1. Ab initio simulations for (the WITCH) Penning traps using a graphics cards for faster coulomb interaction calculations S. Van Gorp, M. Breitenfeldt, M. Tandecki, F. Wauters, E. Traykov,, N. Severijns (K.U.Leuven, Belgium), M. Beck, P. Friedag, C. Weinheimer (Univ. Munster, Germany), A. Herlert (ISOLDE-CERN, Geneva, Switserland), V. Kozlov, F. Gluck (Univ. Karlsruhe, Germany), D. Zakoucky (NPI-Rez, Prague, Czech)

2. Simon Van Gorp – TCP Saariselkä- 14.04.2010 WITCH introduction Simulation motivation Coulomb interactions Tree codes Chamomile scheme: Coulomb on a GPU. Performance GPU vs CPU Simonion, a Penning Trap simulation program Integrator Buffer gas collisions Conclusion and Outlook 2/14 Overview

3. Simon Van Gorp – TCP Saariselkä- 14.04.2010 WITCH Introduction 3/14 The WITCH experiment looks for scalar currents in nuclear beta decay. A scattering free source is needed because of the low recoil energy. A retardation barrier is applied and the # ions reaching an MCP detector are counted.

4. Simulation Motivation Simon Van Gorp – TCP Saariselkä- 14.04.2010 The retardation spectrometer is a combination of E and B fields. A particle tracking routine was developed to understand the behavior of the ions by F. Gluck. A good source of ions is needed to describe the process correctly. Understand space charge effects in the Penning traps. 4/14 WITCH: 10 6 ions per cycle -> Computer simulations which are dominated by the Coulomb interaction calculation

5. Coulomb interactions Simon Van Gorp – TCP Saariselkä- 14.04.2010 Coulomb force scales with O(N 2 ) Tree methods (Barnes Hut, PM, P 3 M, FMM) reduces this to O(N log N) 5/14 Space is divided in nodes. Which are subdivided A node has the total charge and mass, and is located on the centre of mass. Approx. long range force by aggregating particles into one particle and use the force of this one particle Scaled Coulomb Force puts more weight to the charge of one ion to simulate more ions. Works well [1] [1]: D. Beck et al, Hyp. Int. 132, 2001

6. Why a GPU? Simon Van Gorp – TCP Saariselkä- 14.04.2010 6/14 GPU CPU -high parallelismSTILL TO DO -very fast floating point calculations -SIMD structure (pipelining!) Geforce 8800 GTX

7. Chamomile scheme Simon Van Gorp – TCP Saariselkä- 14.04.2010 Calculating gravitational interactions on a Graphics Card via the Chamomile scheme from Hamada and Iitaka (in 2007). 7/14 Why a GPU? -parallelism! -only 20 float operations -CUDA programming language for GPU’s J-bag I-pot force [2]: T. Hamada and T. Iitaka, arXiv.org:astro-ph/0703100, 2007

8. Chamomile scheme: practical usage Simon Van Gorp – TCP Saariselkä- 14.04.2010 Function provided by Hamada and Iitaka: Gravitational force ≈ Coulomb Force Conversion coefficient: Needed: -64 bit linux -NVIDIA Graphics Card that supports CUDA - CUDA environment v2.3 Not needed: -CUDA knowledge -… 8/14

9. Simon Van Gorp – TCP Saariselkä- 14.04.2010 3000 35 Ar + ions No Buffergas 9/14 Movie

10. Simon Van Gorp – TCP Saariselkä- 14.04.2010 GPU vs CPU GPU blows the CPU away. The effect becomes more visible with even more particles simulated. Simulated is a quadrupole excitation for 100ms with buffer gas. This takes 3 days with a GPU compared to 3-4 years with a CPU! GPU improvement factorCPU and GPU simulation time

11. Simon Van Gorp – TCP Saariselkä- 14.04.2010 11/14 Simonion overview Simonion is a modular Penning Trap simulation package. Reading external fieldmaps Trap excitations 3 different integrators 2 buffergas routines Possibility to include external fieldmaps Can run on CPU and GPU Compile with g++ or icpc A root analysis file is provided A Makefile is provided http://sourceforge.net/projects/simonion/

12. Integrators and buffer gas models Simon Van Gorp – TCP Saariselkä- 14.04.2010 Integrators: 4 th and 5 th order Runga Kutta with adaptive stepsize and error control. 1 st order (predictor corrector) Gear method. Buffer gas models: Langevin or polarizability model (= for all mases) Ion Mobility based model ( ≈ for all mases) 12/14

13. Simon Van Gorp – TCP Saariselkä- 14.04.2010 Other GPU bases libraries: Kirin: + corrector and predictor integrator [3] 2 x faster Sapporo: double precision, corrector on CPU [4] 2 x faster ? N-Body from Nvidia [5] 2 x faster ? Tree codes Scaled Coulomb force 13/14 Possible improvements [3]: Belleman et al, New Astronomy, 13(2),103-112,2007 [4]: Evghenii et al, New Astronomy, 14(7),630-637,2009 [5]:Nyland et al, GPU Gems 3, Chapter 31, Addison-Wesley, 2007

14. Simon Van Gorp – TCP Saariselkä- 14.04.2010 A Penning Trap simulation package Simonion is presented that is stable and intuitive to use. The first program that uses a GPU to calculate Coulomb interactions much faster! GPU computing is a new field of which we barely scratched the surface. Possible improvements like tree codes and scaled Coulomb force will push the limit to 10 6 particles 14/14 Conclusion

15. Thank you for your attention

16. Simon Van Gorp – TCP Saariselkä- 14.04.2010 16/24