A thermal model for cooling the nEDM $^{3}$He services

The neutron electric dipole moment (nEDM) experiment proposed for the Spallation Neutron Source is a precision test of time reversal symmetry, probing the same physics believed to be responsible for the matter-antimatter imbalance in the universe. In the experiment, polarized neutrons and polarized 3He atoms suspended in a bath of superfluid $^{4}$He at 0.35 K precess in a weak magnetic field. When a strong electric field is applied parallel or antiparallel to the B-field, a change in the neutron precession rate signifies a nonzero nEDM. The polarized $^{3}$He, which acts as a co-magnetometer, must be replenished every 1000--2000 seconds. Electrical heaters produce heat flows to sweep $^{3}$He in and out of the measurement cells. The heat is transferred to a dilution refrigerator through plastic or sintered metal heat exchangers. We have modeled the heat flows needed for $^{3}$He transport, to determine the heat load to the refrigerator and to guide the design and placement of the heat exchangers.