EGU General Assembly 2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

Young Dae Yoon1 and Paul Bellan2
Young Dae Yoon and Paul Bellan
  • 1Caltech, Pasadena, California USA; current address is Pohang Accelerator Laboratory, Pohang, Republic of Korea (
  • 2Caltech, Pasadena, California USA

A recent study and a companion talk [1] showed that an exact rearrangement of the relativistic particle equation of motion under a coherent circularly-polarized electromagnetic wave leads to an equation describing the motion of the “frequency mismatch” parameter ξ under a pseudo-potential ψ(ξ). When the particle undergoes a so-called “two-valley motion” in ξ-space, it experiences large changes in ξ and thus its pitch-angle because ξ is a function of the particle’s velocity parallel to the background magnetic field. This single-particle analysis is extended [2] to a distribution of relativistic particles. First, the condition for two-valley motion is derived with parameters relevant to magnetospheric contexts. Single-particle simulations verify that particles which satisfy this condition indeed undergo large pitch-angle fluctuations. Second, assuming a relativistic Maxwellian particle distribution, the fraction of particles that undergo two-valley motion is analytically derived and is numerically verified by Monte-Carlo simulations. A significant fraction (1% - 5%) of the distribution undergoes two-valley motion for typical magnetospheric parameters. For sufficiently fast interactions where a uniform background magnetic field and a constant wave frequency can be assumed, the widely-used second-order trapping theory [3] is shown to be an erroneous approximation of the present theory.


[1] P. M. Bellan, Phys. Plasmas, 20 (4), Art. No. 042117 (2013)

[2] Y. D. Yoon and P. M. Bellan, JGR Space Physics, 125 (6), Art. No. e2020JA027796 (2020)

[3] D. Nunn, Planet. and Space Sci., 22 (3), 349-378 (1974)


How to cite: Yoon, Y. D. and Bellan, P.: Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3604,, 2021.

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