2n-Stream Conservative Scattering

TL;DR

This paper introduces a $2n$-stream matrix method for accurately modeling highly anisotropic, conservative scattering in clouds, extending previous techniques to handle the case where single scattering albedo equals one.

Contribution

It develops a modified $2n$-stream approach that effectively handles conservative, highly anisotropic scattering, building on and extending prior neutron transport methods.

Findings

The $2n$-stream method accurately models anisotropic conservative scattering.

Minor modifications enable the method to handle the case of single scattering albedo equal to one.

The approach improves computational efficiency and accuracy over traditional methods.

Abstract

We show how to use matrix methods of quantum mechanics to efficiently and accurately calculate axially symmetric radiation transfer in clouds, with conservative scattering of arbitrary anisotropy. Analyses of conservative scattering, where the single scattering albedo is $\tilde\omega =1$ and no energy is exchanged between the radiation and scatterers, began with work by Schwarzschild, Milne, Eddington and others on radiative transfer in stars. There the scattering is isotropic or nearly so. It has been difficult to extend traditional methods to highly anisotropic scattering, like that of sunlight in Earth's clouds. The $2n$-stream method described here is a practical way to handle highly anisotropic, conservative scattering. The basic ideas of the $2n$-stream method are an extension of Wick's seminal work on transport of thermal neutrons by isotropic scattering to scattering with arbitrary anisotropy. How to do this for finite absorption and $\tilde\omega<1$ was described in our previous paper (arXiv:2205.09713v2). But those methods fail for conservative scattering, when $\tilde \omega = 1$. Here we show that minor modifications to the fundamental $2n$-scattering theory for $\tilde\omega <1$ make it suitable for $\tilde\omega = 1$.