Cosmic Ray Flux in the Presence of a Neutral Background

The study of cosmic rays (CRs) is a very mature subject developed around the concept of radiative particle flux phi as a mono-variant function of energy E, that is phi = phi(E). This is based on the notion of the cosmos as being filled with cosmic radiation in the form of a collisionless exosphere of plasma. Neutrals, however, are likewise ubiquitous in space and planetary trapped-radiation belts. It will be shown that in the presence of a neutral background of density rho, flux phi is actually bivariant in energy E and rho, creating a surface phi(E,rho). This is an intrinsic property of charged-particle flux, that flux is not merely a function of E but is dependent upon density rho when a background of neutrals is present. The effect is produced by multiple scattering of charged particles off neutral and ionized atoms along with ionization loss where charged and neutral populations interact. For the harder portion of CR spectra, flux is mono-variant but at nonrelativistic energies (below approx, 350 MeV) it becomes sensitive to the presence of neutral backgrounds. The dependence of phi(E,rho) upon background neutrals is helpful in discussing the anomalous CR (ACR) flux made up of ionized components of the heliospheric neutral atmosphere.