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.