Calculations of the integral invariant coordinates <i>I</i> and <i>L</i>^* in the magnetosphere and mapping of the regions where <i>I</i> is conserved

Abstract

Abstract. The integral invariant coordinate I and Roederer's L or L* are proxies for the second and third adiabatic invariants respectively, that characterize charged particle motion in a magnetic field. Their usefulness lies in the fact that they are expressed in more instructive ways than their counterparts: I is equivalent to the path length of the particle motion between two mirror points, whereas L*, although dimensionless, is roughly equivalent to the distance from the center of the Earth to the equatorial point of a given field line, in units of Earth radii, in the simplified case of a dipole magnetic field. However, care should be taken when calculating the above invariants, as the assumption of their adiabaticity is not valid everywhere in the Earth's magnetosphere. This is not clearly stated in state-of-the-art models that are widely used for the calculation of these invariants. In this paper, we compare the values of I and L* as calculated using LANLstar, an artificial neural network developed at the Los Alamos National Laboratory, SPENVIS, a space environment related online tool, IRBEM, a source code library dedicated to radiation belt modelling, and a 3-D particle tracing code that was developed for this purpose. We then attempt to quantify the variations between the calculations of I and L* of those models. The deviation between the results given by the models depends on particle starting position geocentric distance, pitch angle and magnetospheric conditions. Using the 3-D tracer we attempt to map the areas in the Earth's magnetosphere where I and L* can be assumed to be conserved by monitoring the constancy of I for energetic proton propagating forwards and backwards in time. These areas are found to be centered on the noon area and their size also depends on particle starting position geocentric distance, pitch angle and magnetospheric conditions.