1. Latest Advances in “Hybrid” Codes & their Application to Global Magnetospheric Simulations A New Approach to Simulations of Complex Systems H. Karimabadi 1,2, N. Omidi 1,2 Collaborators on application to the magnetosphere: K. B. Quest 1 H. X. Vu 1 D. Krauss-Varban 1 J. Raeder (UCLA) 1 UCSD, San Diego, CA 2 SciberNet, Inc.

2. Challenges in Global Simulations Multi-scale Coupled Systems - Spatial scales vary from centimeters to 200 RE - Temporal scales vary from less than milliseconds to days - kinetic effects have large-scale consequences Multi-physics - electron physics: e.g., controls reconnection - ion physics: e.g., dominates formation of boundaries and transport - global features and dynamics: e.g., extent of the magnetotail - coupling to the ionosphere

3. Ideal Code 1.Each region would evolve based on its own spatial and temporal scales 2. Allow distinct physical models at different spatial scales Mixed Resolution Modeling Code-code coupling

4. Standard Recipe 1. Pick one physics model (e.g., MHD or hybrid) 2. Use space and time differencing of the eqns a. introduce spatial grid b. Advance the equations based on a uniform time step

5. A Typical Cycle in the Simulation

6. Nonuniform Mesh

7. Some Numerology Assuming that: a. Nonuniform mesh saves a factor of 50 in # of cells b.   t = 0.025 (optimistic value!) c. Can use all 1152 processors of the Blue Horizon 1 min in real time = 1500 minutes of run time (1 day)

8. Three Approaches to Global Simulations MHD - used extensively - does not resolve important ion physics - not suitable for studies of boundaries & discontinuities Hybrid (fluid electrons, kinetic ions) - it is the next stage of advance in global simulations - resolves ion spatial scales (ion inertial length) and ion temporal scales (gyroperiod) Full Particle - not feasible or necessary

9. Hybrid Simulations Formation of boundaries occur on ion time scales The length scale of discontinuities is on ion spatial scales Hybrid code properly captures the scaling properties of reconnection process Yields details about plasma distribution functions Can be used to study different types of magnetospheres including asteroids

10. Why Is the Current State-of- the-art Not Adequate? 1. Time advance scheme is too inefficient - Every cell is updated regardless of whether a change has occurred - Time step is not based on local conditions 2. Existing time advance schemes do not allow code-code coupling

11. Our Roadmap 1. Software: Further develop MRM code 2. Hardware: PC cluster 3. Science: Scaling study: Phase transition of magnetospheres as a function of dipole strength a) 2D global hybrid b) 3D global hybrid – include ionospheric model c) Code-code coupling

12. MRM Methodology Time-stepped: Allow time step to be different in each region Event driven: (a) Defines a true temporal mesh where time step can be different for each cell (b) Quantities are updated only when a “change” (event) has occurred

13. MRM N 1 /N 2 = 10, B 1 /B 2 = 0.6,  1 /  2 = 1/3

14. MRM Application to Plasma Sails: I Regions I and II evolve on time scales that are different by a factor of more than 200

15. MRM Application to Plasma Sails: II

16. Event Driven Methodology: I Based on concepts from computer science, control theory, and operations research Uses irregularly time-stamped events that only updates what needs to be updated when it needs to be updated Requires construction of: a) Simulation Engine b) Simulation Model: Objects and Events

17. Event Driven Methodology: II

18. Event Driven Methodology: III

19. Event Driven Methodology: IV Table 1: Timing of various methods Simulation Methodology Timing (seconds) PIC (time- stepped) 1237 Discrete (tol = 0.2) 129 Discrete (tol = 2)42 Discrete (no persistent events) 11

20. PC Cluster vs Blue Horizon “Blue Horizon is the most powerful computer available to the U.S. academic community and currently the 8th most powerful computer in the world.” Using all of its processors, BH is faster than our cluster by a factor of 1.96

22. Simulation Model

23. Scaling Study: Phase transition of model magnetospheres

24. Omidi et al., JGR 2002

25. D p = 130 c/  p

27. Summary New MRM codes are much faster Global hybrid simulations are now possible: We can for the first time look at the magnetosphere on ion scales 2D offers many advantages and can be used to address many important issues PC cluster offers many advantages to traditional supercomputers