We have modeled ion velocity distributions in the near-Earth
magnetotail, the part of the Earth1s 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:
Charged Particles in Magnetic Fields
- Lorentz Force: F = q v x B
- Newton1s 2nd Law: F = ma = mr"
- Simplest Case: Uniform B
- =>
- cyclotron (gyro) radius:
- =>
- cyclotron (gyro) frequency:
- Helical Orbit
- Guiding Center Approximation and Adiabatic Invariance [Alfven
1950, Northrup 1963]
- =>
- separate length scales:
- short: gyro motion
- long: motion of "guiding center"
Parameters
- Particle energy, H (conserved if E=0)
- Field ratio: bn = Bz/Bx
- Kappa Parameter:
- Definition:
- = field line
curvature radius
- = 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]
- Transient (Speiser, resonant)
k>=1
k<1
- Regular (trapped in CS)
k<1
- Quasi-trapped (chaotic, "cucumber")
k>=1
k<1
Intermediate Regime
- Breakdown of adiabatic and current sheet approximations predicts
3-branch behavior
- A.
- Large : no
µ change (adiabatic)
- B.
- Small : predictable µ increase
- C.
- Intermediate : phase
dependent µ increase or decrease
Question
- Is there an observable effect of this 3-branch behavior?
Plan
- Look for features in modeled ion velocity distribution
function.
- If present: determine if observable by Geotail spacecraft.
Methodology
- 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
- 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.
- We1ve found that with the current pitch angle resolution of Geotail
spacecraft, these structures should be observable.
- 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.
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