Pitch angle distribution of magnetospheric trapped particles: A test-particle simulation

Abstract

• PAD of magnetospheric trapped particles is studied using test-particle simulations. • When adiabatic invariants are conserved, particles follow butterfly-type PAD. • All three adiabatic invariant violate when gyro-radius of trapped particles is large. • Particles follow Gaussian type PAD when adiabatic invariants are not conserved. • Theoretically estimated bounce/drift period is invalid as adiabatic invariant violate. This article aims to understand the pitch angle distributions (PADs) of the charged particles in the Earth’s inner magnetosphere using test-particle simulations. The emphasis is on characterizing the variation in pitch angle of the charged particles trapped along the Earth’s magnetic field lines. These charged particles undergo gyration, bounce, and azimuthal drift motions in the Earth’s inner magnetosphere. They are trapped until their pitch angle falls into the loss-cone to get lost into the upper atmosphere. We have developed a three-dimensional test-particle simulation model in which the relativistic equation of motion is solved numerically to track these trapped particle’s trajectories. We have examined the pitch angle distributions of the electron, proton, and oxygen for the cases where adiabatic invariants are conserved and non-conserved. For this purpose, we have considered the particle’s trajectory in the latitudinal range of [ - 40 ° , 40 ° ] for one complete drift around the Earth. We found that when adiabatic invariants are conserved, the particles possess butterfly-type pitch angle distributions. Whereas, when adiabatic invariants are not conserved, the particle’s pitch angle distribution bunches toward the 90°-peaked distribution. The situation of non-conservation of adiabatic invariants demonstrated in the present simulation is arising due to larger gyro-radius (few Earth radii) over which the ambient magnetic field is not constant. We have noticed that in the static dipolar magnetic field, all three, 1st, 2nd, and partly 3rd adiabatic invariants are non-conserved when gyro-radius is larger. The information on the change in the pitch angle distribution pattern from butterfly-type to 90°-peak distribution will be useful to understand the pitch angle distributions observed by the recent spacecraft in the Earth’s radiation belts.