The earth1s magnetosphere is the region of space where the earth1s
magnetic field dominates the physics. The magnetosphere consists of a low
density gas of charged particles, i.e. a plasma. Due to the solar wind,
the magnetosphere is compressed on the sunward, or day, side and elongated
on the night side to form a "tail". This region, called the magnetotail,
extends for several hundred earth radii. Particles in the plasma sheet at
the center of the tail, can become energized and accelerated through the
plasma sheet boundary layer (PSBL) between the plasma sheet and the tail
lobes, into the auroral region. Particles entering the auroral region are
accelerated into the ionosphere and upper atmosphere, colliding with atoms
to produce visible light in the polar regions. These dynamic, colorful
displays of light in the night sky are called auroras. The whole process
is a magetospheric or auroral substorm. During substorms, ground based
and satellite communication can be disrupted and the electric power grid
can feel strong perturbations.
One way to study magnetotail plasma is to investigate the motion of
individual charged particles. Associated with each particle is a quantity
known as the magnetic moment, which is nearly constant except near a small
region at the equatorial plane of the magnetotail. In this region, a
particle1s magnetic moment can undergo large jumps which are associated
with the chaotic nature of the particle motion. We define a parameter ,
where rg is the gyroradius of the particles orbit, and Rc is the radius of
curvature of the magnetic field. The k parameter can be used to describe
types of orbits. There are three main behavior types which are
exhibited. Adiabatic behavior occurs when k >> 1. It is characterized by
helical orbits about magnetic field lines and by the conservation of the
magnetic moment. When k < 1, the magnetic moment is not conserved and the
particle will oscillate about the plasma sheet center. This is known as
current sheet behavior. Intermediate behavior is our area of interest and
occurs when k ~ 1. In this case, we find that the magnetic moment is
scattered according to a 3-branch pattern: particles with large pitch
angle are nearly adiabatic, those with small pitch angles have current
sheet behavior, while internediate particles scatter chaotically with
potentially large decreases in magnetic moment. We are particularly
interested in observational evidence for this 3-branch behavior.
Our research involves a numerical simulation of the motion of many
particles as they progress through the plasma sheet These particles are
then collected by a "virtual satellite" and the ion velocity distribution
function is computed. We then search for any signatures of the
three-branch behavior in the distribution function graphs, and analyze its
source by tracing individual particles. We find some beam-like strucutres
that appear to be related to the intermediate branch. Such signatures
will be useful in analyzing data from the GEOTAIL spacecraft.
Earth's magnetosphere
Charged Particles in Magnetic Fields:
- Lorentz Force: F=q vxB
- Newton's 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"
- small parameter:
- =>average over short lengthscale
- =>adiabatic invariants
- conserved on fast (gyro) timescales
- associated with fast oscillatory motion
- magnetic moment:
- =>very useful for inner magnetosphere
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)
Example: Truncated Linear Current Sheet
- Model:
- Field:
Intermediate Regime (k~0.7 - 3)
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Breakdown of adiabatic and current sheet approximations
Predicts 3-branch behavior: |
- Large : =>
adiabatic
- Small : => µ increase
- Intermediate : phase dependent
µ increase or decrease
-
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
Question
- Is there an observable effect of this 3-branch behavior?
Plan
- Look for features in modeled ion velocity distribution
function.
- If present: compare to spacecraft observations.
Methodology
- Follow 10,000 ions through model current sheet magnetic field,
ending at "virtual detector" at spacecraft position.
- Calculate Distribution function.
Related Graphs
T=10,000 km, bn=.2, Bz0=4 nT,
Hmax=4.75 keV
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Current Sheet Crossings
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log(µ ratio) kslice=5
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f(v) for kappa>.8
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CS Crossings f(v) correlation
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µ Ratio f(v) correlation
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Simulation predicts small beams:
- "Islands" in distribution function are of iterest.
- They represent beams in the plasma.
- They are formed from transient (single-crossing) orbits.
- They correspond to high µ ratio: branch 2.
Simulation predicts ridges and valleys for higher bn:
- Ridges and valleys represent a variation of f in pitch angle
=> pitch angle scattering.
- Ridges are single orbit transient: branch 2.
Signature of 3-branch behavior
- Branch 2: Beams
- Branch 3: between the beams are low µ ratio
orbits: multiple-crossing, chaotic orbits.
- Next step: vary model parameters to see how distribution
changes
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