In this document, the technical details of the JSNS$^2$ (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source) experiment are described. The search for sterile neutrinos is currently one of the hottest topics in neutrino physics. The JSNS$^2$ experiment aims to search for the existence of neutrino oscillations with $Delta m^2$ near 1 eV$^2$ at the J-PARC Materials and Life Science Experimental Facility (MLF). A 1 MW beam of 3 GeV protons incident on a spallation neutron target produces an intense neutrino beam from muon decay at rest. Neutrinos come predominantly from $mu^+$ decay: $mu^{+} to e^{+} + bar{ u}_{mu} + u_{e}$. The experiment will search for $bar{ u}_{mu}$ to $bar{ u}_{e}$ oscillations which are detected by the inverse beta decay interaction $bar{ u}_{e} + p to e^{+} + n$, followed by gammas from neutron capture on Gd. The detector has a fiducial volume of 17 tons and is located 24 meters away from the mercury target. JSNS$^2$ offers the ultimate direct test of the LSND anomaly. In addition to the sterile neutrino search, the physics program includes cross section measurements with neutrinos with a few 10s of MeV from muon decay at rest and with monochromatic 236 MeV neutrinos from kaon decay at rest. These cross sections are relevant for our understanding of supernova explosions and nuclear physics.
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