Radiation belt particle dynamics Prepared by Kevin Graf Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network
Basic Motion Motion of charged particle q in presence of electric and magnetic fields governed by Lorentz Force Equation with external force: dv F m q( E + v B ) + Fext dt For static, uniform magnetic field, no electric field, and no external force, particle gyrates around magnetic field line: v x v cos( ωct + ψ ) dv dv q B B zˆ 0 0, ( v B ) v y v sin( ωct + ψ ) dt dt m v v z Note the pitch angle of the motion. 1 v α tan v Gyrofrequency and Gyroradius derived from force balance. mv r c qv B r c mv qb ω c r c v ω c qb m
Particle Drifts Imposing external force causes particle drift across B, but not simply in the direction of the external force: dv m qv B + dt F ext v m v D ( t) dv m dt dv m dt F ext qv B + Fext Gyromotion (same as before) Fext B qb Drift Velocity v F m ext () t t + () 0 v ( t) vm ( t) v D v + Force affects radius of gyromotion, resulting in drift orthogonal to both B and F ext.
Specific Particle Drifts mg B Gravity: v g qb E B Electric Field: v E B B-Gradient: v mv ( B B) qb 3 B-Curvature: v R mv ( R B ) qr C C B
Magnetic Mirror A charged particle traveling along a magnetic field line can be reflected by converging magnetic field. Force Picture 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. μ As Derived From Adiabatic Invariance of Magnetic Moment μ mv B constant ( ) sin ( α ) sin α B Increasing B as field lines converge leads to increase in pitch angle α until particle reflects. B 0 0
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
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 South Atlantic Anomaly
Loss Cones Bounce loss cone Particles with sufficiently small pitch angles will be precipitated Drift loss cone Charge dependent drift B lowest over South Atlantic Anomaly (SAA) Particle can drift into region of low B and precipitate
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 Single Particle Dynamics & Plasma Physics 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 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, 385-396. Inan, U. S., M. Golkowski, M. K. Casey, R. C. Moore, W. Peter, P. Kulkarni, P. Kossey, E. Kennedy, S. Meth, and P. Smit (007), Subionospheric VLF observations of transmitter-induced precipitation of inner radiation belt electrons, Geophys. Res. Lett., 34, L0106, doi:10.109/006gl08494.