Evolution Of Pitch Angle Distributions Research Articles

Evolution of Pitch Angle Distributions of Relativistic Electrons During Geomagnetic Storms: Van Allen Probes Observations

AbstractWe present a study analyzing relativistic and ultra relativistic electron energization and the evolution of pitch angle distributions using data from the Van Allen Probes. We study the connection between energization and isotropization to determine if there is a coherence across storms and across energies. Pitch angle distributions are fit with a J0sinnθ function, and the variable “n” is characterized as the pitch angle index and tracked over time. Our results show that consistently across all storms with ultra relativistic electron energization, electron distributions are most anisotropic within around a day of Dstmin and become more isotropic in the following week. Also, each consecutively higher energy channel is associated with higher anisotropy after storm main phase. Changes in the pitch angle index are reflected in each energy channel; when 1.8 MeV electron pitch angle distributions increase (or decrease) in pitch angle index, so do the other energy channels. We show that the peak anisotropies differ between coronal mass ejection (CME)‐ and corotating interaction region (CIR)‐driven storms and measure the relaxation rate as the anisotropy falls after the storm. The isotropization rate in pitch angle index for CME‐driven storms is −0.15 ± 0.02 day−1 at 1.8 MeV, −0.30 ± 0.01 day−1 at 3.4 MeV, and −0.39 ± 0.02 day−1 at 5.2 MeV. For CIR‐driven storms, the isotropization rates are −0.10 ± 0.01 day−1 for 1.8 MeV, −0.13 ± 0.02 day−1 for 3.4 MeV, and −0.11 ± 0.02 day−1 for 5.2 MeV. This study shows that there is a global coherence across energies and that storm type may play a role in the evolution of electron pitch angle distributions.

Correction to “Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 1. Evaluation for electrostatic electron cyclotron harmonic waves,” “Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 2. Evaluation for whistler mode chorus waves,” and “Evolution of pitch angle distributions following injection from the plasma sheet”

Correction to “Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 1. Evaluation for electrostatic electron cyclotron harmonic waves,” “Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 2. Evaluation for whistler mode chorus waves,” and “Evolution of pitch angle distributions following injection from the plasma sheet”

Pitch Angle Distribution Evolution of Energetic Electrons by Whistler-Mode Chorus

We develop a two-dimensional momentum and pitch angle code to solve the typical Fokker-Planck equation which governs wave—particle interaction in space plasmas. We carry out detailed calculations of momentum and pitch angle diffusion coefficients, and temporal evolution of pitch angle distribution for a band of chorus frequency distributed over a standard Gaussian spectrum particularly in the heart of the Earth's radiation belt L = 4.5, where peaks of the electron phase space density are observed. We find that the Whistler-mode chorus can produce significant acceleration of electrons at large pitch angles, and can enhance the phase space density for energies of 0.5 ∞ 1 MeV by a factor of 10 or above after about 24h. This result can account for observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm.

The effect of the shock of 15:43 UT March 23, 1991 on 50 keV to 5 MeV ions at Ulysses

The intensities, angular distributions, and energy spectra of 50 keV to 5 MeV ions are examined in the several hour time interval when an interplanetary shock passed the Ulysses spacecraft. The increase in intensity, evolution of pitch angle distribution from upstream flow away from the shock to a post‐shock “pancake” distribution, the earlier arrival of more energetic particles, and the presence of non‐gyrotropic effects at the time of shock passage all can be understood in terms of kinematical behavior of the particles crossing the shock.

The solar proton event of April 16, 1970, 3. Evolution of pitch angle distribution as ≲1‐MeV protons propagate into the high‐latitude magnetotail

The solar proton event of April 16, 1970 was monitored by Vela satellites, of orbit r=18 RE, in the solar wind and high‐latitude magnetotail (lobe). Intensity structure at ≲1 MeV indicates a delay of 85–102 min in access of protons to near the center of the north lobe, corresponding to entry points at 340–370 RE from the earth. In three sequential periods, of 16, 181, and 124 min duration, the average intensity in the north lobe was lower, higher, and lower, respectively, than that in interplanetary space by factors which varied from 2 to 5. These reversals were a consequence of reversals in field‐aligned anisotropy in interplanetary space, the interplanetary magnetic field remaining southward. Pitch angle distributions were measured in three dimensions in interplanetary space and in the north lobe. In the lobe the distributions were essentially isotropic at r=18 RE. Comparison is made with theoretical propagation of solar particles along field lines in an open tail model, under the following conditions along a trajectory: (1) adiabatic motion all the way (Liouville theorem)—the ‘adiabatic access model’ or (2) isotropization at the magnetopause followed by adiabatic motion—the ‘nonadiabatic access model.’ Neither mode of access explains the observations adequately. A hybrid mode is proposed, in which a minimal amount of scattering occurs as particles enter the tail, followed by amplification (attenuation) of intensity as the pitch distribution is transformed to near 18 RE in the favored (unfavored) lobe. In this mode a large part of the isotropization at Vela orbit is accomplished by the Liouville transformation, since particles entering the tail beyond ≈100 RE will see an increase in magnetic field by a factor of 3 as they propagate along the tail. The amount of scatter at the magnetopause is estimated to be Δµ(rms)=0.3, where µ is cosine of pitch angle. Intensity discrepancies later in the event are interpreted as (1) a brief adjustment in the topology of the magnetotail in which the field line through Vela 6A changed its exit point to ≈530 RE, compared to ≈350 RE before and ≈420 RE after and (2) interconnection between interplanetary and magnetotail fields determined by the radial component of the interplanetary field, as distinct from the southward component during the main portion of the event (the particle access window, however, remained at the same distance from the earth).