The adiabatic invariants (M, J, Φ) and the related invariants (M, K, L∗)
have been established as effective coordinate systems for describing
radiation belt dynamics at a theoretical level, and through numerical
techniques, can be paired with in-situ observations to order phase-space
density. To date, methods for numerical techniques to calculate
adiabatic invariants have focused on empirical models such the
Tsyganenko models TS05, T96, and T89. In this work, we develop methods
based on numerical integration and variable step size iteration for the
calculation of adiabatic invariants, applying the method to the
Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) simulation
code, with optional coupling to the Rice Convection Model (RCM). By
opening the door to adiabatic invariant modeling with MHD magnetic
fields, the opportunity for exploratory modeling work of radiation belt
dynamics is enabled. Calculations performed using LFM are
cross-referenced with the same code applied to the T96 and TS05
Tsyganenko models evaluated on the LFM grid. Important aspects of the
adiabatic invariant calculation are reviewed and discussed, including
(a) sensitivity to magnetic field model used, (b) differences in the
problem between quiet and disturbed geomagnetic states, and (c) the
selection of key parameters, such as the magnetic local time step size
for drift shell determination. The rigorous development and
documentation of this algorithm additionally acts as preliminary step
for future thorough reassessment of in-situ phase-space density results
using alternative magnetic field models.