1. Computational Model of Energetic Particle Fluxes in the Magnetosphere Computer Systems 2005-2006 Yu (Evans) Xiang Mentor: Dr. John Guillory, George Mason University

2. The Magnetosphere Figure 1 Earth’s magnetosphere http://liftoff.msfc.nasa.gov/academy/space/Magnetosphere.GIF

3. Problems Gathering data from direct observation of particle motion in the magnetosphere is very difficult. Electronic equipment, such as on satellites and orbiting telescopes, can be damaged by collisions with energetic particles. Disturbances and particle fluxes in the magnetosphere have direct effects on the ionosphere.

4. Potential Solutions Creation of software to assist scientists studying energetic particle motion in the magnetosphere. Prediction of events involving charged particle fluxes in this region of space. Testing tool for future models of the magnetosphere.

5. Description Use of available MHD (Magnetohydrodyamics) code Use of available MHD (Magnetohydrodyamics) code Guiding center approximations Guiding center approximations –North-South bounce –ExB drift –Drift due to magnetic field inhomogeneity Fast gyromotion Fast gyromotion Visualization Visualization

6. Coordinate System Figure 2 Coordinate system images from http://www.solarviews.com/raw/earth/earthafr.jpg and http://solarsystem.nasa.gov/multimedia/gallery/PIA03149.jpg

7. Condition for Guiding Center Approximation Conservation of magnetic moment Conservation of magnetic moment Requirement of the magnetic field behavior Requirement of the magnetic field behavior

8. Effective Parallel Force Caused by longitudinal gradient of the magnetic field Caused by longitudinal gradient of the magnetic field Gives rise to the north-south bounce motion Gives rise to the north-south bounce motion

9. ExB Drift Interaction between the electric and magnetic field Interaction between the electric and magnetic field Perpendicular to both the electric and magnetic field Perpendicular to both the electric and magnetic field

10. Magnetic Field Inhomongenieity Drift due to gradient of magnetic field strength Drift due to gradient of magnetic field strength Has larger effect than the ExB drift Has larger effect than the ExB drift Depends on the energy of the particle Depends on the energy of the particle

11. Gyromotion Geometry Figure 3 Geometry for calculating the gyromotion

12. Calculation using the Lorentz Force Law For q<0, For q<0, For q>0, For q>0,

13. Field Behavior near Earth’s Surface Static magnetic dipole field Static magnetic dipole field Electric field due to solar wind and motion of the ionosphere Electric field due to solar wind and motion of the ionosphere

14. Interpolation MHD code calculates field values at discrete grid points. MHD code calculates field values at discrete grid points. Lagrange polynomial interpolation Lagrange polynomial interpolation Generating 3 such polynomials to interpolate over all 3 dimensions. Generating 3 such polynomials to interpolate over all 3 dimensions.

15. How good is the interpolation? Figure 4 Comparison of calculated (left) and interpolated (right) magnetic field

16. Model Structure Figure 5 Structure of the model

17. Sample Run Three 1 MeV protons with 45 degrees initial pitch angle and starting positions 4 Re apart in the radial direction. Three 1 MeV protons with 45 degrees initial pitch angle and starting positions 4 Re apart in the radial direction. Figure 6 Output from sample run Figure 7 Output from sample run

18. Sample run Three protons with initial energies of 1 KeV, 10 KeV, 100 KeV, pitch-angles of 60, 30, and 45 degrees respectively, starting positions separated by 5 Re. Three protons with initial energies of 1 KeV, 10 KeV, 100 KeV, pitch-angles of 60, 30, and 45 degrees respectively, starting positions separated by 5 Re. Figure 8 Output from sample runFigure 9 Output from sample run

19. Conclusion Successful in creating a working model of particle motion in the magnetosphere. Successful in creating a working model of particle motion in the magnetosphere. Further optimization and correction can improve precision and accuracy. Further optimization and correction can improve precision and accuracy. Parallelization can improve performance. Parallelization can improve performance. Combining with available MHD code can create a complete model that includes particle motion and more sophisticated field behaviors. Combining with available MHD code can create a complete model that includes particle motion and more sophisticated field behaviors.