Ion Distribution Function Structures Caused By Non-Adiabatic Motion in the Geomagnetic Tail

By Michael Asbury, R.F. Martin, Jr.

Illinois State University Physics Department
Presented at the Argonne Symposium for Undergraduate Research
November, 2000


We have modeled ion velocity distributions in the near-Earth magnetotail, the part of the Earth's magnetosphere on the anti-sunward side of the planet. The megnetotail is thought to be the crucial region in energy storage and release during magnetospheric substorms, so an understanding of the plasma properties in this region is essential. Velocity distribution functions are measured on satellites and give a great deal of information about the dynamics of ions and electrons in the plasma. Our magnetic field model is a standard one consisting of a Harris current sheet with a uniform normal component. In our simulation, we use a "virtual detector" at a fixed location in the model field and trace particles from the detector, backwards in time, until they reach a source region. In this study the source region is located in the large z asymptotic region above and below the current sheet field reversal region, one of the known sources of plasma for the magnetotail plasma sheet. We have found structuring in the ion distributions consisting of peaks and valleys in the pitch angle distribution for precipitating particles near the edge of the magnetic field reversal. The structuring only occurs for a certain range of energies and field parameters. We have re-binned our simulation data to see how detector resolution affects the observability of these structures. We find that the CPI detector on the GEOTAIL spacecraft has the capability to resolve such structures if observations are taken at a fixed gyrophase. The sturctures depend on gyrophase such that as phase increases from 0 to 360 degrees, the ridges move to higher parallel velocities. If the phase angles are averaged over, however, the structuring cannot be as easily resolved, and a higher resolution detector may be required. If observable, these particle structures could be used as a remote sensing method for magnetotail fields and may help us better understand the interaction between the magnetotail and the polar ionosphere during ion precipitation.


The Earth's Magnetosphere

  • A cavity within the solar wind within which the Earth1s magnetic field controls the physics
  • Magnetosphere Cartoon:
    Magnetosphere Cartoon

Charged Particles in Magnetic Fields

  • Lorentz Force: F = q v x B
  • Newton1s 2nd Law: F = ma = mr"
  • Simplest Case: Uniform B
    • Equation
      • cyclotron (gyro) radius: equation
      • cyclotron (gyro) frequency:eqution
    • equation
  • Helical Orbitequation
  • Guiding Center Approximation and Adiabatic Invariance [Alfven 1950, Northrup 1963]
    • separate length scales:
      • short: gyro motion
      • long: motion of "guiding center"


  1. Particle energy, H (conserved if E=0)
  2. Field ratio: bn = Bz/Bx
  3. Kappa Parameter:
    • Definition: equation
    • equation= field line curvature radius
    • equation= gyro-radius of particle
    • Meaning
      • k>>1: adiabatic motion
      • k<1: current sheet motion
      • k~1: complex motion (what we're interested in!)

Field Reversal Particle Dynamics

  • Field Reversal Orbit types:
    [Chen and Palmadesso,1986; Buchner and Zelenyi, 1986,1989; Chen, 1992]
    1. Transient (Speiser, resonant)
      graphk>=1 graphk<1
    2. Regular (trapped in CS)
    3. Quasi-trapped (chaotic, "cucumber")
      graphk>=1 graph k<1

Intermediate Regime

  • Breakdown of adiabatic and current sheet approximations predicts 3-branch behavior
    1. LargeAlpha  naught : no µ change (adiabatic)
    2. Small Alpha  naught: predictable µ increase
    3. Intermediate Alpha  naught: phase dependent µ increase or decrease

Research Project


  • Is there an observable effect of this 3-branch behavior?


  • Look for features in modeled ion velocity distribution function.
  • If present: determine if observable by Geotail spacecraft.


  • Follow 60,000 ions through model current sheet magnetic field, ending at "virtual detector" at spacecraft position.
  • Calculate distribution function.

Distribution Function at various values of bn

  • small bn; characteristic of mid/far tail
  • medium bn; characteristic of near-Earth to mid tail
  • large bn; characteristic of ring current - Near Earth tail

graph graph graph


  • We have found that there is an observable effect of three branch behavior for k~0.7-3.
  • This effect can be seen as peaks and valleys in the modeled ion distribution function.
  • We've found that with the current pitch angle resolution of Geotail spacecraft, these structures should be observable.

Graph Graph Graph

Next Step

  • We intend to compare our results with those of a simulation using a different method. This is the simulation of Dr. Holland of ISU.
  • We are also searching the database of a satellite which could have possibly observed such structuring. This is also being done by Dr. Holland.