Resolution of a Few Problems in the Application of Quasilinear Theory to Calculating Diffusion Coefficients in Heliophysics

• Published in: Journal of geophysical research. Space physics 2023-10, Vol.128 (10), p.n/a
• Main Author: Cunningham, Gregory S.
• Format: Article
• Language: English
• Subjects: Aerospace environments; ASTRONOMY AND ASTROPHYSICS; Coefficients; Computation; Coordinate systems; Coordinates; Diffusion; Diffusion coefficient; diffusion coefficients; Electric power distribution; Electromagnetic radiation; Electrons; Gyrofrequency; Heliospheric and Magnetospheric Physics; Mathematical models; pitch‐angle diffusion coefficients; Plasma frequencies; quasilinear theory; radiation belt; Relativistic effects; Transformations (mathematics); Wave power; Wave propagation; wave‐particle interactions
• ISSN: 2169-9380; 2169-9402
• DOI: 10.1029/2023JA031703

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence. Plain Language Summary Electrons can become trapped in the near‐Earth space environment and stay trapped for days to years, damaging sensitive electronics on space assets. The flux of relativistic electrons varies over time due to source and loss processes, some of which are due to interactions with electromagnetic waves. When the wave amplitudes are small, the effect of the waves on electrons can be modeled as a diffusion equation, with the diffusion coefficients proportional to the wave power. The theory currently used to compute diffusion coefficients was developed in the 1960s using a coordinate system based on all three components of the wave propagation direction. The theory was adapted to a coordinate system that uses the wave frequency and wave normal angle, and has been used for 50 years in a variety of heliophysics models. It is shown for the first time here that the transformati