive model of tokamak plasma transport, these results are also useful for studying how long-duration discharges are maintained by bootstrap current. Extension of the theory to include angular momentum transport and implementation of the algorithms will be attempted in future work.
Highlights for August 2002
A new facility was added to the ONETWO transport code to limit the growth rate of the safety factor q near the magnetic axis. This is done by dynamically adjusting a seed current to flatten the toroidal electric field when the current density is decreasing. This option prevents the formation of multiple magnetic axes, which would otherwise cause the transport calculations to break down.
A new working version of IDL 5.5 for OSF V5.1 was implemented by the Data Analysis Group. This eliminates the problems with the previous unpatched version of IDL, which locked up under certain circumstances. Several LSF hosts have already been upgraded and are using the patched version of IDL; other hosts will be upgraded in the next few weeks.
The GA Theory group successfully hosted the Magnetofluid Modeling Workshop on August 19 and 20. This was followed by several satellite workshops August 21 through 23, devoted to detailed discussions for the major national extended MHD modeling efforts: the Center for Magnetic Reconnection Studies (Amitava Bhattacharjee, U Iowa); the Center for Extended MHD Modeling (Steve Jardin, PPPL); and the NIMROD Project (Dalton Schnack, SAIC).
See http://web.gat.com/workshops/mmw02 for details.
Analytic solutions for "doublet FRC" equilibria with double magnetic axes and two teardrop-shaped private flux regions, have verified an earlier speculation that these configurations possess more favorable stability properties than standard FRCs. General expressions for the interchange functions V( and V(( at the O-point - the least interchange stable point - were derived, and the stability criteria compared, for the standard and doublet FRCs; this also revealed a correction to the published expression for V in L. Sparks, R. Sudan, Phys Fluids 27, 626 (1984). For the proposed Swarthmore SSX-FRC experiment (elongation ~ 1.5), stability requires a minimum ratio of edge separatrix-to-O-point pressure of 0.4, compared to 0.58 for a conventional FRC with the same pressure profile. However, more oblate doublet FRCs, or increased indentation at the waist, can lower the edge pressure required for interchange stability, making doublet FRCs a more viable fusion configuration.
Several DIII-D discharges have in the past exhibited apparent phase reversals or 'phase folding' in the Mirnov signals on the inboard side; that is, a signal that superficially appeared to be a simple m = 3 structure but with a region along the inboard side where the mode seemed to be m = -1. These apparent phase reversals were a long-standing puzzle that had prompted a number of somewhat complicated and non-standard explanations. In collaboration with the FARtech group, a re-analysis of the comparison of the Mirnov prediction from the ideal mode computed by the GATO code with the measured signal for DIII-D discharge #87009, however, revealed that there is, in fact, no mystery and no non-ideal processes need be invoked. The phase reversal is only apparent, and is due to the rich poloidal spectrum of the unstable ideal mode, coupled with the noncircular discharge geometry and relative placement of the Mirnov loops.
Highlights for July 2002
In previous analyses of a DIII-D discharge where successive decaying, and ultimately destabilized, 3/2 modes are triggered by a series of saweeth, the decay/growth rates of each 3/2 island qualitatively correlated with changes in delta_prime calculated from PEST-III. New detailed analyses have made this correlation quantitative in both the decay rates of the 3/2 islands and the onset time of the final unstable island. Taking the computed linear delta_prime values from reconstructed equilibria at eight time slices, plus the calculated neoclassical terms and the measured island widths w at the same time slices, the dw/dt values were calculated from the Modified Rutherford Equation (MRE). These were compared directly to the dw/dt values inferred from the measured island decay rates. The resulting growth and decay rates agree very well, including the change in sign from a decaying to a growing mode. A single free parameter was retained in the polarization term. This was assumed to be constant throughout the discharge and adjusted to obtain the best fit. The best fit value is stabilizing, and also agrees well with the most commonly used theoretical polarization model. This is strong confirmation that the MRE, including the often-disputed polarization model, and linear delta_prime, is a valid quantitative model for island evolution.
The renormalized GLF23 confinement model was installed in the ONETWO code and benchmarked against the XPTOR code for several experimental DIII-D discharges as well as several proposed burning plasma experiments (BPX) currently under consideration. Several of the BPX simulations included sawtooth modeling in combination with GLF23. The results indicate that agreement between the codes is satisfactory and the (small) differences that are observed can be explained in terms of understood differences in t
Oral talks were presented at the recent European Physical Society (EPS) meeting in Montreux, Switzerland by J. Candy and A. Turnbull describing the Theory Group's work on the development of the GYRO code and the MHD stability analysis for DIII-D. Both were well received. L. Lao and A. Turnbull also made presentations at the IEA Workshop on ELMs at JET following the EPS meeting. These covered our work on developing the model for Type I ELMs based on ideal stability of intermediate n modes and complemented experimental talks by T. Osborne and A. Leonard.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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