Reduction of magnetic perturbation for SR-POEM

SR-POEM is a Galilean test of the weak equivalence principle that aims to measure the fractional acceleration difference η with a mission uncertainty $\sigma \left(\eta \right)=1\times {10}^{-17}$ for a pair of test substances. It is to be conducted during the low-drag free fall portion of a sounding rocket flight. The interaction of the magnetic field gradient with tiny remanent magnetic moments of the test masses will produce a spurious acceleration that is not sufficiently reduced by a single Mu-metal shield. In this paper, we study configurations with two and three shields. Approximate analytic formulae are used to study the shielding factor as a function of geometry. We use finite element analysis (FEA) to determine the magnetic field and gradient for certain cases that satisfy the mission requirements. FEA results are compared with analytic expressions wherever appropriate. Several configurations reduce both axial and transverse magnetic field within the shielding volume by at least the required factor of $4\times {10}^5$. (paper)