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Radiation belt particle dynamics
Prepared by Kevin GrafStanford University, Stanford, CA
IHY Workshop on Advancing VLF through the Global AWESOME
Network
Note the pitch angle of the motion.
||
1tanv
v
Basic Motion
Motion of charged particle q in presence of electric and magnetic fields governed by Lorentz Force Equation with external force:
extFBvEqdt
vdmF
For static, uniform magnetic field, no electric field, and no external force, particle gyrates around magnetic field line:
,0|| dt
dv Bvm
q
dt
vd
zBB ˆ0
||
sin
cos
vv
tvv
tvv
z
cy
cx
Bqvr
mv
c
2Gyrofrequency and Gyroradius
derived from force balance. qB
mvrc
vrcc
m
qBc
Particle Drifts
Imposing external force causes particle drift across B, but not simply in the direction of the external force:
extFBvqdt
vdm
||||
extFdt
dvm
extFBvqdt
vdm
0|||||| vt
m
Ftv ext
Dm vtvtv
tvm Gyromotion (same as before)
2qB
BFv extD Drift Velocity
Force affects radius of gyromotion, resulting in drift orthogonal to both B and Fext.
Specific Particle Drifts
Gravity: 2qB
Bgmvg
Electric Field: 2B
BEvE
B-Gradient: 3
2
2qB
BBmvv
B-Curvature: 22
2||
BqR
BRmvv
C
CR
Magnetic Mirror
A charged particle traveling along a magnetic field line can be reflected by converging magnetic field.
Force Picture As Derived From Adiabatic Invariance of Magnetic Moment μ
B
mv
2
2
constant
0
022 sinsin
BB
Increasing B as field lines converge leads to increase in pitch angle α until particle reflects.
• Particles can be confined in a magnetic mirror configuration.
• Note that if a particle is traveling very parallel to the magnetic field line (small α) it can escape through the ends of the mirror rather than reflecting.
Geomagnetically Trapped Radiation
Energetic, charged particles (occasionally referred to as “radiation”) trapped in the Earth’s Magnetosphere: Gyrate around and travel along the geomagnetic field lines. Are trapped in a magnetic mirror, bouncing from North to
South and back. Experience gradient and curvature drifts to the West for
protons and to the East for electrons (drift due to gravitational force is present, but it is of significantly smaller magnitude).
Mechanism of electron precipitation by whistler waves
South Atlantic Anomaly
Earth’s dipole is not centered
South Atlantic Anomaly – weak spot along Earth’s surface
Smaller B larger drift loss cone
Particles precipitate due to larger loss cone
Loss Cones
Drift loss cone Charge dependent drift |B| lowest over South
Atlantic Anomaly (SAA) Particle can drift into
region of low |B| and precipitate
Bounce loss cone Particles with sufficiently small pitch
angles will be precipitated
Precipitation of Energetic Electrons
Particles escaping the geomagnetic mirror, colliding with the denser atmosphere of the lower ionosphere, are said to “precipitate” and can create such phenomena as the aurora borealis.
Application to VLF Research(This material is discussed more thoroughly in the tutorials on LEP.)
VLF electromagnetic waves, created by lightning, transmitter, or otherwise, can induce precipitation of energetic electrons by altering the pitch angle of their motion.
The precipitation results in an ionospheric enhancement which perturbs subionospherically propagating VLF signals beneath the disturbed region.
The perturbation on this subionospheric VLF signal can be detected in data acquired by AWESOME VLF receivers.
Example Detection of Transmitter Induced Precipitation
Periodic precipitation induced by periodic keying of NPM transmitter is detected on NLK-MI signal using superposed epoch averaging and Fourier analysis.
Texts to Reference
Fundamentals of Plasma Physics by J.A. Bittencourt Introduction to Plasma Physics and Controlled Fusion by F. F. Chen Introduction to Plasma Physics: With Space and Laboratory Applications by
D. A. Gurnett and A. Bhattacharjee
Single Particle Dynamics & Plasma Physics
Geomagnetically Trapped Radiation Introduction to Geomagnetically Trapped Radiation by Martin Walt
Transmitter-Induced Precipitation Abel, B., and R. M. Thorne (1998), Electron scattering loss in Earth’s inner
magnetosphere - 1. Dominant physical processes, J. Geophys. Res., 103, 2385-2396. Inan, U. S., M. Golkowski, M. K. Casey, R. C. Moore, W. Peter, P. Kulkarni, P. Kossey, E.
Kennedy, S. Meth, and P. Smit (2007), Subionospheric VLF observations of transmitter-induced precipitation of inner radiation belt electrons, Geophys. Res. Lett., 34, L02106, doi:10.1029/2006GL028494.