Theory Weekly Highlights for January through June 2005
Highlights for June 2005
A gyrokinetic entropy diagnostic has been derived and added to GYRO. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key new confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor flux is changed by a four-fold increase (from 64 to 256 grid points per cell) in velocity-space resolution. Third, the measured flux is invariant to an eight-fold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure.
In a more detailed analysis of the simulations using ORBIT-RF with TORIC4 for DIII-D it was found that the ORBIT-RF simulation predicts a much weaker absorption at 8ΩD than expected from the linear theory result. Linear theory predicts non-negligible absorption at 8ΩD due to a large k⊥ ρi at the resonance location. The ORBIT-RF simulations use experimentally reconstructed equilibria and profiles of the wave fields and wave numbers from the 2-D full wave code TORIC4 with Monte-Carlo collision operators for pitch angle scattering and fast particle slowing down. Steady state is modeled by re-injecting thermalized ions. Stochastic RF resonant kicks are then modeled using a quasilinear diffusion operator. By analyzing the finite orbit and pitch angle scattering effects, the weak absorption in the simulations is explained by Coulomb scattering of finite orbit resonant ions, which curtails the resonant interaction.
Joint PPPL-GA Theory Highlight:
The Green's function calculation for the magnetic scalar potential used for the vacuum in most delta-W stability codes currently employs a recursion relation to generate modified elliptic functions at finite toroidal mode number, n. The recursion is initiated from the complete elliptic integrals of the first and second kind, E(ρ) and K(ρ) of the normalized source-observer distance 0 < ρ < 1. At each recursion there is a loss of precision due to subtraction of increasingly large terms scaling like n*((1+ρ)/(1-ρ)n times E(ρ) and K(ρ). For an NSTX or MAST case ρmax ~ a/R ~ 0.7 and approximately 108 precision (the precision of the standard expansions for E(ρ) and K(ρ)) is lost for n ~ 9. In joint work between PPPL and GA, a new method to calculate the Green's function was developed by directly integrating the relevant integral representation. A judicious treatment of the singular behavior of the function, together with a transformation of the independent variable, and an accurate quadrature scheme enable a precision that is much greater than before, even approaching machine accuracy at high n. This should eliminate the limit to calculating stability at high n and low aspect ratios.
GA Theory Highlight:
A videoconference using the Access Grid was held with Korean Basic Science Institute (KBSI) physicists to discuss the GA-KBSI KSTAR Modeling and Analysis Collaboration Plan. The agreed plan consists of 4 collaboration topics: EFIT equilibrium reconstruction, ONETWO transport, GATO ideal stability, and KSTAR scenario development. KBSI physicists will become familiar with ONETWO and GATO through participation in the development of those codes for the Fusion Grid. Dr. K.I. You of KBSI is visiting GA 6/6 - 6/17 under this plan to collaborate on the application of EFIT and GATO to KSTAR, and the installation of EFITTools at KBSI.
In collaboration with Dr. Christian Konz from IPP Garching, a successful three-way benchmark of the ELITE, GATO and MISHKA MHD stability codes was performed for intermediate n peeling-ballooning modes in simple geometry using an equilibrium from the HELENA code. HELENA is a commonly used equilibrium code and is tightly interfaced with the European stability code MISHKA. All three stability codes agree to within 2% accuracy on this benchmark case. In order to perform this study, we have set up both ELITE and GATO to work with HELENA. This will enhance our ability to routinely collaborate on studies of edge stability on JET, ASDEX-U and MAST. Dr. Konz will continue working with the GA theory group this summer, studying the effect of rotation on edge stability.
Highlights for May 2005
Application of the GLF23 transport model to ITER predicts that the toroidal rotation generated in ITER by negative ion neutral beams injected in the direction of the plasma current can significantly increase the fusion power produced compared to heating without torque. The increase in fusion power with beam power is predicted to be steeper for co-injected than for balanced beams. Beam voltages in the range of present technology (300-400kev) produced the highest rotation and fusion power enhancement for fixed beam power. The pedestal pressure needed to reach a target fusion power is also lower for co-injection.
New numerical investigations of edge stability using the NIMROD code have resolved an earlier apparent discrepancy between the NIMROD results and ideal linear stability codes DCON and ELITE. Kinetic equilibrium reconstructions from DIII-D discharges with edge localized modes including accurate edge reconstructions, as well as similar model equilibria, were typically found to be unstable at the edge with ELITE and DCON but unstable to a resistive interchange like mode located at the top of the pedestal with NIMROD. The NIMROD formulation includes resistivity and viscosity. Simulations of edge-localized modes in other cases had generally shown agreement between all three codes in mode structure and, in the case of ELITE and NIMROD, in growth rate. In the new analysis, when the resistivity and viscosity are significantly reduced in the edge region, and the ideal mode is fully converged, the linear eigenfunction transitions to an edge mode with growth rates in agreement with the ideal codes. The interchange-like mode in NIMROD is being investigated for a possible role in the large radial transport observed just inside the pedestal region in the experiments.
An analytic formula for the "effective" number of electrons Zeff to be used in calculating the penetration range of plasma electrons in target gases was derived for the case of target gases with many electron atoms, (e.g. argon). The electron penetration range is an important ingredient in the construction of gas jet penetration models in the low temperature edge of tokamaks (Te < 1 keV) and during the post thermal quench phase. In the many electron Thomas-Fermi model of the atom, the orbital electrons are considered as a completely Fermi-degenerate gas and the Fermi energy Ef and the local charge density distribution of the electron cloud, n ~ Ef3/2, are uniquely related to the radial coordinate. The incident electron can only lose energy on cloud electrons with Fermi energy less than the incident electron energy. This criterion, due to Sugiyama (1985), yields an analytic formula for the "effective" number of electrons Zeff to be used in the Bethe-like stopping power formula providing an important low-energy correction below ~1 keV. For a 400 eV electron incident on argon (atomic number Z = 18), the Zeff = 9.67 (see figure in pdf)
This correction increases the penetration range by a factor of almost two from that predicted by the standard Bethe-like formula.
Between-shot TRANSP simulations using the FusionGrid resource were successfully tested during DIII-D operation. The requests were triggered by the between-shot data analysis event system and submitted to the FusionGrid computer at PPPL. With advanced CPU reservation, the request preempted other processes on the computer to guarantee 100% CPU to the between-shot TRANSP run. The process was monitored by the Data Analysis Monitor (DAM) and the results were written back to the MDSplus server at DIII-D.
Highlights for April 2005
A general drift-kinetic equation has been derived without assuming the flow velocity is small or specializing its form. The drift-kinetic equation is the starting point for calculations of neoclassical transport fluxes and turbulent transport. In tokamak plasmas heated by neutral beam injection, ions and impurities flow in the toroidal direction at speeds that are comparable to the impurity thermal speed. In the new equation, the kinetic energy and magnetic moment of the particles are defined in a frame moving with the flow. As a result of rotation shear effects, these are not constant but change with time due to the fact that energy and magnetic moment are defined with their rotational components subtracted out. The variation depends on details of the flow. The guiding center drifts allow particles to carry some of the rotational kinetic energy radially, causing changes in the velocity distributions and therefore affecting the transport. We are presently attempting to simplify the drift-kinetic equation using a particular form for the flow corresponding to sheared toroidal rotation.
The new cluster computer for fusion applications is now operational. This new system has 116 AMD Opteron processors (64-bit, 2.4 MHz) with both gigabit ethernet and Infiniband interconnects. The network filesystem uses the gigabit backbone, while MPI is implemented over Infiniband. Per-processor, the system is four times as fast as the NERSC IBM Power3 (seaborg), twice as fast as the ORNL IBM Power4 (cheetah) and nearly twice as fast as the ORNL SGI Altix (ram). The GYRO and ORBIT-RF codes have been ported to the new cluster and are running in production mode. Porting of the NIMROD and BOUT codes is underway.
In collaboration with Alex James (UCSD) an option to substitute the GATO disk I/O routines with F90 dynamic allocation to memory was tested successfully. The original I/O system was developed to reduce memory requirements in the eigenvalue solver when memory was expensive. Ultimately, flexibility for trading memory and disk depending on the system load will be provided. The new version, however, presently uses either all memory or all disk and the potential savings are undergoing testing. As anticipated, there is little saving in CPU time but savings in wall clock time are expected to be significant when the system load is high. The remainder of the eigenvalue solver is also being converted to F90 syntax with dynamic allocation. In parallel, options for reducing CPU time in the Cholesky decompositions are being evaluated.
Myunghee Choi delivered an invited talk on the Simulation of Fast Wave Damping on Resonant Ions in Tokamaks at the Topical Conference on Radio Frequency Power in Park City, Utah. Carlos Estrada-Mila and Dylan Brennan respectively gave oral presentations on Gyrokinetic simulations of ion and impurity transport and on Nonlinear Evolution of Edge Localized Modes at the Sherwood Fusion Theory Conference in Stateline, Nevada.
The interaction between resonant plasma ion species and the fast Alfven wave was investigated by coupling fast wave electric fields from the 2D full wave code TORIC4 to the Monte-Carlo code ORBIT-RF and compared to recent measurements from Alcator C-Mod. An experimental C-Mod discharge with 5% hydrogen minority fundamental harmonic heating at 78 MHz and 1.0 MW RF power was used in the study. The wave field solutions from TORIC4 were approximated using a single dominant toroidal and poloidal wave number and input to ORBIT-RF. Results from the coupled ORBIT-RF and TORIC4 simulation agree well with the experimentally measured fast ion distribution from a CNPA diagnostic on C-Mod. Compared to the linear absorption result obtained directly from TORIC4 with an assumed tail temperature of 20 keV, ORBIT-RF produces a much broader power deposition profile. The broadening is due to radial diffusion from the fast ion finite orbits and pitch angle scattering, which are treated properly in ORBIT-RF. More detailed validation work is underway.
A recent GYRO simulation of non-local transport shows how local gyroBohm transport scaling is broken. The study used piecewise flat profiles to distinguish the nonlocal breaking of gyroBohm scaling from local breaking due to profile shearing. The simulations are consistent with the following picture of nonlocal transport: The transport is proportional to a locally averaged growth rate where the averaging length L is proportional to the ion gyroradius ρ*. Turbulence drains from locally unstable regions and spreads into stable (or less unstable) regions. Local gyroBohm scaling is then broken in the direction of Bohm scaling in the locally unstable draining regions and in the direction of super-gyroBohm in the less unstable spreading regions. As ρ*, and therefore L, get very small, local gyroBohm scaling in the locally unstable regions with no transport in locally stable regions is recovered. We have developed a heuristic theory of L/a that shows it to be linear in ρ* and inversely proportional to the square root of the local driving rate, in agreement with the simulations. This model of nonlocality will be built into our new GLF23 model and will allow modeling with some nonlocal transport in locally stabilized regions of ITB's and H-mode pedestals.
Highlights for March 2005
Atlas, the primary MDSplus data server for DIII-D data, was upgraded to most recent Red Hat Enterprise operating system and the disk space was expanded to add capacity. The additional disk space is expected to provide sufficient capacity through the end of operations and into the next fiscal year. The operating system upgrade was needed to keep Atlas up-to-date with the latest security patches, to keep it in synch with our other Linux machines, thus simplifying maintenance, and is a requisite for adopting MDSplus access restrictions. Options for solving the long-term problem of keeping up with increasing storage demands through some sort of mass storage solution are being considered.
A new "momentum model" has been constructed to describe jet penetration in disruption mitigation experiments using massive gas injection from a collimated supersonic argon jet. In the DIII-D experiments, camera images indicate that the jets do not penetrate much past the separatrix. In the model, the jet forms a thin ionized boundary layer as it enters the plasma and the plasma and magnetic field are pushed aside. The net magnetic field inside is slightly less than outside the jet. The net magnetic force opposing the jet motion then balances the neutral pressure piling up as a shock behind the tip of the jet. Force balance yields an equation for the actual jet "tip speed" in terms of the "jet speed" in the absence of the shock. The jet cannot penetrate significantly unless the ratio of tip speed to jet speed, U > Ucrit = 1/4, since otherwise the backward propagating shock wave reaches the rear surface. For DIII-D at B ~ 2 T, the model suggests that U is near Ucrit so that penetration may be possible by lowering the field.
Professor Shaojie Wang completed a three-month visit to GA and returned to the Hefei Institute of Plasma Physics in China. During the visit, Professor Wang completed a series of ideal MHD stability calculations with a double transport barrier (DTB). This work extended a previous study of plasmas with an internal transport barrier (ITB), which suggested that beta limit improves with increasing ITB width or moving the ITB location to the edge. The DTB stability calculations assumed a conducting wall at 1.5 times the minor plasma radius. Model equilibria for the study are computed using the TOQ code with a hyperbolic tangent pressure profile for both the ITB and edge transport barrier (ETB). By varying the ratio of ETB to ITB height with the location and width of the ETB fixed, the study suggests that modest ETBs can improve plasma stability. However, strong ETBs drive ideal MHD instabilities, and there is a window in the pedestal pressure, above which the ETBs drive instabilities with a substantial edge component.
A new certificate-based Secure MDSplus system, developed by MIT researchers as part of the National Fusion Collaboratory, was implemented for DIII-D. Regular MDSplus uses host-based authentication, which requires access through a list of known hosts. The new secure system allows users to be authenticated based on their certificate regardless of their host; this means that scientists can access MDSplus while on travel from anywhere offsite, whether from a DHCP-assigned address from home or another laboratory, or through wireless Internet from a coffee shop, library, or airport. For more information see http://www.fusiongrid.org/
Highlights for February 2005
Nonlinear GYRO simulations with kinetic electrons predict a strong turbulent particle pinch for positive magnetic shear with or without finite alpha (Shafranov shift) stabilization included. These calculations are being performed to create a transport database from GYRO scans over magnetic shear around a standard (STD) test case. The simulations are electrostatic and assume shifted circle geometry in an annulus with flat profiles. The particle diffusivity switches sign with weak positive shear, and is positive (outward flux) for reversed shear. The electron and ion energy diffusivities, however, remain positive for all values of magnetic shear and alpha. The database is part of a larger scan that also includes ExB shear scans for ITG and TEM transport, as well finite beta, safety factor, and alpha scans. The database will be used for benchmarking and to fit and test our new GLF transport model that is currently under development.
Instant Messaging (IM) service has been deployed in the fusion group. A secure jabber.gat.com server and multi-user chat module were installed, configured and tested. With this service, DIII-D researchers and collaborators can exchange text messages and present information in approximately real time. Multiple users can hold text conferencing as well. Two public chat rooms have been created and connected to several DIII-D operations-related software applications. By simply entering these chat rooms, users can monitor the experiment status, electronic logbook entries, and Data Analysis Monitor messages.
In a new calculation of angular momentum flux in the small rotation limit of neoclassical transport theory, a significant correction to a 34-year old result of M.N. Rosenbluth et al. from the 1970 IAEA (Plasma Physics and Controlled Nuclear Fusion Research Vol. 1, p495, 1971) was obtained. This correction involves both a sign and magnitude change, predicting a steady-state rotation in the opposite direction from the earlier theory. The new calculation relies on recent large-aspect-ratio perturbative results on distribution functions and involves a formulation using an equation adjoint to the customary linearized drift kinetic equation, bypassing the need to solve a second-order (in ion poloidal gyroradius over scale length) drift kinetic equation. The result can be used to predict steady-state toroidal rotation profiles for discharges with no momentum source using density, temperature, and q profiles.
The raw compute power of the LSF cluster was doubled and the number of processors increased by 42% with the addition of three new dual Xenon Linux computers. Each new machine is a 3.06 GHz Xeon, supporting hyperthreading, with 4 GB RAM and Gigabit Ethernet and is comparable to or better than the existing machines on the cluster in compute power. The new machines can be accessed directly using the new hostnames Eos, Hestia, and Phoebe. However, since most DAAG applications are automatically load leveled on the cluster, users do not need to change anything to take advantage of the new machines.
Highlights for January 2005
A new Gyro-Landau Fluid (GLF) model was tested against the full database of 1799 Gyro-Kinetic Stability (GKS) runs and found to agree markedly better overall with the GKS results than the GLF23 model. The database is divided into three groups representing three different plasma conditions: STD for the core of L and H-modes, NCS for the internal transport barrier region of negative central shear discharges, and PED for the steep gradient region of the H-mode edge. For only four Hermite basis functions in the ballooning mode wavefunction expansion, the errors for the new GLF growth rates were 12% for the STD and NCS group and 17% for the PED group. The frequency errors were respectively 20%, 23% and 41%.
GYRO simulations of D-T plasmas show that in an initial 50-50 D-T mixture, tritium experiences better confinement than deuterium. This asymmetry will give rise to a small (but likely insignificant) build-up of tritium in the core. This effect is robust, and persists over a wide temperature gradient and collisionality range. In related studies, the D-v (diffusion versus convective velocity) model of impurity flow was shown to be consistent with fully nonlinear gyrokinetic simulations. These results, accepted for publication in Phys. Plasmas, represent the first systematic gyrokinetic study of particle transport in tokamak plasmas.
In collaboration with scientists at NIFS (National Institute for Fusion Science, Japan), a method has been formulated to compute the growth rate of a weakly unstable RWM in 3D configurations using results from ideal stability codes. It is shown that the growth rate of the RWM is given reasonably well by the rate at which the available free energy for the ideal external kink can be dissipated by the resistive wall. The eigenfunction is also approximately that of the external kink mode (the mode rigidity condition). This formulation is demonstrated numerically by coupling the computation of dissipation on the resistive wall to the computation of the ideal MHD stability code KSTEP that computes ideal stability of 3D toroidal systems by transforming them into their 2D equivalent systems.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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