1. Dressed Spin Simulations Steven Clayton University of Illinois nEDM Collaboration Meeting at Arizona State University, February 8, 2008 Contents 1.Goals 2.Strategy 3.Test case: diffusion 4.Test case: uniform field gradient 5.UIUC table top experiment

2. 2 Goals 1.quantitatively understand T 2 of dressed 3 He spins –in UIUC room temperature setup compare simulation to experiment –in nEDM cell 2.eventually, for the nEDM plumbing, simulate depolarization of 3 He before it reaches the measurement cell

3. 3 Simulation strategy use Geant4 particle physics code –sophisticated tracking routines –convenient to add physics processes simulate one particle at a time –other particles can only be represented by some mean field form an ensemble from many 1-particle simulations –average spin vectors to get magnetization

4. 4 Diffusion model isotropic scattering from infinite-mass scattering centers. particle velocity v 3 = sqrt(3 k B T/m) mass m = 2.4 m 3 (in LHe4), or m = m 3 (gas) mean free path = 3D/v 3, D = 1.6/T 7 cm 2 /s (in LHe4), or D = 1370.2/P cm 2 /s (T = 300 K, P in torr)

5. 5 test: diffusion in large box (L >> ) simulation results agree with diffusion equation solution Average displacement from starting point

6. 6 Boundary interactions diffuse reflection could be switched to specular or partially diffuse reflection Other wall interactions could be added –sticking –depolarization –transmission (e.g. at a LHe-vacuum boundary)

7. 7 diffusion out of a small box example event in 20x20x20 cm cell The particle is killed when it reaches the top surface (transmission probability  lv is set to 1). time to reach top surface (The particle mass was m 3, not 2.4 m 3 in this study, so v 3 was too high.)

8. 8 Spin precession Bloch equation is solved over the step length. “Quality-controlled” Runge-Kutta (implementation of Numerical Recipes routine): maximum error of each spin component is constrained

9. 9 Test Case: Uniform Field Gradient H z = H 0 + (dH/dx) x, H x = H y = 0 x z Theory: McGregor (1990), PRA 41, 2631 L 2a

10. 10 Results: Uniform Field Gradient McGregor (1990) formula gives T 2 = 0.42 s. T = 300 K, P = 1 torr, N = 1000 particles (H 0 = 0.53 gauss, dH/dx = 20 nT/cm)

11. 11 Results: Uniform Field Gradient (N = 100 particles for most of these plots) fits to exp(-t/T 2 )

12. 12 Test Case: Oscillating, Uniform Field Gradient H z (t) = H 0 + cos(2  f 1 t) (dH/dx) x, H x = H y = 0 x z Theory: Bohler and McGregor (1994), PRA 49, 2755 L 2a

13. 13 Results: Oscillating, Uniform Field Gradient (f 1 = 60 Hz, T = 300 K, N = 200 particles)

14. 14 UIUC Dressed Spin Experiment holding field coils (B 0 ) earth field canceling coils (B v ) dressing coils (B 1 ) 3 He cell: P = 1 torr, T = 300 K z x y The fields from ideal Helmholtz coils are used in the simulation (actually, for each coil pair, 4th order Taylor expansion in cylindrical coordinates).

15. 15 Experimental data: T 2 vs Dressing Field (plot from Pinghan Chu’s talk)

16. 16 Simulation: T 2 vs Dressing Field Simulation gives much longer T 2 than the experiment. Shifting (simulation) cell off center by 2 cm: T 2 (X=0) = 9 s.

17. 17 Simulation of 3 He in nEDM Cell H0H0 x y long times can be simulated because collision time is much longer requires field H(t,x,y,z) at all points in the cell N  1000 T2 = 4202 s Here, the optimized, 3D field map was (poorly) parameterized by 4th order polynomials in x, y, z. Long T 2 can be simulated. Dressing effect can be simulated.

18. 18 3 He transport into nEDM cell (Jan’s model, view courtesy S. Williamson) Eventually, we would like to simulate 3 He starting from injection until arrival in the measurement cell. injection measurement cell Needed to do the simulation: B-field model of heat flush?

19. 19 Status of these simulations Several studies are posted on the TWiki site: https://nedm.bu.edu/twiki/bin/view/NEDM/DressedspinSimulation https://nedm.bu.edu/twiki/bin/view/NEDM/DressedspinSimulation UIUC dressed spin setup –still need to understand observed short T 2 Dressed spin in nEDM cell –need dressing field map Depolarization during transport into nEDM cell –need field map along plumbing –need to figure out how to model heat flush process

20. 20 Heat flush in simple geometry 20x20x20 cm cell connected to 3-m long, 5-cm diameter pipe uniform normal fluid flow in pipe particles start in cell and exit system at end of the pipe cell normal fluid velocity v n exit

21. 21 scattering off of moving normal fluid implemented as isotropic in the reference frame of the normal fluid –a random direction is chosen for v 3, then v n is added. –after the vector addition, the length may be reset to the mean thermal velocity.

22. 22 cell emptying time from Golub, “flush it away”