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We present version X of the hammurabi package, the HEALPix-based numericsimulator for Galactic polarized emission. Improving on its earlier design, wehave fully renewed the framework with modern C++ standards and features.Multi-threading support has been built in to meet the growing computationalworkload in future research. For the first time, we present precision profilesof hammurabi line-of-sight integral kernel with multi-layer HEALPix shells. Inaddition to fundamental improvements, this report focuses on simulatingpolarized synchrotron emission with Gaussian random magnetic fields. Two fastmethods are proposed for realizing divergence-free random magnetic fieldseither on the Galactic scale where a field alignment and strength modulationare imposed, or on a local scale where more physically motivated models like aparameterized magneto-hydrodynamic (MHD) turbulence can be applied. As anexample application, we discuss the phenomenological implications of Gaussianrandom magnetic fields for high Galactic latitude synchrotron foregrounds. Inthis, we numerically find B/E polarization mode ratios lower than unity basedon Gaussian realizations of either MHD turbulent spectra or in spatiallyaligned magnetic fields.

hammurabi X: Simulating Galactic Synchrotron Emission with Random Magnetic Fields