1. Computational Plasma Physics: Examples from Turbulence Research W Dorland University of Maryland With images from: W M NevinsD Applegate G W HammettG D Kerbel B I CohenG G Howes UKAEAJ Stone J CandyR E Waltz

2. Advancing Science with Simulations

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

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

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

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

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

8. Advancing Science with Simulations Common Denominator:

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

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

11. Advancing Science with Simulations 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?

12. Advancing Science with Simulations 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!

13. Tokamaks 101 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… JET tokamak

14. 5 Steps to Asymptotic Freedom

15. 1.Define problem in precise mathematical terms

16. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes

17. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes 3.Benchmark codes in simple limits and against each other

18. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes 3.Benchmark codes in simple limits and against each other 4.Use simulations to

19. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes 3.Benchmark codes in simple limits and against each other 4.Use simulations to a)Study cases of immediate interest

20. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes 3.Benchmark codes in simple limits and against each other 4.Use simulations to a)Study cases of immediate interest b)Develop analytical understanding

21. 5 Steps to Asymptotic Freedom 1.Define problem in precise mathematical terms 2.Develop multiple, independent algorithms and simulation codes 3.Benchmark codes in simple limits and against each other 4.Use simulations to a)Study cases of immediate interest b)Develop analytical understanding 5.“Turn off” the computer

22. Define Problem in Mathematical Terms

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

24. Define Problem in Mathematical Terms h=h s (x, y, z, ,  ; t) “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:

25. Define Problem in Mathematical Terms h=h s (x, y, z, ,  ; t) “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:

26. Define Problem in Mathematical Terms h=h s (x, y, z, ,  ; t) “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: Plus Maxwell’s Eqs to get gyro-averaged potential:

27. Bessel functions represent averaging around particle gyro-orbit

29. Easy to evaluate in pseudo-spectral code. Fast multipoint Padé approx. in other codes. Fast multipoint Padé approx. in other codes.

30. Highly Anisotropic Structures with Long Mean Free Path 

31. Independently Develop Multiple Algorithms and Codes

32. 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. Linear micro- stability calcu- lations for NCSX stellarator with GS2 and FULL agree: very challenging linear benchmark Benchmark Codes in Simple Limits and Against Each Other 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]