1. www.eu-eela.eu E-science grid facility for Europe and Latin America Drift Kinetic Equation solver for Grid (DKEsG) A J. Rubio-Montero 1, L. A. Flores 1, F. Castejón 1,2, M. Rodríguez-Pascual 1, E. Montes 1 and R. Mayo 1. 1 CIEMAT(Spain) 2 Lab. Nacional de Fusión (Spain) 21st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6th, 2009.

2. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 2 Outline  Nuclear Fusion introduction –Motivation –Plasma physics and Fusion reactors  Neoclassical transport and DKE solvers –Variational DKES code  DKEsG –Objectives –Status and future –Performance results on (EELA) Grid

3. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 3 Fusion Plasmas  How do D and T get plasma state and overcome Coulomb barrier that prevents the collisions and, hence, avoids the fusion? –Increasing its energy  Rising temperature (T)  Increasing velocity (kinetic energy, K) –Rising pressure  Injecting particles (density, n)  Plasma magnetically confined –Coil configuration (magnetic champ, |B|) When they exceeds Lawson’s criterion reactor reaches ignition

4. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 4 Plasma behaviour simulation  High cost of a experimental discharge in a reactor  Complexity of simulating plasmas –Plasma Physics are related to Statistical Physics, Thermodynamics, Fluid, Kinetic and Chaos Theories. –1ms of complete simulation = several days in a 50-100 TFlops machine like Mare Nostrum  Mathematical methods suitable to run on distributed environments as Langevin and Fokker-Plank equations, Monte Carlo, are used to solve: –Plasma-wall interaction –Neutral particle orbits –Transport –Massive Ray Tracing –Coil optimization They could take advantage from the large amount of resources being already in Grid

5. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 5 NC transport and DKE solvers  Neoclassical (NC) transport is –a fundamental step of the complete simulation cycle of the behaviour of plasmas inside Fusion reactors. –caused by magnetic field inhomogeneities and by collisions –always present in all Fusion devices (stellarators and 3D tokamaks). –It is a low boundary of total transpport –usually used to study the efficiency of a certain coil configuration before it is implemented (i. e. ITER).  NC transport can be simulated by Drift Kinetic Equation (DKE) solvers and Monte Carlo (MC) methods –DKE advantage over MC: can calculate all transport coefficients, MC only can estimate the diagonal ones. –DKE drawback under MC:  high computation time and memory consumption, being usually executed on shared memory computers.  MC methods should be easily deployed on Grid.

6. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 6 DKE solver reference code  Variational DKES version (W.I. van Rij & S.P. Hirshman) –Obtain upper and lower bounds for the NC diffusion coefficients of a prescribed toroidal plasma equilibrium. –Widely accepted by the Fusion Community. –Applied to stellarators such as TJ-II, HSX, CHS, LHD, ATF, W7-AS; and to projected ones: V7-X, NCSX, QPS. –We plan also apply it to 3D tokamaks like ITER.  Available code –Developed in Fortran77 in 1989 –Implemented for obsolete shared memory hosts (CRAY-1, CRAY-X-MP) –Modified (~2001) to run on SGI Origin 3000 MIPS machines (IRIX64). –Parametric and sequential nature

7. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 7 How work with Variational DKES  Requires continuously manual configuring, recompiling code and compilation of high number of output data files  Magnetic configuration is described by Fourier series  Energy distribution function of particles by a a series of Legendre polynomials.  Parameter sweep of normalized collisionatillity and electrical field.  Results: only normalized diffusion coefficients (independent of temperature and density).

8. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 8 New framework: DKEsG (Drift Kinetic Equation solver for Grids) to  Easily retrieve all neoclassical transport coefficients:  Reducing time execution and increasing precision making use of heterogeneous resources from different Grid infrastructures.  Filling a broad database with the complete [configuration - transport matrix – state] for several Fusion reactors to: –Bring results to Fusion Community –Avoid performing the same simulation twice and easy re-analysis  Easy interaction with other Fusion applications to build complex workflows to –Perform complete simulations of plasma –Find more optimized TJ-II configurations DKEsG - Objectives

9. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 9 Calculus of specific NC coefficients  Diffusion coefficients –Normalized coefficients returned by DKES depends of energy K: –Diffusion of n and T –Bootstrap current –Resistivity enhancement  Transport coefficients –Need >10 6 D ij to fit correctly the integral and solve only 1 L ij Depends of n and T

10. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 10 DKEsG current status  All code in a nutshell –Algorithms from DKES software up-to date and extended –Ported and optimized to Linux x86-32, x86-64 and ia-64 platforms –Only a binary per architecture and algorithm –No software must be installed in resources  Grid-enabled: –Automatic generation of input files and unatended submission of jobs to Grid through GridWay –Run on Globus and gLite Grids –Tested on EGEE-III, EELA-2 and regional infrastructures.  A module to calculate NC transport coefficients has been developed

11. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 11 DKES vs. DKEsG Each DKES3 instance is submited with its input to Grid Returns : NC diffsion coefficients for a specific Temperature and density. 9 element matrix of NC transport coefficients

12. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 12 Some results for TJ-II  Applied to TJ-II Flexible Heliac –Sited at CIEMAT Madrid (Spain) –Began fully operational in 1997 –1.5 m major plasma radius  DKEsG Inputs: –Normallized collisionallity [0.1..100] with 0.5 step –5 electrostatic potentials (assumed constant on every magnetic surface) –Fixed: 4cm plasma radius, 100 Legendre, 343 Fourier polynomials –Temperature and atomic mass set to 1.  Total : –2500 pairs processed within 500 jobs –Distributed among 12 EELA-2 Grid sites. –1 job ~ 4 mins in a core Xeon 5160(3.0Ghz)  500 jobs ~ 33 hours –Total time spent: ~53 mins. –Wallclock: ~ 45 hours (middleware & file transfer overhead not included)

13. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 13 Some results for TJ-II  Diffusion of density and temperature Normalized diffusion coefficient by normalized electrical field NC diffusion coefficient D11 for T=1 KeV and M=1u

14. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 14 DKEsG: Future  High level implementation on java DRMAA standard –Suitable to run on Globus/gLite Grids through GridWay or on local clusters through PBS, SGE or LSF –Integration in complex application level workflows and databases  VMEC – DKEsG  FAFNER-2 – DKEsG  MaRaTra – DKEsG –Independent GUI  Fill coefficients database and offer it as virtual observatory

15. www.eu-eela.eu 21 st Intern. Conf. on Numerical Simulation of Plasmas. Lisbon, Portugal. Oct 6 th, 2009 15 Thanks for you attention ?