Synchrotron and inverse Compton spectra of cosmic ray electrons during their transport from 1AU to the Sun

Fermi-LAT routinely observes gamma-rays from non flaring phases, or the quiet Sun (QS), produced by cosmic ray (CR) protons (via pion production at the photosphere), and cosmic ray electrons (CRes) via inverse Compton (IC) scattering of solar optical photons. This problem has received considerable attention. CRes can also produce synchrotron radiation near the Sun in the X-ray to sub-millimeter range, which has not received much attention. RHESSI has provided some upper limits on the SQ X-ray emission that can shed line on this subject. Fluxes and spectra of CRes are observed around 1 AU by several near Earth instruments, but calculation of QS radiation requires flux-spectrum from the Earth to the Sun. The common practice to this end is to use some phenomenological modulation procedure. This procedure may be useful for evaluation of the CRs variation in the outer (>1 AU) heliosphere, but the transport from one AU to the Sun requires a kinetic approach, including effects of large scale magnetic field, turbulence and more importantly for CRes, the energy loss rate due to synchrotron and IC processes. In a recent paper (arXiv22212.00929) we presented a preliminary treatment of the CRe transport, including the variations of magnetic field and plasma density, and energy density and spectrum of turbulence measured by Parker Solar Probe (PSP) from 1 AU to ~0.1 AU. In arXiv:2212.01364 we describe synchrotron spectra ignoring the transport effects. In this talk I will review the main features of the transport and procedures to calculate the synchrotron and IC spectra using full transport effects, in particular energy losses, which when used in conjunction with gamma-ray and X-ray observations can constrain the transport process.