Propagation of Ultra-high-energy Protons in Cosmic Magnetic Fields

We simulate the arrival distribution of ultra-high-energy (UHE) protons by following their propagation processes in several strengths of a structured extragalactic magnetic field (EGMF). Comparing our result to observational one by Akeno Giant Air Shower Array, we constrain the number density of UHE cosmic ray sources with the small-scale anisotropy. As a result, the source number density is $\sim {10}^{-5}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-3}$ with uncertainty of about an order of magnitude due to the small number of observed events. This hardly depends on our structured EGMF strength. We also investigate future prospects for this approarch. The near future observations, such as Pierre Auger Observatory, can distinguish ${10}^{-6}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-3}$ accurately from the more source densities. Number of events to discriminate between ${10}^{-4}$ and ${10}^{-5}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-3}$ is dependent on the EGMF strength.