# Presentation: 512322

## Numerical Calculations of Wave-Plasma Interactions in Multi-dimensional Systems

**D. B. Batchelor – ORNL, Principal Investigator**
**L. A. Berry, M. D. Carter, E. F. Jaeger – ORNL Fusion Energy**
**E. D’Azevedo– ORNL Computer Science and Mathematcs (OASCR – SSAP)**
**C. K. Phillips, H. Okuda – PPPL**
**P. T. Bonoli, John Wright – MIT**
**D. N. Smithe – ATK Mission Research Corp.**
**R. W. Harvey – CompX**
**D. A. D’Ippolito, J. R. Myra – Lodestar Research Corporation**
**Presentation to PSACI**
**June 5 - 6, 2003**
**Princeton, NJ**

**Progress made toward achieving scientific targets with respect to clear deliverables**
** ****How have super-computing resources enabled the achievement of the  **** targeted  scientific goals in the timeliest manner?**
**What role have collaborative interactions within the project and also with **** other SciDAC activities played?**
**What the next steps would have been**

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## From 2001 proposal – “The research program consists of 3 elements:”

**Physics generalization, computational scale-up and interconnection of the elements of a complete wave/plasma modeling capability**
- Development of generalized plasma conductivity operator modules and macroscopic source modules with increased physics content and that are structured using modern programming techniques for flexibility of application and ease of extension in capability.
- Creation of a core suite of wave solution codes covering the various needs in physics capability.
- Computationally efficient interface of the conductivity operator modules and wave solvers with Fokker-Planck solutions, macroscopic source calculations and antenna solvers.
**Demonstration of the enhanced simulation capabilities by exploring**** four major unsolved problems in wave-plasma interactions important to ongoing experiments.**
- To what extent do realistic 2D and 3D equilibrium variations modify the local deposition of wave energy and momentum in the plasma?
- To what extent does the presence of non-Maxwellian particle velocity-space distributions modify local deposition of wave energy and momentum in plasma?
- What is the mechanism by which lower hybrid waves, launched with a phase velocity several times the electron thermal speed, are able to couple strongly to electrons and drive currents?
- What is the effect of global plasma modes on the wave fields produced by launching structures?
**Exploratory research into completely reformulating wave-plasma problems and solution methods to permit further extension of physics scope, such as to non-time-harmonic or highly non-linear phenomena, and to examine possibilities for increases in computational efficiencies such as through alternate field representations like wavelets.**

- DBB

## Progress made toward achieving scientific targets with respect to clear deliverables

**Element 1**
**Physics generalization, computational scale-up and interconnection of the elements of a complete wave/plasma modeling capability**
- Development of generalized plasma conductivity operator modules and macroscopic source modules with increased physics content and that are structured using modern programming techniques for flexibility of application and ease of extension in capability.
- Creation of a core suite of wave solution codes covering the various needs in physics capability.
- Computationally efficient interface of the conductivity operator modules and wave solvers with Fokker-Planck solutions, macroscopic source calculations and antenna solvers.

- DBB

## We advanced four wave solver codes within our project for various physics applications

**All Orders Spectral Algorithm (AORSA) – 1D, 2D & 3D (Jaeger)**
**Spectral in all 3 dimensions**
**Cartesian/toroidal coordinates**
**Includes all cyclotron harmonics**
**No approximation of small particle gyro radius ******** compared to wavelength ******
**Produces huge, dense, non-symmetric, indefinite, complex matrices **
**TORIC –  2D (Brambilla/Bonoli/Wright)**
**Mixed spectral (toroidal, poloidal), finite element (radial)**
**Flux coordinates**
**Up 2****nd**** cyclotron harmonic**
**Expanded to 2****nd**** order in ******
**Sparse banded matrices**

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## We advanced four wave solver codes within our project

**METS-1D (D. N. Smithe/Phillips) ******** All orders, fully spectral code in 1D**
**Includes all cyclotron harmonics**
**No approximation of small particle gyro radius ******** compared to wavelength ******** **
**Used for benchmarking studies compared to 2D, development platform for non-Maxwellian conductivity operator routine****s**
**EMIR4**
**Finite difference, MUMPS parallel solver**
**Adapted for open field line systems: plasma edge, plasma propulsion, simplified stellarator geometry, semiconductor processing**
**Iterates with source/transport model**
**ICW simulation and design for VASIMIR (NASA collaboration)**

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## Code speedup and optimization makes a qualitative impact on what physics can be included, what problems can be solved

**These problems are big – resolution limited in all-orders calculations by memory size to store dense matrix (, e.g. 2.5 terabytes spread over 2560 processors on NERSC Seaborg)**
**These problems are long – 80,000 processor-hours on 2000 Seaborg processors for moderate resolution LHD stellarator calculation **

**Capability:**
**Higher resolution****	****	****Shorter wavelengths, larger machines**
**More physics detail****	****	****Better treatment of nonlocal, nonlinear effects**

**Capacity:**
**Faster turnaround****	****	****Physics parameter studies**
**Runs on clusters or ****	****	****Iteration with Fokker-Planck, transport, MHD****workstations****	****	****Experimental operations and data analysis**

**Close partnership with applied math and computer science**

**Parallelization, vectorization, code structuring and tuning**
**Optimum matrix solver, iteration**
**Specialized methods – Domain decomposition, adaptive grids, Kronecker products**
**Optimized field basis sets,** ...

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## Physics generalization, computational scale-up and interconnection of the elements of a complete wave/plasma modeling capability

**Development of generalized plasma conductivity operator modules and macroscopic source modules with increased physics content ...**
- Fast parallel gradient, “quasi-local”,  plasma dispersion function formulated implemented in AORSA-2D, leading to significant speed-up of code, required for convergence in 3D
- 2D version of dielectric tensor routines with gyrotropic but otherwise arbitrary distributions implemented on numerical grid – validated in METS-95 1D all orders code
- Non-Maxwellian conductivity in AORSA-2D all orders code – optimization resulted in speed-up of ~100
- FLR version of non-Maxwellian for TORIC under construction
**Creation of a core suite of wave solution codes covering the various needs in physics capability.**
- 1D “all orders” METS code parallelized and generalized to include gyrotropic but otherwise arbitrary particle velocity space distribution functions. – used for testing and to simulate various experimental scenarios
- 2D all orders AORSA2D code –  physics extended, optimization resulted in speedup factor of 8, ported to NERSC Seaborg, ORNL Eagle, Cheetah, Ram (Altix), and Cray X1, physics studies of mode conversion in 2D, non-Maxwellian distributions
- 3D all orders code AORSA3D developed – optimization resulted in speedup factor 27, physics studies of LHD and QPS stellarators
- FLR 2D full wave code TORIC  parallelized – incorporated out of core solver allows increase of 500 in problem size
- The EMIR4 code suite was developed to solve the nonlinear problem of RF power deposition and transport in helicon plasmas, with relevance to the fusion edge.  Kinetic effects were also added to study ion cyclotron wave absorption.  Numerical improvements allowed solution speed up of more than a factor of 10 by implementing the MUMPS parallel sparse** **matrix solver.

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## Physics generalization, computational scale-up and interconnection of the elements of a complete wave/plasma modeling capability

**Computationally efficient interface of the conductivity operator modules and wave solvers with Fokker-Planck solutions, macroscopic source calculations and antenna solvers**
- CQL3D distributions interfaced to non-Maxwellian conductivity for METS and AORSA2D
- MPI code for Lorentz force calculation of bounce averaged quasilinear operator on a single flux surface
- Local Fourier analysis of AORSA2D full wave fields adapted for approximate quasilinear operator in CQL3D
- A rigorous calculation (including correlation of partial waves in the spectral representation) of local power deposition and the nonlinear forces driving flows. Developed a technique for making these calculations feasible using new algorithms such as domain decomposition and local Fourier transforms, code restructuring, and interpolation techniques, to reduce the CPU time by more than a factor of 100.
- Previous nonlinear flow drive theory models were extended and reformulated into a new unified model compatible with AORSA-2D (or any Fourier-basis wave solver).
- The RANT3D antenna code was enhanced with a Kronecker product formulation to quickly solve for inter-strap coupling of phased array antennas.  The NSTX phased array was analyzed and compared with experiment.  The RANT3D code was also interfaced with the FELICE code and publicly released to the fusion community.

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## Details of electromagnetic field structure are compared using two very different codes – TORIC and AORSA2D

**     ****TORIC at 240N****r**** x 255 N****m****	****	****	****           ****          ****AORSA at 230N****x**** x 230 N****y**
**Both codes are using the same equilibrium from an Alcator C-Mod discharge with mixture of D-****3****He-H in (21%-23%-33%) of n****e**** proportion.**
**The previous state of the art was qualitative comparison of integrated quantities such as power deposition profiles**

- ICW

- IBW

- FW

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## An example of parallelization and optimization allowing qualitative new problems to be investigated

**Out-of-core parallel linear solver enable fully resolved TORIC models for IBW and Ion Cyclotron Waves (ICW) using  (N****m****=1023) ******** (N****r**** = 240) modes on 128 CPUs on Cheetah. **
**Medium models with 255 modes can be solved in about 4hrs on a single Pentium 4. **
**Original serial version limited to (N****m****=161) ******** (N****r**** = 240) modes required over 12hrs on NERSC CRAY.**
**Today problem 500 times larger than previous maximum-feasible takes 4 times the clock time**** ******** speedup x100**
**Old serial computation would have required ****6000 wall clock hours (250 days)**

**We have obtained converged solutions with ****(N****m****=1023) ******** (N****r**** = 480) modes****.**
**This is sufficient to proceed with full wave treatment of lower hybrid physics**

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## Optimization is particularly crucial for fully-spectral codes that require solution of large, dense matrices

**AORSA codes**
**Code restructuring and optimization leads to 50X speedup in matrix construction in AORSA2D.**
**ScaLAPAC MPP dense linear solver is very effective. Up to 68% of peak theoretical efficiency on IBM SP.  Scales essentially linearly to2024 processors**
**New AORSA formulation transforms from Fourier space back to configuration space – results in large reduction in matrix size and solution time**
**AORSA2D – linear solve speedup x3.7, matrix memory 1/2.5**
**AORSA3D – linear solve speedup x100, matrix memory 1/40**
**Can eliminate boundary points in conducting wall – huge savings in 3D**
**Ultimately should be able to exploit sparseness in configuration space for additional savings**

|  | Fourier space | Configuration space |
| --- | --- | --- |
| Number of equations | 248,832 | 39,492 |
| Matrix size | 990 Gbytes | 25 GBytes |
| Time to load matrix | 1.2 min | 7.1 min |
| Matrix solve (ScaLAPACK | 344 min | 3.5 min |
| Fourier transform | 9.5 min | 0.04 min |
| Total CPU time | 358 min | 13.4 min |
| Flops/processor | 1.1 Gflops | 0.25 Gflops |

**3D example: Compact Stellarator**
**Note: **
**Performance improves ******** 27**
**Efficiency drops/4**

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## Integration with transport or stability models requires calculation of “macroscopic” plasma response rather than details of f0

**Calculation of local power deposition P****loc****(x), RF driven current, RF macrosopic force to drive fluid flows, or construction of the Quasi-linear operator, involve bilinear functions of the wave field amplitudes**
**Example: when the plasma response is non-local the power deposition P(x) is not the standard local WKB result**
**P****loc**** is neither symmetric nor positive definite unless:**
** ******** ****is independent of k (i.e. local) or**
**Only one mode is present (zero spectral width) **
**In general (finite spectral width) P(x) is a nested double sum over spectrum E****n**
**In 2D this is 6 nested sums (8 sums in 3D)**** – not computationally feasible in this form**
**To evaluate these macroscopic responses we have developed a technique transforming the field spectrum back to real space, then evaluating a local windowed Fourier transform with fewer modes than the full spectral solution**
**Speedup of 2000******** in AORSA2D with 80 ******** 80 mode solution**

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## Capabilities not previously available

**Obtain converged solutions in 2D for processes involving short wavelength modes – IBW, ICW**
**Obtain converged solutions in 3D for fast wave electron and ion heating in stellarators**
**Obtain converged solutions in 2D and 3D including ‘quasi-local’ conductivity**
**Obtain wave solutions for arbitrary non-Maxwellian distributions (e.g. from CQL3D)**
**Obtain converged full-wave solutions for very short wavelength modes in the lower hybrid range of frequencies, without geometrical optics approximation**
**Rigorously calculate local power deposition and nonlinear RF induced fluid force in 2D**

- CQL3D
- Fokker Planck solver

- METS
- non-Maxwellian ****

- AORSA2D
- wave solver

***f*****0****(v****||****, v********, ********p****  = 0)**

***Connect in 2004***

***f*****0****(v****||****, v********, ********p****)**

- Quasilinear operator

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## Progress made toward achieving scientific targets with respect to clear deliverables

**Element 2**
**Demonstration of the enhanced simulation capabilities by exploring**** four major unsolved problems in wave-plasma interactions important to ongoing experiments.**
- To what extent do realistic 2D and 3D equilibrium variations modify the local deposition of wave energy and momentum in the plasma?
- To what extent does the presence of non-Maxwellian particle velocity-space distributions modify local deposition of wave energy and momentum in plasma?
- What is the mechanism by which lower hybrid waves, launched with a phase velocity several times the electron thermal speed, are able to couple strongly to electrons and drive currents?
- What is the effect of global plasma modes on the wave fields produced by launching structures?

- DBB

## To what extent do realistic 2D and 3D equilibrium variations modify the local deposition of wave energy and momentum in the plasma?

**Completed analysis of 2D mode conversion in light minority case.  Developed new understanding of roles of IBW and ion cyclotron wave conversion.**
**Close comparison of TORIC with PCI measurements on Alcator C-Mod – Phys. Rev. Lett.  90, 155004 (2003)**
**TORIC is used routinely as an analysis tool by Alcator C-Mod experimentalists**
**Demonstration of possibility for either electron or ion heating in compact stellarators – AORSA3D**

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## 2D ICRF Mode Conversion Physics

**2D ICRF Mode Conversion Physics**

-  The intermediate wavelength ICW travel   towards the low field side above and   below the midplane.
-  Poloidal field introduces asymmetries in   ICW (Perkins 1977)

-  Three waves – IBW, ICW, FW – are    resolved at the MC layer.
-  The 2-3 wavelengths of IBW seen in   simulations have been verified by PCI    measurements on Alcator C-Mod

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## Experimental Observation of ICW**[E. Nelson-Melby et al, Phys. Rev. Letter, 90 (15) 155004 (2003)]

**Experimental Observation of ICW******[E. Nelson-Melby *****et al*****, Phys. Rev. Letter, 90 (15) 155004 (2003)]**

- Detected wave propagates towards the low field side.
- Wavelength shorter than FW, but generally longer than IBW.
- Signal is located on the low field side of the H-3He hybrid layer.  Theoretical and full wave analysis identifies this wave as the ICW.
- Recent PCI diagnostic upgrades permit simultaneous measurement of IBW and ICW.
- 2D full wave analysis agrees with the PCI observations in spatial location and wavelength

- Contour Plot of Fourier Analyzed PCI Data

- PCI Signal Structure

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## Off-axis Mode Conversion in C-Mod**[Y. Lin et al, 15th Top. Conf. On RF Power in Plasmas, 2003] 

**Off-axis Mode Conversion in C-Mod******[Y. Lin *****et al*****, 15th Top. Conf. On RF Power in Plasmas, 2003]**** **

**Off-axis MC**
**D-H hybrid layer at r/a = 0.35 (HFS)**
**Good agreement of experiment curve and TORIC.**
**Total ********MCEH**** in the MC region (0.35 < r/a < 0.7)**** **
**Experiment: 20%**
**TORIC: 18%**
**TORIC is now used routinely by C-Mod experimentalists to analyze ICRF heated discharges.**

- frf = 80 MHz, 22.5%H, 77.5% D
- Bt = 5.27 T, Ip = 1 MA,
- ne = 1.8  1020 m-3, Te = 1.8 keV
- t = 1.502 sec, E antenna

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## 3D calculations with AORSA3D for high harmonic fast wave heating for QPS compact stellarator

**2002  ******** One full 3D calculation of LHD**
**2003 ******** Now routine analysis of QPS developing viable heating scenarios, guiding machine design**
**f = 42 MHz, 2 strap antenna, T****e**** = T****i ****= 500 ev, ne = 1.8 ********10****19****m****-3**** , 64********64********64 modes**

**Fast wave electron heating in QPS**

**Lowering the frequency to 35 MHz gives 2nd harmonic ion heating in QPS**

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## To what extent does the presence of non-Maxwellian particle velocity-space distributions modify local deposition of wave energy and momentum in plasma?

**1D all orders code, METS, applied to assess effects on non-Maxwellian distributions in various regimes**
**Combined High Harmonic Fast Wave Heating with Deuterium Neutral Beam Injection in NSTX **
**Beam anisotropy due to injection angle can modify fast ion absorption by a factor of 2**
**D-T Mode conversion in TFTR with Tritium Neutral Beam Injection **
**Tritium ion absorption profile is much narrower with slowing down distribution than with equivalent Maxwellian**
**Minority ****3****He heating of D-T plasmas in ITER with co-resonant fusion alphas **
**Power partitioning between alphas and the minority ****3****He is sensitive to the equilibrium velocity distributions and that coupling with a Fokker-Planck module is required for accurate analysis**
**First 2D full wave solutions obtained for arbitrary distribution functions**
**Neutral injection on NSTX**
**Absorption on fast D+ is comparable in magnitude to prediction with equivalent bi-Maxwellian, but much more spatially localized**
**Fast alpha effects in ITER**

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## First converged 2D full wave solutions for ITER scale device, with non-Maxwellian distribution

**Calculations confirm that fast alpha absorption can be held to low levels with appropriate choice of frequency**
**Fast alpha population does effect anti-Hermitian part of conductivity enough to modify wave propagation**

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## What is the mechanism by which lower hybrid waves, launched with a phase velocity several times the electron thermal speed, are able to couple strongly to electrons and drive currents?

**Implemented a full-wave EM field solver in the millimeter LHRF regime and elucidated the role of full-wave effects on closing the spectral gap in LH current drive:**
**Demonstrated that significant spectral broadening caused by diffraction, can occur at LH wave caustics, where geometrical optics (ray tracing) breaks down.**
**This spectral broadening leads to strong local electron Landau damping that can be sufficient to close the spectral gap in LH current drive experiments:**
**Especially important when toroidal variations in the poloidal mode number are weak.**
**New boundary conditions at the plasma surface allow modeling of simple waveguides and permit coupling directly to the slow lower hybrid wave.**
**The E****||**** component shows mm scale wavelengths.**

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## At 4.6 GHz, a FW polarization is launched from the low field side. (n||=1.5, nacc=2)
It is propagative at X=19 cm, and undergoes mode transformation to slow LH wave at X=14 cm
Loci of LH reflections canbe seen in the full wave field pattern at caustics and cutoffs

**It is propagative at **X=19** ****cm****, and undergoes mode transformation to slow LH wave at **X=14** ****cm**
**Loci of LH reflections can****be seen in the full wave field pattern at caustics and cutoffs**

_**Plasma Parameters:**_
- D(5% H), n=1.5, f=4.6 GHz
- B0 = 5.3 T, Te=3.5 keV, Ti=2.0 keV
- ne(0)=1.5×1020 m-3,I=1 MANm=1023, Nr=960

**Caustic formation simulated by coupling of inaccessible LH waves**

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## The FW is coupled at the edge,  then mode converts to a slow wave at the confluence. 
The slow wave propagates out to the edge cutoff and reflects inward again to the confluence.
All wave power is absorbed on the electrons by Landau damping.
There is a suggestion of resonance cones in the full wave field patterns.  Note also, the tangential reflection at the caustic and the normal reflection at the cutoff.

*The FW is coupled at the edge,  then mode converts to a slow wave at the confluence. *
*The slow wave propagates out to the edge cutoff and reflects inward again to the confluence.*
*All wave power is absorbed on the electrons by Landau damping.*
*There is a suggestion of resonance cones in the full wave field patterns.  Note also, the tangential reflection at the caustic and the normal reflection at the cutoff.*

**LH waves are trapped in ring between caustics and cutoffs**

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## Spectral shift is large at confluence

**The distribution of ****n****||**** on flux surfaces shows a significant upshift from an averaged launched ****n****||**** of 2 to >4 in the middle of the annulus at ****r/a=0.75****.**
**This rapid upshift at the caustic causes all the power to be absorbed in the narrow region bound by the caustic and the edge cutoff.**

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## k|| upshifts as wave travels inward

**The left plot shows the distribution of energy in the wave field perpendicular to **B **vs. flux averaged parallel wavenumber, ****k****||****(cm).  Note the the shift upwards in ****k****|| ****at ********=0.7**
**For the frequency and units in this case, ****k****||**** is approx. ****c/v********, so this shift corresponds to a slowing down of the phase velocity and an increase in damping at ********=0.7 ****as seen in the power deposition (all eld) on the right. **

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## The local n|| evolves to 2.5 on the high field side from 1.5 at the antenna.
N|| evolution is due primarily to geometric effects of major radius position, and results in different damping.
Rays penetrate farther into the plasma and damp, whereas damping in the full-wave simulation is confined to an annulus.

*N**||** evolution is due primarily to geometric effects of major radius position, and results in different damping.*
*Rays penetrate farther into the plasma and damp, whereas damping in the full-wave simulation is confined to an annulus.*

**Ray tracing simulations show important  differences**

- magneticaxis

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## Progress made toward achieving scientific targets with respect to clear deliverables

**Element 3:**
**Exploratory research into completely reformulating wave-plasma problems and solution methods to permit further extension of physics scope, such as to non-time-harmonic or highly non-linear phenomena, and to examine possibilities for increases in computational efficiencies such as through alternate field representations like wavelets.**

- DBB

## Exploratory work into advanced wave field representations and solution algorithms based on Gabor transforms and Morlet wavelets

**GEM: combines the best of the finite element method (FEM) and FFT**
**Solution is expanded in Gabor wave packets (smooth to all orders)**
**Can capture short wavelength features**

- “Gabor” is “sine wave” multiplied by Gaussian envelope

**GACO: combines Gabor transform with collocation method**
**faster, easier to implement, and often more accurate than GEM**
**submitted as module to NTC library**

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## Experimental 1D ‘lab’ code in MATLAB, arbitrary basis functions

**Have experimented with various spline and wavelet bases.  Initial success using 64 quadratic splines with non-uniform knots to solve 1D problem requiring 256 Fourier modes.  Peak error ~ 5********10****-4**
**Factor 4 compression could lead to (4****2****)****3**** = 4096 saving in 2D**
**Not adaptive.  Have to know where to put the knots ******** physics insight, working on numerical adaptive techniques**

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## We investigated two methods to reduce all-orders problem to a sparse system

**Local windowed Fourier transform**
**How non-local is the all-orders system?**
**Windowed Fourier transform in local regions + overlap zones to include region of influence of conductivity operator**
**Has already resulted in substantial reduction in calculation of power deposition**
**Perform inverse transformation of all-orders equations Fourier space back to configuration space**
**Should yield diagonally dominant system**
**So far neither direct solution with thresholding nor use of diagonal part as iterative preconditioner has been successful**

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## What role have collaborative interactions within the project and also with other SciDAC activities played?

**We are involved in 3 types of  collaborations, each of which is essential.**
**	****Collaborations within the project**
**	****Collaborations with other SciDAC activities**
**	****Physics collaborations with people outside of the project**

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## Collaborations within the project

**      ****Ultimate success of each project element requires the interconnection of the various parts**
**      ****Every institution in the project is involved in project collaborations with one or more other institution e.g.**
**Full wave code common development and comparisons (ORNL AORSA-xD, MIT TORIC, PPPL METS) **
**Preparation of TORIC and conductivity operator development of full wave lower hybrid studies (MIT, PPPL, ORNL computer science)**
**Flow drive formulations, reduced spectral width methods, fast numerical wave diagnostics (Lodestar, ORNL) **
**Interface of Fokker Planck (CQL3D) with full wave codes and generalized conductivity modules (CompX, PPPL, MIT, ORNL)**
**Update of parallel gradient plasma response (generalized Z function) – incorporated in AORSA2D/3D, (Mission research, PPPL, ORNL)**
**Advanced field and conductivity representations based on wavelet / Gabor transforms developed (PPPL, MRC, Lodestar and ORNL)**

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## Collaborations within the project – project communication

**Monthly (almost) conference calls**
**Research visits**
**2****nd**** SciDAC Wave Plasma Interaction workshop, Sept.11-13, 2002, PPPL**
**Meeting at APS Nov. 2002, Orlando**
**3****nd**** SciDAC Wave Plasma Interaction workshop, Jan. 29-31, 2003, San Diego**
**4****nd**** SciDAC Wave Plasma Interaction workshop, July, 2004, Oak Ridge**

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## Collaborations with other SciDAC activities

**     ****Collaborative activities with SAPP project and with computer scientists at ORNL and PPPL was extremely productive and critical to success**
**Massive parallelization and acceleration of  AORSA 2D and 3D all orders wave codes**
**Restructuring configuration space version of AORSA to eliminate boundary points**
**Acceleration and parallelization of finite Larmor radius wave code TORIC**
**Acceleration of non-Maxwellian conductivity module**
**Development of advanced field representations**
**Acceleration of antenna modeling codes**
**     ****Further collaborations with other SciDAC projects were proposed in follow on project – particularly Fusion Grid, and CEMM as well as SAPP**

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## Physics collaborations with people outside our project

**Experimental collaborations are playing a key role in code validation and application**
**Close collaboration has been established with RF experimentalists at Alcator C-mod**
**Computational tools developed through SciDAC are routinely used to understand RF experiments**
**TORIC calculations for E. Nelson-Melby *****et al*****, Phys. Rev. Letter, 90 (15) 155004 (2003) and for Y. Lin *****et al*****: Invited paper, 15th  Topical Conf. On RF in Plasmas were done by experimenters**
**Close collaboration established with NSTX RF experimental team – extensive code comparison on NSTX**
**Initial tests of non-Maxwellian conductivity + METS fast ion distribution obtained from TRANSP simulation of NSTX: NBI+HHFW discharge**
**New theory and computational collaborations will extend the applicability of codes**
**Monte Carlo calculation of ICRF induced plasma rotation – General Atomics**
**Global mode effects on antenna fields (TOPICA + EMIR3 codes) – Poleticnico di Torino**
**Collaboration with U. Colorado on more general treatment of orbit integral**
**Johan Carlsson of TechX has received SBIR funding to work with us on PIC calculation of ICRF wave-particle interactions**
**We are making a real effort to forge connections to other branches of the fusion program**
**Presentation at TTF on Nonlinear RF generation of sheared flows, Myra, Lodestar**
**We organized a special session at RF Topical Conf. to engage experimentalists and promote collaborations**

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## What was the vision/scientific roadmap for the next 3-year phase

- Develop an integrated wave simulation capability for the ion cyclotron, lower hybrid and electron cyclotron range of frequencies with self-consistent wave fields and plasma distributions.
- Assemble a prototype system with the 4 basic elements - wave solver, non-Maxwellian conductivity module, quasilinear operator module, Fokker-Planck solver – all communicating and interacting in an automated way on the same computing platform..
- Establishing connection to other disciplines setting the stage for an integrated fusion simulation – To what extent, and how in practice, can waves be used to heat and control the nonlinearly coupled plasma processes at work in a burning plasma device?
- current drive interactions with MHD
- fast particle effects on plasma rotation
- flow drive interaction with turbulence and internal transport barriers
- RF antenna/edge interactions
- Investigate power losses to RF sheaths at any point where magnetic field lines terminate on material surfaces inside, on, or near the RF antenna;
- Investigate global power losses in the edge region surrounding the entire tokamak core, especially in the presence of a large divertor gap, as expected in ITER; and
- Calculate the launch spectrum and mutual strap inductance caused by the plasma in full tokamak geometry.** **
- Preparation for burning plasma experiment

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