Theory Weekly Highlights for July through December 2004
Highlights for December 2004
A Monte-Carlo code ORBIT-RF coupled with TORIC full wave solutions along the equatorial plane using a single dominant toroidal and poloidal wave number was applied to compare its results with TORIC calculations, and with DIII-D and C-Mod experimental measurements. TORIC assumes Maxwellian plasma distributions. For a previous DIII-D discharge with 4th harmonic damping on injected deuterium beam ions, the predicted ICRF power absorption from ORBIT-RF falls within a range of TORIC calculations. Experimentally measured enhanced neutron rate is reproduced to within 30% from ORBIT-RF simulations. Preliminary C-Mod results of fundamental harmonic damping on minority H ions indicate that the computed RF absorbed power from ORBIT-RF is within 50% of the power absorption predicted from TORIC. Since ORBIT-RF treats the non-Maxwellian ion distribution self-consistently, the difference with TORIC results appears reasonable. Benchmarking the predicted tail energy spectrum from ORBIT-RF with C-Mod NPA spectrum is underway. For more quantitative comparisons, coupling of TORIC 2D full wave solutions as a function of (R,Z) to ORBIT-RF will be done.
For disruption mitigation using massive gas injection, the rate of delivery of neutrals into the plasma must be sufficiently fast to prevent avalanche runaway growth. The propagation of a neutral gas and cold temperature front into the plasma has been calculated assuming poloidally and toroidally symmetric injection and by solving for the cooling front propagation velocity as an eigenvalue problem. Although the neutral penetration distance into the plasma is small, the radiation cooling of the plasma is exceedingly fast for high Z dense gases. Thus, the plasma can very quickly cool down to a temperature where the neutrals become transparent to the plasma. For ITER-like parameters and with a gas density at the boundary about 100 times the plasma density, the calculations indicate that the neutral gas penetration time is similar in magnitude to the time required to initiate the runaway current, and the avalanche runaway may be avoided.
Previous simulations of nonlinear dynamics of peeling-ballooning modes exhibited explosive bursts of filamentary structures. However, the full energy and particle losses during the ELM crash could not be accounted for solely from loss of the filaments themselves. Two plausible mechanisms have been proposed to explain the increased losses, both of which may be important: 1) The filaments, which remain connected at the ends to the hot core plasma, act as conduits, transporting heat and particles along the filament which is then lost onto open field lines via fast diffusion and/or secondary instabilities. 2) The growth and propagation of the modes strongly damps the sheared rotation in the edge region, collapsing the edge barrier and leading to a temporary return to enhanced L-mode transport. Detailed predictions of these mechanisms are being investigated.
Highlights for November 2004
Dr. Deng Zhou from the Hefei Institiute of Plasma Physics completed his one-year tenure at General Atomics and returned to China this week. During his stay Dr. Zhou contributed to the development of transport analyses by coupling the TOQ inverse equilibrium solver to the ONETWO transport code and initiating coupled transport and stability calculations. He subsequently went on to develop discharge scenarios for the EAST Experimental Advanced Superconducting Tokamak using the tools he developed at GA. He will continue his work on various EAST simulations using ONETWO after he returns to China.
Simulations of nonlinear dynamics of peeling-ballooning modes utilizing the 3D, two-fluid electromagnetic BOUT code show an explosive burst of one or many filamentary structures occurs, transporting heat and particles radially outward into the open field line region. Peeling-ballooning modes are believed to be responsible for edge localized modes (ELMs) in tokamaks. In the early phase of the simulations, the modes exhibit behavior consistent with linear peeling-ballooning studies. In the nonlinear phase, the explosive behavior is qualitatively similar to expectations from nonlinear ballooning theory, though significantly more complex dynamics is seen in the simulations, including a characteristic lull as perturbations approach equilibrium amplitude. Results have been compared to experimental observations of ELMs on DIII-D and MAST, and numerous similarities have been noted, including the poloidal extent and filamentary structure of the modes. This work was highlighted in the invited talk by P. Snyder at the 2004 APS Meeting in Savannah.
Preliminary nonlinear simulations of Edge Localized Modes using the extended MHD NIMROD code (http://nimrodteam.org) show an interesting distribution in the growth rates with toroidal mode number n. When the higher n modes are most unstable linearly, they grow to energies large enough for nonlinear coupling to become important and then nonlinearly drive low n modes. These are driven at much larger growth rates than the high n linear growth rates. This group of low n modes thus forms a "shelf" with increased instantaneous growth rate. The distribution is reversed when the lowest n modes are most unstable linearly and grow to large amplitude first. In this case groups of higher n modes are driven until each group reaches the nonlinear coupling energy and in turn begins driving the next higher group of modes. This causes multiple "shelves" at successively larger growth rate with increasing n. The physical meaning of these "shelves" and how they relate to the final nonlinear state of the system is being investigated.
The GATO ideal MHD stability code is now available as a worldwide computational service on FusionGrid. This Grid computing deployment offers a very easy and convenient facility for running GATO in a secure environment. Presently, the service runs on a 2-CPU server. Data preparation and the invoking of a run are done through an IDL-based PreGATO utility. Both input and output data are written into MDSplus in a tree structure designed to be appropriate for any stability code. Future plans for the GATO service include adding a batch run feature, adding a run queue for efficient use of resources, expanding the server to include many more compute nodes, creating a non-commercial software based PreGATO, and building a set of general MDSplus tools to process and visualize the results. This service is expected to be a prototype for future stability codes. For more information on the National Fusion Collaboratory Project (FusionGrid), see http://www.fusiongrid.org/
Highlights for October 2004
A new analysis has clarified the effects of electron-ion collisions on the linear zonal flow polarization. Previously, GYRO simulations found little or no effect of electron-ion collisions on zonal flows. Though this agreed with the Rosenbluth-Hinton collisionless residual obtained including only the m=0 potential, it was a puzzle because the electron-ion collision frequency is much larger than the ion-ion collision frequency so the effect was expected to be much larger than the effect of ion-ion collisions. By including the m=0, +1, -1 potentials in the gyrokinetic equation for ions and the drift kinetic equation for electrons, a new damped root appears in the "dispersion relation" for the zonal flows at approximately the electron-ion collision frequency. However, when the system of equations is solved to determine all three potentials, the additional m= +1, -1 potentials are found to be smaller than the m=0 potential by two orders in the ion Larmor radius, because the coupling between the m= +1, -1 potentials and the m=0 potential is small in the Larmor radius. The residual in the m=0 potential is therefore only weakly affected by the electron damping from the m= +1, -1 potentials.
A Singular Value Decomposition (SVD) method was developed to calculate surface perturbations from measurements of the magnetic field at the DIII-D vessel wall. Normally, the VACUUM code calculates the magnetic field at or near the surface of the vacuum vessel as a response matrix to the normal component of the perturbed magnetic field at the plasma surface. In inverting this relation, the SVD provides an effective way to deal with the different dimensionalities of the variables as well as the possible singular behavior of the response matrix. For model cases with 256 data points describing the plasma surface, as few as 64 observation points (Mirnov loops), are sufficient to accurately reproduce the plasma surface perturbation in DIII-D. Both the poloidal and toroidal components of the Mirnov loop measurements are now calibrated with respect to the plasma magnetic perturbation.
Simple ITG-adiabatic electron simulations have been to quantify the nonlocal transport mechanism for breaking gyroBohm scaling. The simulations are described by a heuristic formula that has been developed for a nonlocal growth rate corresponding to a localized radial average of local growth rates. The nonlocal growth rate can be used in place of the local growth rate in local gyroBohm transport models like GLF23. This will quantify how turbulence from locally unstable regions drains into locally stable region as ρ* increases and growth rates decrease. GyroBohm transport scaling will be broken toward Bohm in the unstable regions and toward super-gyroBohm scaling in the stable regions.
Modeling of feedback stabilization using the MARS-F stability code has yielded an improved understanding of RWM active stabilization experiments using the internal I-coils in DIII-D. The optimum phasing angle of the upper and the lower I-coils with respect to the sensor signal has been obtained and agrees with the experimentally measured angle. Moderate deviations from this phasing angle lead to a reduced feedback effectiveness. Large deviation of more than 90 degrees leads to a failure of the feedback, as expected from general theoretical expectations. This also correlates with the observation of disruptions in the experiments.
During a visit to GA by Alan Glasser, significant progress was made in understanding the source of the major difficulty in the linear resistive asymptotic matching code TWIST-R, namely that the calculated _' values are clearly unphysical despite solutions that look reasonable. This problem also occurred in the DCON-resistive code; the source of the difficulty turned out to be that the usual equilibrium accuracy for input to ideal codes is insufficient for a linear resistive asymptotic matching code. This is also the likely source of the problems in TWIST-R and is suggested by the observation that the results are sensitive to numerically implementing different analytically equivalent expressions for j and curl(B). A new method is being developed by Glasser to obtain 'refined equilibria' from input equilibrium codes. Several alternative options were discussed but equilibrium refinement may be solution in both approaches.
Highlights for September 2004
The new version of SAV (Signal Analysis and Visualization Code) is ready to be tested. In this version, the user interface is improved so that the user can input or change data parameters and computational parameters interactively, more signal arrays and test signal options are provided, and the visualization functionality is improved with better proper annotations and a resizable plot window. The action log and status message mechanism are also improved. With these and several other enhancements and corrections, this version is expected to be more robust than the previous version. By comparing against similar functionalities in the previous Heat Pulse Analysis code, the results of currently available computational functionalities were validated.
The ONETWO transport code was updated recently with several new NTCC modules. This includes the updated fast ion physics package NUBEAM and it's associated support codes, the PEDESTAL code and the inverse equilibrium code TOQ. Other NTCC modules previously included in the ONETWO code are TORAY, CURRAY, and GLF23. TOQ was recently reworked for submission as an NTCC module and was benchmarked within ONETWO by running a sample current evolution simulation case. The results are in general agreement with those using the inverse equilibrium solver and the direct solver present in ONETWO.
The model developed to explain the variety of tearing mode phenomena observed in DIII-D, in which the instability growth and the equilibrium time development are both taken into account, was shown to reproduce maximum and minimum heating rates for NTM onset. Similar qualitative behavior has been observed in DIII-D experiments; at slow beam power ramp rates NTMs do not appear, at extremely fast rates disruptions occur, and in between NTMs are triggered. Classically destabilized NTM evolution was analyzed in the presence of different heating rates. In the fast heating regime, the change in the linear stability as beta approaches the ideal limit dominates the evolution and the tearing mode grows faster than the rate of current relaxation. Above the maximum rate the integrated tearing mode growth time is longer than the heating time and the ideal mode becomes unstable before the NTM can grow. In the slow heating regime, the enhanced transport losses from the mode modify the current distribution and change the linear stability and this dominates the evolution; the tearing mode grows slowly enough to be affected by the current redistribution. Below the minimum heating rate, the seed island remains saturated and does not evolve into a large NTM. Between the two critical heating rates, classically destabilized NTMs are observed, and the predicted beta value reached as a function of island size agrees with experiment. Nonlinear initial value simulations are being used to test the simple model predictions in the presence of nonlinear mode coupling and so far confirm this picture.
A new, more accurate method for treating the finite Larmor radius (FLR) terms in the gyro-fluid equations has been derived. With this improvement the growth rate for the ITG mode remains accurate for very large temperature gradients, deep into the region of perpendicular wavelength shorter than an ion gyroradius. In previous models the FLR terms fell off too suddenly in this region, resulting in a growth rate that also decayed too rapidly. This improvement is expected to be important for the near separatrix region where the temperature and density gradients can be very steep.
Highlights for August 2004
GYRO simulations were used to study the interaction between the n=0 neoclassical radial transport and high-n ExB transport from ITG turbulence. It was found that the conventional addition of independent neoclassical and turbulent flows is a good approximation. At vanishing rho-star there is no interaction. For finite rho-star global simulations, GYRO now computes the radial neoclassical flows with the addition of the neoclassical n=0 driver, as well as number, energy, and momentum conserving Krook ion-ion collisions. In the presence of turbulence, the neoclassical flows are the local space average of the large orbit neoclassical flows. The n=0 radial modes (zonal flows) induce corrugations in the ambipolar neoclassical flows centered about the null flow. The neoclassical driver combined with a neoclassical n=0 initial value, produces a parallel ion velocity shear which provides the Kelvin-Helmhotz drive to the ITG mode via the nonlinear interaction. The neoclassical drive and neoclassical flows have little effect on the high-n EXB turbulent flows apart from the Kelvin-Helmhotz drive. The ion-ion collisions weakly damp the zonal flows and yield slightly higher ITG transport as expected.
Extensive numerical studies have been performed using the ICRF full wave code TORIC coupled to the ORBIT-RF Monte-Calro code to model DIII-D ICRF discharges, in collaborations with J. Wright and P. Bonoli of MIT. As a first test, a set of converged TORIC ICRF wave solutions for a DIII-D discharge is passed on to ORBIT-RF to compute the wave absorbed power. Initial results indicate that using a single dominant poloidal and toroidal wave number to model the wave spectrum the computed absorbed power from ORBIT-RF is within a factor of two of the power absorption from TORIC. This difference is likely due to the approximation of the poloidal wave spectrum as a delta function, that neglects effects due to other poloidal and toroidal mode numbers. By refining the wave spectrum, we expect further improvement in agreement.
Version one of the ProfileViewer has been made available on the GA Fusion LSF cluster. This new tool allows for plotting of experimental signals versus various radial flux surface labels using EFIT reconstructed equilibria from MDSplus. ProfileViewer fully supports profile overlaying and interactive time slicing, in addition to the full array of features inherited by using the GAPlot Objects.
Recent GYRO nonlinear scans in ExB shear with adiabatic electrons have shown that two different states can exist at low transport levels yielding two different quench points. Without the destabilization effects of parallel velocity shear, simulations with ExB shear on from the beginning yield no transport above a critical shear rate. However, if the simulation is restarted from a previous one with a finite saturation level, then the transport drops to a nonzero saturation level using the same critical shear rate value. This effect has only been observed in simulations without any parallel velocity shear. When the destabilizing effect of parallel velocity shear is included, transport is not quenched by ExB shear. This will be further investigated.
The characteristics of feedback stabilization of the n=1 resistive wall mode in DIII-D geometry are studied systematically using the MARS-F code for a set of equilibria with beta varying from the no wall to the ideal wall limit, and with experimentally measured characteristics of the amplifier and feedback circuit. It is found that the limiting beta value that can be feedback stabilized is related to the inherent phase lag introduced by the amplifier circuit and to a lesser extent introduced by the time delay. The frequency range of the feedback circuit needs to be extended upward before an equilibrium with beta approaching the ideal wall limit can be stabilized. Improvements in performance by using improved feedback circuits are being investigated.
Highlights for July 2004
The Friday Science Meeting has been made available for remote participation. The presentation video is captured with a high-resolution network camera and is broadcast via the camera's web-server. The meeting audio is broadcast using the ESNET Telephone Bridge. Remote DIII-D researchers and collaborators can now conveniently participate in the Friday Science Meetings with their office computers and telephones. The remote participation information is available on the web at Science Meeting Access
and is included in the regular Friday Science Meeting announcements.
A detailed investigation of a spherically symmetric plasma liner from multiple high-velocity plasma jets imploding on a magnetized plasmoid, found that to obtain ignition conditions, extremely supersonic jets (Mjet ~ 60) are required in order to deliver the requisite ram pressure to the target. It had previously been assumed that the merged jets would form a homogeneous plasma liner with the same Mach number as the original N jets. Instead, a supersonic, radially inward flow is created along the contact surface at the edges of the intersecting jets, where the small change in direction at an angle θ ~ 2/N has to be accomplished through a standing shock. The flow is refracted across this shock into a narrow hexagonal boundary layer surrounding each jet and containing the hot shocked material. After the merging is completed, the shocked layer is no longer in stable pressure equilibrium and starts to break up, thus exchanging heat with the cool interior. In the strong shock limit pertaining here, (Mjet*θ)2 >>1, the resultant energy equipartition reduces the liner Mach number to Mliner ~ (1/θ)(3/2) ~ N(3/4) independent of Mjet. For N = 78, Mliner = 9.1. A more refined examination to confirm this result is underway.
In an experiment to investigate the effects of 3D error fields on magnetic surfaces in DIII-D, slowly rotating n = 1 traveling waves at 5 Hz and various amplitudes (~ 0.1 - 0.3% of the poloidal equilibrium field) were applied to perturb the edge magnetic surfaces by pre-programming the I-Coil currents. At 0.1% perturbation, the observed difference in the vertical separatrix location between magnetic reconstructions, which assume toroidal symmetry, and Thomson scattering measurements of electron temperature at a single toroidal location, responds in phase with the applied perturbed field with an oscillation amplitude ~ 2 cm. At 0.3% perturbation, however, the amplitude of the difference in separatrix location grows in time, correlated with an early discharge termination, due to the appearance of a locked mode. The results are consistent with the conjecture that the observed separatrix location differences between magnetic and Thomson scattering measurements in some DIII-D discharges are due to the small toroidal asymmetry of the external shaping coil locations and that the plasma response is important in amplifying the error field and can enhance this difference. This will be investigated in future work.
Convergence tests for the latest version of the TWIST-R linear resistive MHD code have now found near-quadratic convergence in the matching data Delta' and Gamma' with radial mesh, over a range of Mercier index 0.5 < mu < 1.5 values for a Solov'ev equilibrium series. The study also showed the expected pole in the tearing mode matching data Delta'(mu) at mu = 1. In the latest version, numerical bugs were corrected, which resulted in physically reasonable solutions, and a more flexible and more consistent implementation of the poloidal fourier decomposition was provided to minimize the expansion truncation errors. Numerically computed, circular cross section toroidal equilibria were also tested and Delta' and Gamma' were computed, with good convergence properties obtained for these cases as well. For all of these studies, a new tool to study and summarize the convergence of the matching data over a range of cases was also developed; this tool analyzes the convergence rate automatically and finds converged values as a best fit from the computed data. This tool should be extremely useful in future studies.
Lang Lao and Vincent Chan participated in the 2nd US-PRC Magnetic Confinement Workshop in Kunming China, June 23-25, and presented two talks on recent DIII-D results and validation of simulations against experiments. The workshop was hosted by the Southwest Institute of Physics and attended by about 30 scientists, including six US institutions. The purpose of the workshop was to discuss collaboration ideas for the next two years.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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