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Pitch-Angle Diffusion of Ions and Electrons (PADIE)

Recent research has demonstrated that electro-magnetic waves present in space can have a dramatic effect on the charged particles in the radiation belts. Under certain conditions the particles can resonate with the waves, causing the particles to gain or lose energy and altering the path on which the particles travel through space. PADIE can calculate the effect that a particular class of waves will have on the behaviour of charged particles.

PADIE [Glauert & Horne, JGR, 2005] calculates relativistic quasi-linear pitch-angle and energy diffusion coefficients for resonant wave-particle interactions in a magnetised plasma. Since PADIE solves the full electro-magnetic dispersion relation for a cold plasma, solutions to be found for any cold plasma wave-mode and any ratio of the plasma-frequency to the gyro-frequency (fpe/fce). PADIE has been used successfully at the Earth, Jupiter and Saturn. It can also be applied to the Sun and solar corona and to laboratory and fusion plasmas.

MLT averaged diffusion coefficients

The BAS wave database contains maps of the wave power and the plasma frequency with L-shell, magnetic local time (MLT) and different levels of magnetic activity for several different wave modes. These maps can be used to average the diffusion coefficients over MLT for each L-shell. The MLT averaged diffusion coefficients are then incorporated into the BAS Global Dynamic Radiation Belt Model.

The PADIE model has been developed at the British Antarctic Survey in Cambridge, UK by Dr Sarah Glauert and Professor Richard Horne.

Summary of features for PADIE

Type of diffusion coefficient Local or bounce-averaged Dαα, DαE and DEE
If bounce-averaged the waves can be present along some or all of the field line
Plasma composition Electron/Proton, heavy ions included if required
If heavy ions are included the plasma composition is specified
Resonant particle Electron or ion
Wave-modes EMIC, Whistler, Z-mode, LO mode or RX mode
Frequency distribution of the wave Gaussian
– specify peak value, width of distribution and cut-off frequencies
Wave-normal angle distribution of the wave Gaussian in tan(wave-normal angle)
– specify peak value, width of distribution and cut-offs
Magnetic field model Usually dipole but other models can be used
Plasma density model Usually constant but other models can be used
Resonances included Any – specified as a range