Computational Model of Energetic Particle Fluxes in the Magnetosphere

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 • Guiding center approximations • North-South bounce • ExB drift • Drift due to magnetic field inhomogeneity • Fast gyromotion • 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 • Requirement of the magnetic field behavior

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

9. ExB Drift • Interaction between 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 • Has larger effect than the ExB drift • 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,

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

14. Interpolation • MHD code calculates field values at discrete grid points. • Lagrange polynomial interpolation • 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. 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. Figure 8 Output from sample run Figure 9 Output from sample run

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