Analytical reduction of pitch-angle scattering in isotropic turbulence

2010 ◽  
Vol 374 (45) ◽  
pp. 4573-4580 ◽  
Author(s):  
R.C. Tautz ◽  
I. Lerche
Keyword(s):  
Pitch Angle ◽  
Isotropic Turbulence ◽  
Angle Scattering

Cosmic-ray pitch-angle scattering in isotropic turbulence

1988 ◽  
Vol 334 ◽  
pp. 470 ◽  
Author(s):  
John W. Bieber ◽  
Charles W. Smith ◽  
William H. Matthaeus
Keyword(s):  
Pitch Angle ◽  
Isotropic Turbulence ◽  
Cosmic Ray ◽  
Angle Scattering

Nongyroresonant Pitch Angle Scattering

1999 ◽  
Vol 518 (2) ◽  
pp. 974-984 ◽  
Author(s):  
B. R. Ragot
Keyword(s):  
Pitch Angle ◽  
Angle Scattering

scholarly journals Resonant scattering of energetic electrons in the plasmasphere by monotonic whistler-mode waves artificially generated by ionospheric modification

2014 ◽  
Vol 32 (5) ◽  
pp. 507-518 ◽  
Author(s):  
S. S. Chang ◽  
B. B. Ni ◽  
J. Bortnik ◽  
C. Zhou ◽  
Z. Y. Zhao ◽  
...  
Keyword(s):  
Test Particle ◽  
Pitch Angle ◽  
Low Frequency ◽  
Resonant Scattering ◽  
High Energy ◽  
Whistler Waves ◽  
Energetic Electrons ◽  
High Energy Electrons ◽  
Angle Scattering ◽  
Vlf Waves

Abstract. Modulated high-frequency (HF) heating of the ionosphere provides a feasible means of artificially generating extremely low-frequency (ELF)/very low-frequency (VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high-energy electrons in the plasmasphere. By ray tracing the magnetospheric propagation of ELF/VLF emissions artificially generated at low-invariant latitudes, we evaluate the relativistic electron resonant energies along the ray paths and show that propagating artificial ELF/VLF waves can resonate with electrons from ~ 100 keV to ~ 10 MeV. We further implement test particle simulations to investigate the effects of resonant scattering of energetic electrons due to triggered monotonic/single-frequency ELF/VLF waves. The results indicate that within the period of a resonance timescale, changes in electron pitch angle and kinetic energy are stochastic, and the overall effect is cumulative, that is, the changes averaged over all test electrons increase monotonically with time. The localized rates of wave-induced pitch-angle scattering and momentum diffusion in the plasmasphere are analyzed in detail for artificially generated ELF/VLF whistlers with an observable in situ amplitude of ~ 10 pT. While the local momentum diffusion of relativistic electrons is small, with a rate of < 10−7 s−1, the local pitch-angle scattering can be intense near the loss cone with a rate of ~ 10−4 s−1. Our investigation further supports the feasibility of artificial triggering of ELF/VLF whistler waves for removal of high-energy electrons at lower L shells within the plasmasphere. Moreover, our test particle simulation results show quantitatively good agreement with quasi-linear diffusion coefficients, confirming the applicability of both methods to evaluate the resonant diffusion effect of artificial generated ELF/VLF whistlers.

scholarly journals Simultaneous Observations of Electromagnetic Ion Cyclotron (EMIC) Waves and Pitch Angle Scattering During a Van Allen Probes Conjunction

2020 ◽  
Vol 125 (4) ◽  
Author(s):  
K. Sigsbee ◽  
C. A. Kletzing ◽  
J. B. Faden ◽  
A. N. Jaynes ◽  
G. D. Reeves ◽  
...  
Keyword(s):  
Pitch Angle ◽  
Angle Scattering ◽  
Van Allen Probes ◽  
Ion Cyclotron ◽  
Emic Waves

scholarly journals Pitch angle scattering of an energetic magnetized particle by a circularly polarized electromagnetic wave

2021 ◽  
Author(s):  
Paul M. Bellan
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Pitch Angle ◽  
Energetic Electron ◽  
Circularly Polarized ◽  
Angle Scattering ◽  
Background Magnetic Field ◽  
Pseudo Potential

&lt;p&gt;The interaction between a circularly polarized electromagnetic wave and an energetic gyrating particle is described [1] using a relativistic pseudo-potential that is a function of the frequency mismatch,&amp;#160; a measure of the extent to which &amp;#969;-k&lt;sub&gt;z&lt;/sub&gt;v&lt;sub&gt;z&lt;/sub&gt;=&amp;#937;/&amp;#947; is not true. The description of this wave-particle interaction involves a sequence of relativistic transformations that ultimately demonstrate that the pseudo potential energy of a pseudo particle adds to a pseudo kinetic energy giving a total pseudo energy that is a constant of the motion. The pseudo kinetic energy is proportional to the square of the particle acceleration (compare to normal kinetic energy which is the square of a velocity) and the pseudo potential energy is a function of the mismatch and so effectively a function of the particle velocity parallel to the background magnetic field (compare to normal potential energy which is a function of position). Analysis of the pseudo-potential provides a means for interpreting particle motion in the wave in a manner analogous to the analysis of a normal particle bouncing in a conventional potential well.&amp;#160; The wave-particle&amp;#160; interaction is electromagnetic and so differs from and is more complicated than the well-known Landau damping of electrostatic waves.&amp;#160; The pseudo-potential profile depends on the initial mismatch, the normalized wave amplitude, and the initial angle between the wave magnetic field and the particle perpendicular velocity. For zero initial mismatch, the pseudo-potential consists of only one valley, but for finite mismatch, there can be two valleys separated by a hill. A large pitch angle scattering of the energetic electron can occur in the two-valley situation but fast scattering can also occur in a single valley. Examples relevant to magnetospheric whistler waves are discussed. Extension to the situation of a distribution of relativistic particles is presented in a companion talk [2].&lt;/p&gt;&lt;p&gt;[1] P. M. Bellan, Phys. Plasmas 20, Art. No. 042117 (2013)&lt;/p&gt;&lt;p&gt;[2] Y. D. Yoon and P. M. Bellan, JGR 125, Art. No. e2020JA027796 (2020)&lt;/p&gt;

scholarly journals The Fokker-Planck Coefficient for Pitch-Angle Scattering of Cosmic Rays

1974 ◽  
Vol 190 ◽  
pp. 417 ◽  
Author(s):  
L. A. Fisk ◽  
M. L. Goldstein ◽  
A. J. Klimas ◽  
G. Sandri
Keyword(s):  
Cosmic Rays ◽  
Pitch Angle ◽  
Angle Scattering ◽  
Fokker Planck
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