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Computational Plasma Physics: Examples from Turbulence Research

Computational Plasma Physics: Examples from Turbulence Research. W Dorland University of Maryland With images from: W M Nevins D Applegate G W Hammett G D Kerbel B I Cohen G G Howes UKAEA J Stone J Candy R E Waltz. Advancing Science with Simulations.

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Computational Plasma Physics: Examples from Turbulence Research

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  1. Computational Plasma Physics: Examples from Turbulence Research W Dorland University of Maryland With images from: W M Nevins D Applegate G W Hammett G D Kerbel B I Cohen G G Howes UKAEA J Stone J Candy R E Waltz

  2. Advancing Science with Simulations

  3. Wide range of problems in plasma physics Advancing Science with Simulations Plasma from START, courtesy Culham Lab, UKAEA

  4. Wide range of problems in plasma physics Wide range of algorithms and codes Advancing Science with Simulations Simulation courtesy G D Kerbel and W Dorland

  5. Wide range of problems in plasma physics Wide range of algorithms and codes Advancing Science with Simulations Turbulent accretion flow courtesy J Stone

  6. Wide range of problems in plasma physics Wide range of algorithms and codes Advancing Science with Simulations Turbulent fluctuations in solar wind Courtesy of S Bale, UC-Berkeley

  7. Wide range of problems in plasma physics Wide range of algorithms and codes What do we have in common? Advancing Science with Simulations Gyrokinetic simulation of MHD turbulence

  8. Common Denominator: Advancing Science with Simulations

  9. Common Denominator: How does one use supercomputers to advance science? Advancing Science with Simulations

  10. Common Denominator: How does one use supercomputers to advance science? I will address this question with examples from my research area. Advancing Science with Simulations

  11. Common Denominator: How does one use supercomputers to advance science? I will address this question with examples from my research area. Common Question: What is the most exciting thing one can do with a powerful supercomputer? Advancing Science with Simulations

  12. Common Denominator: How does one use supercomputers to advance science? I will address this question with examples from my research area. Common Question: What is the most exciting thing one can do with a powerful supercomputer? Answer:Turn it off! Advancing Science with Simulations

  13. A tokamak is a toroidal magnetic chamber to confine plasma Stable equilibria demonstrated for hours on superconducting machines Problem is rapid transport of energy, momentum and particles out of machine by turbulence. One major goal of fusion program: understand and control this turbulence. Understanding comes from studying simulations… Tokamaks 101 JET tokamak

  14. 5 Steps to Asymptotic Freedom

  15. Define problem in precise mathematical terms 5 Steps to Asymptotic Freedom

  16. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes 5 Steps to Asymptotic Freedom

  17. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes • Benchmark codes in simple limits and against each other 5 Steps to Asymptotic Freedom

  18. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes • Benchmark codes in simple limits and against each other • Use simulations to 5 Steps to Asymptotic Freedom

  19. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes • Benchmark codes in simple limits and against each other • Use simulations to • Study cases of immediate interest 5 Steps to Asymptotic Freedom

  20. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes • Benchmark codes in simple limits and against each other • Use simulations to • Study cases of immediate interest • Develop analytical understanding 5 Steps to Asymptotic Freedom

  21. Define problem in precise mathematical terms • Develop multiple, independent algorithms and simulation codes • Benchmark codes in simple limits and against each other • Use simulations to • Study cases of immediate interest • Develop analytical understanding • “Turn off” the computer 5 Steps to Asymptotic Freedom

  22. Define Problem in Mathematical Terms

  23. “Gyrokinetic equations” describe small scale turbulence in magnetized plasma; written down from 1978-1982 Define Problem in Mathematical Terms

  24. “Gyrokinetic equations” describe small scale turbulence in magnetized plasma; written down from 1978-1982 Equations describe self-consistent evolution of 5-dimensional distribution functions (one for each plasma species) in time: Define Problem in Mathematical Terms h=hs(x, y, z, e, m; t)

  25. “Gyrokinetic equations” describe small scale turbulence in magnetized plasma; written down from 1978-1982 Equations describe self-consistent evolution of 5-dimensional distribution functions (one for each plasma species) in time: Define Problem in Mathematical Terms h=hs(x, y, z, e, m; t)

  26. “Gyrokinetic equations” describe small scale turbulence in magnetized plasma; written down from 1978-1982 Equations describe self-consistent evolution of 5-dimensional distribution functions (one for each plasma species) in time: Define Problem in Mathematical Terms h=hs(x, y, z, e, m; t) Plus Maxwell’s Eqs to get gyro-averaged potential:

  27. Bessel functions represent averaging around particle gyro-orbit

  28. Bessel functions represent averaging around particle gyro-orbit

  29. Bessel functions represent averaging around particle gyro-orbit Easy to evaluate in pseudo-spectral code. Fast multipoint Padé approx. in other codes.

  30. Highly Anisotropic Structureswith Long Mean Free Path q=p q=0

  31. Independently Develop Multiple Algorithms and Codes

  32. Independently Develop Multiple Algorithms and Codes GS2: continuum, flux tube

  33. Independently Develop Multiple Algorithms and Codes GS2: continuum, flux tube PG3EQ: PIC flux tube

  34. Independently Develop Multiple Algorithms and Codes GS2: continuum, flux tube PG3EQ: PIC flux tube GYRO: continuum, global

  35. Independently Develop Multiple Algorithms and Codes GS2: continuum, flux tube PG3EQ: PIC flux tube GYRO: continuum, global GENE: continuum, flux tube

  36. Independently Develop Multiple Algorithms and Codes GS2: continuum, flux tube PG3EQ: PIC flux tube GYRO: continuum, global GENE: continuum, flux tube FULL: continuum, linear

  37. Benchmark Codes in Simple Limits and Against Each Other

  38. Benchmark Codes in Simple Limits and Against Each Other Linear micro- stability calcu- lations for NCSX stellarator with GS2 and FULL agree: very challenging linear benchmark Benchmarks by E Belli, G Rewoldt, Hammett and Dorland

  39. Benchmark Codes in Simple Limits and Against Each Other Radial correlation functions from three independently developed gyrokinetic codes, run for identical physics parameters. This was a difficult nonlinear benchmark.

  40. Benchmark Codes in Simple Limits and Against Each Other GS2 and GENE (a European code by F Jenko) benchmark of heat flux for toroidal ETG turbulence Average value agrees well -- another example of nonlinear benchmark

  41. Develop models of physical systems – and use them! Accretion flow luminosity model [Goldston, Quataert, Igumenshchev, 2005]

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