1. Neutron EDM Monte Carlo Simulation Uniform E+B fields Riccardo Schmid B. Plaster, B. Filippone Chicago June 6, 2007 EDM Collaboration Meeting

2. EDM Measurement Cell 50cm 7.6cm 10.2cm x z y B 0 = 10mGauss E 0 = 50kV/cm Neutrons are confined to moving inside a rectangular box and reflecting on its boundaries. An E field is applied parallel to the magnetic field. The E and B fields in these simulations are uniform in space. Simulation coded such that wall collisions can be diffuse or specular

3. Depolarization (T1) A moving neutron experiences an apparent magnetic field of the form: Effective B field changes as velocity changes due to wall bounces Spin relaxation due to bouncing: Neutron spin starts out parallel to B field ( ) and precesses about the effective B field. After some time spin depolarization occurs and Interested in the mean depolarization as a function of time

4. T 1 from effect for diffusive wall collisions [following Gamblin & Carver, Phys. Rev. A 138, 946 (1965)]  SI!! After each collision spin is “kicked” away from B Total by an angle

5. Between collisions the spin also precesses about Thus deviation of the spin following a collision is After n collisions (assumed random) the spin has “wandered” by And T 1 is the time to achieve See Gamblin and Carver

6. Thus Evaluating the averages: Leading to Where is the average time between collisions and 100% diffusive reflections

7. t (s) N.B.: (this fig.) v = 2.5 m/s B0 = 10mGauss E0 = 300kV/cm (Exponential behavior more evident) Fit to: Depolarization with time of parallel component of spin. The parameter T1 is calculated from the fit. run129 T1 = (5.4243 ±.0006)x10^4 s Estimated T1 = 3.83x10^4s

8. T1 Velocity Dependence B0 = 10mGauss E0 = 50kV/cm

9. T1 E field Dependence v = 2.5 m/s B0 = 10mGauss

10. T1 B field Dependence v = 2.5 m/s E0 = 50kV/cm T1 depends on the square of the B field and a constant term that originates from the term:

11. Conclusion and Future Two independent Monte Carlo Simulations agree on the depolarization times. Different methods used: Brad Plaster’s numerical (Runge-Kutta) approach Riccardo Schmid’s analytic solution approach ~30% agreement with Brad Filippone’s kinetic theory estimate of the depolarization time. Simulation of E and B field inhomogeneities and the effect on depolarization times. Geometric phase simulations for EDM coils