Nonadiabatic Particle Motion Research Articles

Particle acceleration in the dynamic magnetotail

The acceleration of charged particles to suprathermal energies is investigated in the context of magnetospheric substorms. Ion and electron test particle orbits are studied in dynamically evolving fields obtained from a three-dimensional resistive magnetohydrodynamic (MHD) simulation of reconnection in the near magnetotail. The simulation leads to plasmoid formation and ejection into the distant tail and an earthward collapse of the field in the inner tail. Energization of particles takes place predominantly in the inner tail region earthward of the neutral line, rather than in the vicinity of the neutral line. The test particle studies reproduce major observed characteristics of energetic particle flux increases (“injections”) in the inner magnetotail; a fast rise, a limited energy range of the flux increases, and spatially varying delays between the onsets of ion and electron injections. Acceleration mechanisms include a “quasipotential” acceleration, resulting from nonadiabatic particle motion in the direction of the cross-tail electric field, as well as betatron and Fermi-type acceleration. The major source region for accelerated ions (electrons) in the hundreds of keV range is the central plasma sheet at the dawn (dusk) flank, outside the reconnection site. Since this source plasma is already hot and dense, a moderate energization by a factor of approximately 2 is sufficient to explain the observed increases in the energetic particle fluxes. Differences between ions and electrons at energies of a few tens of keV are found to be associated with differences in the bounce periods, which enables ions to circumvent the acceleration region, so that only electron fluxes in that energy range become enhanced.

Onset of nonadiabatic particle motion in the near‐Earth magnetotail

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.

A model of ring current based on the Dessler-Parker-Sckopke theorem

The model of ring current is founded on the Dessler-Parker-Sckopke theorem and data of the AMPTE (Active Magnetospheric Particle Tracer Explorers) and ‘Intercosmos-17’ satellites. The model of ring current connects the altitude of the maximum of ring current and D st-variation during the main phase of a magnetic storm. It predicts the radial distribution of the ring current energetic density, and the decay of the ring current energy in the recovery phase. The model can be used for the analysis of the adiabatic and nonadiabatic particle motion and the injection depth of energetic particles in the main phase.

An assessment of a magnetospheric model by tracing the energetic particle trapping boundary

We use the two most recent empirical magnetosphere models of Tsyganenko [1987; 1989] to find the energy dependent boundary of isotropic precipitation due to the nonadiabatic particle motion in the nightside current sheet. Model predictions are compared with the earlier published satellite observations of this boundary at low altitudes. A dramatic difference has been found between the predicted position of the isotropy boundary based on T87 and T89 model. The most recent magnetosphere model of Tsyganenko featuring the warped current sheet with thickness dependent both on XGSM and YGSM predicts that the isotropy boundary is situated at much lower latitudes than inferred from the previous models. This is in agreement with observations. However, even this model with very stretched tail magnetic field lines has difficulties in explaining the frequently observed very steep profile of critical rigidity vs L.

Stationary distribution function for non-adiabatic particle motion in a one dimensional current sheet

The problem of pitch angle scattering in field configurations similar to those found in the geomagnetic tail has been studied previously by Tsyganenko (1982). Tsyganenko used a scattering matrix to map pitch angle distributions through the current sheet. By using numerical solutions of the resulting integral equations he showed for weakly non-adiabatic particles the Stationary Distribution Function (SDF) was isotropic. Using his procedure the SDF was found to develop anisotropies with increasing non-adiabaticity. The work presented here shows analytically that for any degree of scattering the SDF must be isotropic for a general planar field reversal. Computations of particle trajectories have been used to verify some aspects of the analytic work.

Solar protons on closed magnetospheric field lines after an interplanetary flux decrease

Particle measurements from the low altitude polar-orbiting satellite GRS-A/Azur and from Explorer 41 in the magnetosheath during a time period after the sudden commencement at 14:30 UT on 8 March 1970, have been used in order to study the access mode of solar particles into the closed field line region of the magnetosphere. A particle decrease in the magnetosheath and over the central polar cap but not in the stable trapping region indicates that solar particles are temporarily trapped and can complete several drifts around the Earth. A single loss cone distribution ∼2° inside of the stable trapping region cannot be explained by strong pitch angle scattering but is probably due to non-adiabatic particle motion.

Nonadiabatic particle motion in the magnetosphere

Using calculations in a model geomagnetic fleld, the influence of nonadiabatic particle motion on the polar cap structure of polar protons is investigated. Breakdown of the first invariant, due to excessive field curvature and gradients near the last closed field line, results in an effect that cannot be differentiated from strong pitch angle scattering using low-altitude detectors, although no time variations of the magnetic field are considered. The results obtalned thus form a basis to which wave-particle interactions and other scattenng effects must be added. In a companion paper, these results are applied to observations of solar protons over the polar caps, and it is shown that the quiettime behavior of these particles is indeed approximately given by the constraints due to the spatial variations of the geomagnetic field.

The entry of solar protons over the polar caps

Observations of solar protons at energies from 1 MeV to 360 MeV are examined in relation to the information that these particles give about the magnetosphere, magnetotail and magnetopause. Trajectory integrations in a realistic model of the geomagnetic field out to 25 R E and a tail field model fitted to observations from 15 R E to 80 R E are used to obtain a better understanding of the particle motion. The mean free path of protons in the tail is found to be 700 R E and 200 R E for 100 MeV and 1 MeV protons respectively, which indicates that trajectory calculations in a static field model are valid. Structure over the polar caps at low altitudes due to interplanetary anisotropies was observed for protons > 30 MeV during the solar flares of November 18th 1968 and February 25th 1969. Apart from an easily explained direct impact zone structure, fluxes corresponding to peak anisotropic interplanetary intensity were observed to come from deep in the magnetotail. A magnetopause model of the generalised rotational discontinuity type, with a diverging tail field, is proposed and it is shown that this allows particle access into the tail with conservation of the distribution function. Particles from the direction of maximum flux (usually the Parker spiral direction) reverse their direction of motion during multiple magnetopause crossings. They eventually stay in the tail with small pitch angles and are thus observable at low altitudes. Observations show that 1 MeV protons become isotropic at the magnetopause. It is suggested that this is due to irregularities in the magnetopause, possibly caused by Kelvin Helmholtz instabilities, which are of comparable dimensions to the Larmor radius of these particles. Intensity differences over the polar cap of ▪40 per cent are expected due to the overall radial intensity gradient, and rapid local gradients can produce even greater differences. It is proposed here that sharp local intensity changes bounded by tangentional discontinuities, which convect past the Earth with the solar wind account for most of the observed polar cap intensity variations for 1 MeV protons. Anisotropies in flux produce gradients across the tail which can also be observed over the polar caps. Particle trajectories crossing the neutral sheet are analysed, and it is shown that dispersion of trajectories produces broadening of sharp interplanetary intensity changes when observed in the tail, not by a diffusion process, but through different trajectory lengths. Results of trajectory integrations at three energies are presented. These can be used to analyse polar cap structure in future work. Results of nonadiabatic particle motion in the pseudo-trapping region are shown. This motion produces effects similar to strong pitch angle scattering although it takes place in a static field.