Authors: M. E. Cuesta (Princeton University), F. Fraschetti (Harvard University; Lunar and Planetary Lab), R. Bandyopadhyay (Princeton University), G. Livadiotis (Princeton University), H. A. Farooki (Princeton University), L. Y. Khoo (Princeton University), M. M. Shen (Princeton University), J. S. Rankin (Princeton University), J. R. Szalay (Princeton University), D. J. McComas (Princeton University), D. G. Mitchell (Applied Physics Lab), E. R. Christian (NASA GSFC), J. G. Mitchell (NASA GSFC), M. E. Hill (Applied Physics Lab), C. M. S. Cohen (California Institute of Technology), R. A. Leske (California Institute of Technology), Z. Xu (California Institute of Technology), F. Pecora (University of Delaware), D. Ruffolo (Mahidol University), W. H. Matthaeus (University of Delaware), J. Giacalone (University of Arizona), N. A. Schwadron (Princeton University; University of New Hampshire), M. A. Dayeh (Southwest Research Institute; University of Texas), S. D. Bale (University of California), M. L. Stevens (Harvard University; Smithsonian Astrophysical Observatory), R. Livi (University of California)

The spatial diffusion coefficient (\kappa) provides important insight on the transport of particles as well as their source of energization. Here, we investigate the relation between \kappa upstream of an interplanetary shock and the intensity of solar energetic particles (SEPs) at the shock (j_shock). A large upstream magnetic fluctuation amplitude (dB/B) would reduce \kappa, suggesting that particles are accelerated more efficiently and trapped for longer periods at the shock. This should result in a higher j_shock. In contrast, a smaller dB/B would enhance \kappa such that the acceleration time is longer, or energetic particles are trapped over a shorter time, resulting in a lower j_shock. We examine this expected relationship between \kappa, dB/B, and j_shock for several interplanetary shocks observed by Parker Solar Probe, allowing an investigation into the radial profile of \kappa for SEPs upstream of shocks. We use the far-upstream (quiescent solar wind) \kappa as a fit parameter of the upstream intensity profile of energetic protons derived from the 1D steady-state transport equation assuming pitch-angle isotropy in the plasma frame (Fraschetti 2021). Also, the field-aligned spatial diffusion coefficient derived from quasi-linear theory (QLT) is examined. For either method, we find that \kappa is inversely proportional to j_shock, which is consistent with our understanding; however, \kappa derived from QLT is ~2 orders of magnitude larger than the \kappa derived from the intensity profiles. Furthermore, we find groupings of shocks classified by their j_shock versus \kappa, which warrants additional investigation into whether shocks within a group share similar shock parameters, such as shock speed, strength, and orientation. These results improve our understanding of energetic particle transport from interplanetary shocks through the upstream medium and improve the modeling of their acceleration by shocks.