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 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 conservation 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. The purpose of this work is thus to investigate where in the near-Earth magnetosphere we can safely calculate I and L* with tools with widespread use in the field of space physics, for various magnetospheric conditions and particle initial conditions. More particularly, in this paper we compare the values of I and L* as calculated using LANL*, an artificial neural network developed at the Los Alamos National Laboratory, SPENVIS, a space environment online tool, IRBEM, a software library dedicated to radiation belt modeling, and ptr3D, a 3-D particle tracing code that was developed for this study. 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 initial position, pitch angle and magnetospheric conditions. Using the ptr3D v2.0 particle tracer we 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 protons propagating forwards and backwards in time. These areas are found to be centered on the noon area, and their size also depends on particle initial position, pitch angle and magnetospheric conditions.
Highlights
The motion of charged particles in the geomagnetic field is complicated, even if one approximates that field with only its dipole component
Using the ptr3D v2.0 particle tracer, LANL*, IRBEM-lib and Space Environment Information System (SPENVIS), we quantified the variations in the calculations of I and L∗ between these models, for various particle initial starting positions in geocentric distances, for various initial pitch angles, for both quiet and disturbed magnetospheric conditions and for particles initiating their motion both in the dayside and nightside
The results for the calculations of I in the dayside show that the models used are in good agreement for all geocentric distances of the particle starting positions, all pitch angles, and both for quiet and disturbed magnetospheric conditions
Summary
The motion of charged particles in the geomagnetic field is complicated, even if one approximates that field with only its dipole component. It is helpful to break down the total motion of the particle into three individual components: gyration around a guiding magnetic field line, bounce along the magnetic field line between magnetic mirror points, and gradient and curvature drift across the magnetic field line in an azimuthal direction around the Earth. Because these components evolve over very different time scales, they are nearly independent of each other and can be summed linearly to obtain the total motion (Prölss, 2004). The second invariant, J , is associated with the bouncing motion along the magnetic field between mirror points and implies that the particle will move in such a way as to preserve the total. Where λe(φ) is the dipole latitude of the intersection C at a given longitude φ (Roederer, 1970)
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