Dressed Spin SimulationsSteven Clayton

University of Illinois

nEDM Collaboration Meeting at Arizona State University, February 8, 2008

Contents1. Goals2. Strategy3. Test case: diffusion4. Test case: uniform field gradient5. UIUC table top experiment

2

Goals1. quantitatively understand T2 of dressed

3He spins– in UIUC room temperature setup

• compare simulation to experiment

– in nEDM cell

2. eventually, for the nEDM plumbing, simulate depolarization of 3He before it reaches the measurement cell

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

Diffusion model

• isotropic scattering from infinite-mass scattering centers.

• particle velocity

v3 = sqrt(3 kBT/m)• mass m = 2.4 m3 (in LHe4),

or m = m3 (gas)• mean free path = 3D/v3,• D = 1.6/T7 cm2/s (in LHe4), or D = 1370.2/P cm2/s (T =

300 K, P in torr)

5

test: diffusion in large box (L >> )

simulation results agree with diffusion equation solution

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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

diffusion out of a small box

example event in20x20x20 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 m3, not 2.4 m3

in this study, so v3 was too high.)

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

Test Case: Uniform Field GradientHz = H0 + (dH/dx) x, Hx = Hy = 0

x

z

Theory: McGregor (1990), PRA 41, 2631

L

2a

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Results: Uniform Field Gradient

McGregor (1990) formula gives T2 = 0.42 s.

T = 300 K, P = 1 torr,N = 1000 particles

(H0 = 0.53 gauss, dH/dx = 20 nT/cm)

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Results: Uniform Field Gradient(N = 100 particles for most of these plots)

fits to exp(-t/T2)

12

Test Case: Oscillating, Uniform Field Gradient

Hz(t) = H0 + cos(2f1t) (dH/dx) x, Hx = Hy = 0

x

z

Theory: Bohler and McGregor (1994), PRA 49, 2755

L

2a

13

Results: Oscillating, Uniform Field Gradient(f1 = 60 Hz, T = 300 K, N = 200 particles)

14

UIUC Dressed Spin Experimentholding field coils (B0)

earth field canceling coils (Bv)

dressing coils (B1)

3He cell:P = 1 torr,T = 300 Kz

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

Experimental data: T2 vs Dressing Field

(plot from Pinghan Chu’s talk)

16

Simulation: T2 vs Dressing Field

Simulation gives much longer T2 than the experiment.Shifting (simulation) cell off center by 2 cm: T2(X=0) = 9 s.

17

Simulation of 3He in nEDM CellH0

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 1000T2 = 4202 s

Here, the optimized, 3D field map was (poorly)parameterized by 4th order polynomialsin x, y, z.

Long T2 can be simulated.Dressing effect can be simulated.

18

3He transport into nEDM cell

(Jan’s model, view courtesy S. Williamson)

Eventually, we would like to simulate 3He starting from injection until arrival in the measurement cell.

injection

measurementcell

Needed to do thesimulation:• B-field• model of heat flush?

19

Status of these simulations

• Several studies are posted on the TWiki site: https://nedm.bu.edu/twiki/bin/view/NEDM/DressedspinSimulation

• UIUC dressed spin setup– still need to understand observed short T2

• 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

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 vn

exit

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scattering off of moving normal fluid

• implemented as isotropic in the reference frame of the normal fluid– a random direction is chosen for v3, then vn

is added.– after the vector addition, the length may be

reset to the mean thermal velocity.

22

cell emptying time

from Golub, “flush it away”