Onset of nonadiabatic particle motion in the near‐Earth magnetotail

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The onset of nonadiabatic proton motion is studied using direct integration of the Lorentz force equation of motion in the T89c magnetic field model with no electric field. Irreversible changes in the magnetic moment μ occur on traversals of the equator and give the gyrophase dependence predicted by Birmingham [1984]. Birmingham's expression δB and the semiemipirical centrifugal impulse model of Delcourt et al. [1996] δCIM2 nave linear regression coefficients with Δμ/μ of 0.99 and 0.95, respectively, for Δμ/μ ≤ 1. By contrast, ε = 1/κ2, where κ is the kappa parameter, has a linear regression coefficient with Δμ/μ of only 0.5. To reliably estimate the onset of nonadiabatic behavior, one must therefore use δB or δCIM2 rather than κ. Using isocontours of constant δB we map the regions of nonadiabatic ion motion. For a given energy the transition to nonadiabatic motion occurs over a radial distance of ∼2 RE on the nightside and is closest to the Earth at midnight. At midnight the nonadiabatic regime for protons extends inward to ∼11 RE (∼7.5 RE) for 1 keV and to ∼6 RE (∼4.5 RE) for 1 MeV with the Kp = 0 (Kp = 6) model. For O+ the nonadiabatic regime is 1.5 to 2 RE closer to the Earth than for protons. Drift trajectory calculations and analytical estimates show that particles drifting through regions with δB > 0.01 suffer net Δμ ∼ μ. The net Δμ is extremely sensitive to initial gyrophase and it is shown that for δB < 0.01 differences in gyrophase diverge exponentially with repeated equatorial crossings. Because the equatorial gyrophase determines the μ scattering, this implies that the μ scattering is chaotic so that no gyrophase‐averaged invariant exists for the nonadiabatic drift motion. Despite this, the average nonadiabatic drift paths are fairly well defined. The resulting hybrid drift consists of dayside adiabatic and nightside nonadiabatic drift. A single nonadiabatic nightside drift path is associated with a family of adiabatic dayside drift paths. If some of the adiabatic drift paths are open to the magnetopause, all of the particles on the family of hybrid drift trajectories will be subject to loss on a timescale comparable to the drift period. Because the nonadiabatic behavior is due solely to field line curvature, the same behavior will be present with a nonzero convection electric field with the important difference that the lower‐energy particles will be on open convection drift paths. The hybrid drift path‐induced loss effects are therefore most important for higher‐energy particles, > 50 keV, whose adiabatic drift paths are closed in the presence of a convection electric field. The implications of nonadiabatic effects for ring current modeling based on Liouville's theorem apply equally well in the zero and finite electric field cases.