Explaining the dynamics of the ultra-relativistic third Van Allen radiation belt

Since the discovery of the Van Allen radiation belts over 50 years ago, an explanation for their complete dynamics has remained elusive. Especially challenging is understanding the recently discovered ultra-relativistic third electron radiation belt. Current theory asserts that loss in the heart of the outer belt, essential to the formation of the third belt, must be controlled by high-frequency plasma wave–particle scattering into the atmosphere, via whistler mode chorus, plasmaspheric hiss, or electromagnetic ion cyclotron waves. However, this has failed to accurately reproduce the third belt. Using a data driven, time-dependent specification of ultra-low-frequency (ULF) waves we show for the first time how the third radiation belt is established as a simple, elegant consequence of storm-time extremely fast outward ULF wave transport. High-frequency wave–particle scattering loss into the atmosphere is not needed in this case. When rapid ULF wave transport coupled to a dynamic boundary is accurately specified, the sensitive dynamics controlling the enigmatic ultra-relativistic third radiation belt are naturally explaine

Variational principles for the guiding-center Vlasov-Maxwell equations

The Lagrange, Euler, and Euler-Poincar____'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric

Variational formulations of guiding-center Vlasov-Maxwell theory

The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric