Calculations of the integral invariant coordinates II/I and IL/I* in the magnetosphere and mapping of the regions where II/I is conserved, using a particle tracer (ptr3D v2.0), LANL*, SPENVIS, and IRBEM

摘要

The integral invariant coordinate I and Roederer's L or L* are proxiesfor the second and third adiabatic invariants, respectively, thatcharacterize charged particle motion in a magnetic field. Their usefulnesslies in the fact that they are expressed in more instructive ways than theircounterparts: I is equivalent to the path length of the particle motionbetween two mirror points, whereas L*, although dimensionless, isequivalent to the distance from the center of the Earth to the equatorialpoint of a given field line, in units of Earth radii, in the simplified caseof a dipole magnetic field. However, care should be taken when calculatingthe above invariants, as the assumption of their conservation is not valideverywhere in the Earth's magnetosphere. This is not clearly stated instate-of-the-art models that are widely used for the calculation of theseinvariants. The purpose of this work is thus to investigate where in thenear-Earth magnetosphere we can safely calculate I and L* with toolswith widespread use in the field of space physics, for various magnetosphericconditions and particle initial conditions.More particularly, in this paper we compare the values of I and L* ascalculated using LANL*, an artificial neural network developed at the LosAlamos National Laboratory, SPENVIS, a space environment online tool, IRBEM,a software library dedicated to radiation belt modeling, and ptr3D, a 3-Dparticle tracing code that was developed for this study. We then attempt toquantify the variations between the calculations of I and L* of thosemodels. The deviation between the results given by the models depends onparticle initial position, pitch angle and magnetospheric conditions. Usingthe ptr3D v2.0 particle tracer we map the areas in the Earth's magnetospherewhere I and L* can be assumed to be conserved by monitoring theconstancy of I for energetic protons propagating forwards and backwards intime. These areas are found to be centered on the noon area, and their sizealso depends on particle initial position, pitch angle and magnetosphericconditions.