Computational Model of Computational Model of Energetic Particle Fluxes in the Energetic Particle Fluxes in the

MagnetosphereMagnetosphereComputer Systems 2005-2006Computer Systems 2005-2006

Yu (Evans) XiangYu (Evans) Xiang

Mentor: Dr. John Guillory, George Mason UniversityMentor: Dr. John Guillory, George Mason University

The MagnetosphereThe Magnetosphere

Figure 1 Earth’s magnetosphere

http://liftoff.msfc.nasa.gov/academy/space/Magnetosphere.GIF

ProblemsProblems

• 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.

Potential SolutionsPotential 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.

DescriptionDescription

Use of available MHD Use of available MHD (Magnetohydrodyamics) code(Magnetohydrodyamics) code

Guiding center approximationsGuiding center approximations– North-South bounceNorth-South bounce– ExB driftExB drift– Drift due to magnetic field inhomogeneityDrift due to magnetic field inhomogeneity

Fast gyromotionFast gyromotion VisualizationVisualization

Coordinate SystemCoordinate System

Figure 2 Coordinate system

images from http://www.solarviews.com/raw/earth/earthafr.jpg and http://solarsystem.nasa.gov/multimedia/gallery/PIA03149.jpg

Condition for Guiding Center Condition for Guiding Center ApproximationApproximation

Conservation of magnetic momentConservation of magnetic moment

Requirement of the magnetic field behaviorRequirement of the magnetic field behavior

Effective Parallel ForceEffective Parallel Force

Caused by longitudinal gradient of the Caused by longitudinal gradient of the magnetic fieldmagnetic field

Gives rise to the north-south bounce motionGives rise to the north-south bounce motion

ExB DriftExB Drift

Interaction between the electric and Interaction between the electric and magnetic fieldmagnetic field

Perpendicular to both the electric and Perpendicular to both the electric and magnetic fieldmagnetic field

Magnetic Field InhomongenieityMagnetic Field Inhomongenieity

Drift due to gradient of magnetic field Drift due to gradient of magnetic field strengthstrength

Has larger effect than the ExB driftHas larger effect than the ExB drift Depends on the energy of the particleDepends on the energy of the particle

Gyromotion GeometryGyromotion Geometry

Figure 3 Geometry for calculating the gyromotion

Calculation using the Lorentz Calculation using the Lorentz Force LawForce Law

For q<0,For q<0,

For q>0,For q>0,

Field Behavior near Earth’s Field Behavior near Earth’s SurfaceSurface

Static magnetic dipole fieldStatic magnetic dipole field Electric field due to solar wind and motion Electric field due to solar wind and motion

of the ionosphereof the ionosphere

InterpolationInterpolation

MHD code calculates field values at MHD code calculates field values at discrete grid points.discrete grid points.

Lagrange polynomial interpolationLagrange polynomial interpolation

Generating 3 such polynomials to Generating 3 such polynomials to interpolate over all 3 dimensions.interpolate over all 3 dimensions.

How good is the interpolation?How good is the interpolation?

Figure 4 Comparison of calculated (left) and interpolated (right) magnetic field

Model StructureModel Structure

Figure 5 Structure of the model

Sample RunSample Run

Three 1 MeV protons with 45 degrees Three 1 MeV protons with 45 degrees initial pitch angle and starting positions 4 initial pitch angle and starting positions 4 Re apart in the radial direction.Re apart in the radial direction.

Figure 6 Output from sample run Figure 7 Output from sample run

Sample runSample run Three protons with initial energies of 1 KeV, 10 Three protons with initial energies of 1 KeV, 10

KeV, 100 KeV, pitch-angles of 60, 30, and 45 KeV, 100 KeV, pitch-angles of 60, 30, and 45 degrees respectively, starting positions separated degrees respectively, starting positions separated by 5 Re.by 5 Re.

Figure 8 Output from sample run Figure 9 Output from sample run

ConclusionConclusion

Successful in creating a working model of Successful in creating a working model of particle motion in the magnetosphere.particle motion in the magnetosphere.

Further optimization and correction can improve Further optimization and correction can improve precision and accuracy.precision and accuracy.

Parallelization can improve performance.Parallelization can improve performance. Combining with available MHD code can create Combining with available MHD code can create

a complete model that includes particle motion a complete model that includes particle motion and more sophisticated field behaviors.and more sophisticated field behaviors.