Drop-in replacement for cosine function for describing plasma production at the height of max plasma production based on the Chapman function (which assumes the earth is round, not flat).

The advantage of this description is that the conductance gradient at the terminator is more realistic. This is important since conductance gradients appear in the equations that relate electric and magnetic fields. In addition, solar EUV conductances above 90° sza are not simply zero (or negative, or imaginary).

A mathematical description of this function is given in Section 2.4 ("Solar EUV conductances") of Laundal et al (2024). It is the function q'(Χ) described by their Equation 26. It is derived from their Equation 24, which is transcendental. In the limit R_E -> infinity, q'(Χ) -> cos(Χ).

NOTE: This code is based on table lookup, and does not calculate the Chapman function.

Author: S. M. Hatch (2024)

Reference
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Laundal, K. M., Reistad, J. P., Hatch, S. M., Madelaire, M., Walker, S., Hovland, A. Ø., et al. (2022). Local mapping of polar ionospheric electrodynamics. Journal of Geophysical Research: Space Physics, 127, e2022JA030356. https://doi.org/10.1029/2022JA030356
