1. FRIB Topical Program: Hadronic EDM
August 23, 2019
Simulations of neutron spin manipulation and transport for the LANL neutron EDM experiment
Doug Wong

2. nEDM searches and Baryon Asymmetry
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
nEDM searches and Baryon Asymmetry
A probe of CP violation
Baryon asymmetry (Sakharov requirements)
- Baryon number violation
- Departure from thermodynamic equilibrium
- C and CP violation
If CP is conserved, any process producing a particle must have a counterpart reaction producing the charge-conjugate particle at the same rate  no net baryon number
Also good at killing off theories
Good probe of BSM physics
Small SM background
Current limit is at e cm, the Lanl nEDM search is aiming for e cm
CP Violation and Strangeness

3. nEDM search at LANL Room temperature nEDM apparatus
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
nEDM search at LANL
Room temperature nEDM apparatus
Double precession chamber, Ramsey’s oscillatory fields method, with 199Hg co-magnetometer.
LANL UCN source capable of providing 200 UCN/cc at exit of the biological shield
Preliminary test:
Cell densities were measured via fill/dump storage experiments to be < 5 UCN/cc
Crude Ramsey fringes created successfully using a test setup in 2017
Magnetically shielded room had 2 layers and a shielding factor of ~150
Projected data collection start: 2021
Ramsey fringes (T1 = 30 sec)
Plaster 2018
R.W.P Jr. 2018

4. nEDM search at Lanl Indicates the B field direction
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
nEDM search at Lanl
Indicates the
B field direction
Guiding field coils
UCN gate-valve
AFP spin flipper (short solenoid)
Spin analyzer (magnetized Fe foil)
UCN detector (B-ZnS foil + PMT)
Frequency (RF) reference
Lanl nEDM TPR 2018

5. FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey’s method: Neutron spin manipulation using an oscillatory field (i.e., RF field)

6. Ramsey’s method: Rabi π flip
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey’s method: Rabi π flip
Circular:
Linear:
ω = 20 [rad/s]
ω0 = 20 [rad/s]
ωC = 1.57 [rad/s]
ωL = 3.14 [rad/s]
t = 2 [sec]
a0 = 1
b0 = 0

7. Ramsey’s method: On resonance sequence
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey’s method: On resonance sequence
Neutron starts spin up at t = 0
Above: Plot of the “tip” of the semiclassical neutron spin vector. Origin of the vector is at
P(x),P(y), P(z) = (0.5, 0.5, 0.5)
Note: this is just for demonstration purposes, the animation skips lots of precession time

8. Ramsey’s method: Making a fringe
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey’s method: Making a fringe
Off resonance
On resonance
Also off resonance
In experiment it is unnecessary to make the whole fringe. Pick 4 points along the central peak along which the slope is fastest changing, and extrapolate resonant frequency from that
Each point on the fringe comes from one ramsey sequence. Experimentally, to make this fringe, all you need to do is to apply a ramsey sequence (for various RF frequencies) on a population of neutrons, and count the number of spin up neutrons at the end.
Note: this is just for demonstration purposes, the animation skips lots of precession time, and the ramsey fringe was made with different parameters

9. Statistical requirements
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Statistical requirements
Takayesu Ito 2018

10. Spin transport into the precession cell
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
What determines α?
Initial polarization
Spin transport into the precession cell
Spin decoherence/depolarization in the precession cell
Spin transport out of the precession cell into the spin analyzer
Spin analyzer efficiency

11. Improving and characterizing α
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Improving and characterizing α
1s free precession
10s free precession
T1 as a function of holding time

12. FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
T1 and T2 spin relaxation
Longitudinal spin depolarization time T1 (no polarization left = no signal)
Transverse spin depolarization time T2
Transverse depolarization time T2
(Spin of precessing neutrons fall out of alignment)
Leung 2018

13. Computational tools PENTrack
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Computational tools
PENTrack
Monte Carlo spin tracking and particle trajectory simulation
Time dependent / static B and E fields (both numerical and analytical)
Supports complicated experimental geometries (e.g. storage chambers, pipes in and out of the chamber, valves)
COMSOL
Finite element physics simulator
Indiana University Carbonate Computing Cluster
72 general-purpose compute nodes, each with 256 GB of RAM, and eight large-memory compute nodes, each with 512 GB of RAM
Each node equipped with 12 two 12-core Intel Xeon E v3 CPUs and four 480 GB solid-state drives

14. https://github.com/wschreyer/PENTrack
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Features:
Spin tracking of neutrons, Hg, neutron decay products via the BMT equations (relativistic)
RK5 integrator w/ adaptive step size
Local tricubic interpolation for non analytic magnetic fields
Allows importing of STL files
Supports time dependent magnetic fields
Diffuse/specular reflection for different materials based on fermi potential

15. Ramsey method: PENTrack vs numerical SE solution
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey method: PENTrack vs numerical SE solution
B0 = 1 uT (w0 = rad/s)
BL = 4 nT (wL = )
Precession = 180s
π/2 pulse time = sec (for an optimized ramsey fringe, wL = π/tpulse)
gyromagnetic ratio of the neutron
x 10^8 rad s^-1 T^-1
Result from integrating Schrodinger equation

16. Ramsey method (For varying B0 gradients, PENTrack)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Ramsey method (For varying B0 gradients, PENTrack)
dB0/dz = 1e-9 [T/m] (1000 neutrons, bin size = 0.1)
dB0/dz = 0 [T/m] (1000 neutrons, bin size = 0.1)
B0 = 1 uT (w0 = rad/s)
BL = 4 nT (wL = )
Precession = 180s
π/2 pulse time = sec
Height of precession chamber = 0.1 m
dB0/dz = 1e-7 [T/m]
(1000 neutrons, bin size = 0.1)

17. T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019
Basic method: Plot <Sx> vs t, which should tend towards 0 as spins decouple
B0 = 1 uT. Specularity = Cylindrical chamber of h = 0.1 m, r = 0.5 m
Neutron energy: Uniform distribution nEv
Number of neutrons simulated: 5000
dB/dZ = 1e-7 [T/m]
dB/dZ = 1e-8 [T/m]

18. T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019
Fit with exp(-(t - c) / T2 ) * sin(w*t + phi)
B0 = 1 uT. Specularity = Cylindrical chamber of h = 0.1 m, r = 0.5 m
Neutron energy: Uniform distribution nEv
Number of neutrons simulated: 5000
dB/dZ = 1e-7 [T/m]
dB/dZ = 1e-8 [T/m]
dB/dZ = 1e-8 [T/m]

19. T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019
Can also get out of the rotating frame by using <Sx>^2 + <Sy>^2
Fit exp(-(t - c) / T2 )
B0 = 1 uT. Specularity = Cylindrical chamber of h = 0.1 m, r = 0.5 m
Neutron energy: Uniform distribution nEv
Number of neutrons simulated: 5000
dB/dZ = 1e-7 [T/m]
dB/dZ = 1e-8 [T/m]

20. T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019
T2 as a function of gradient: non-specularity = 30%

21. FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Spin transport
Before we can validate our T1/T2 models with experimental data, we must first understand the polarization of the neutrons entering the precession chamber
Rough field map taken in Dec. 2019, not enough to characterize transport into the chamber
Planned neutron transport through the magnetically shielded room in Fall 2019
New magnetic field mapper recently built will also provide a better field profile

22. December 2019 field mapping
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
December 2019 field mapping
Non-adiabaticity parameter k
Wall
B0 coil
Center of MSR
transport coils
(3 solenoids)
We want k << 1 for good spin transport
vn = 4m/s
Fluxgate inserted into the MSR starting at z=0
B0 generates a field along the y axis

23. Comsol simulation FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Comsol simulation
~100 uT (1 gauss) external uniform field along +y
B0 generates field along -z
MSR walls modeled as a fixed magnetic boundary w/ 2mm thickness, which is a little thin z y
transport coils
Center of MSR
B0 coil
transport coils
Wall
Center of MSR
Wall
B0 coil
transport coils

24. Comsol simulation FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Comsol simulation
~100 uT (1 gauss) external uniform field along +y
B0 generates field along -z
MSR walls modeled as a fixed magnetic boundary w/ 2mm thickness, which is a little thin z y
transport coils
B0 coil
transport coils
Center of MSR
Wall
B0 coil
transport coils

25. PENTrack simulation Spin tracking output (single pass)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
PENTrack simulation
Neutrons are propagated along y in a pipe of ID 3 inches
Starting from outside the MSR at y=-2m, absorbed at center of the MSR at y=0
Specular reflection, magnetic vector field imported from Comsol and interpolated
Ending polarization calculated using the relation
1000 neutrons
Storage time = 5s
Av = 0.92
Spin tracking output (single pass)
1000 neutrons
Storage time = 20s
Av = 0.73

26. B0 coil design and new MSR
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
B0 coil design and new MSR
We also need to model spin transport for the recently-ordered magnetically shielded room (MSR)
This includes transport past B0 coils

27. B0 coil design and new MSR
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
B0 coil design and new MSR

28. B0 coil design and new MSR
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
B0 coil design and new MSR
Polarization after transport (single pass): 
B field along guide
Spin polarization in transport (single pass): 
Non adiabaticity along pipe
Note: the shield walls are at 1.2[m], 1.3[m], 1.5[m], 1.75[m]

29. Approaching a full simulation of the nEDM experiment
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Approaching a full simulation of the nEDM experiment
Complete fill and dump, with Ramsey sequence in the chamber
Spin analyzer simulation (AFP spin flipper with polarized iron foil. Examine drop height effect)
AFP spin flipper (short solenoid)
Spin analyzer (magnetized Fe foil)
UCN detector (B-ZnS foil + PMT)
Lanl nEDM TPR 2018

30. FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Window study at LANL (2018)
Pre-polarizing magnet (PPM) is ramped up from 0 to 5 T
We measure neutron count as a function of B field strength, both with and without a ‘window’

31. UCN Transmission: No window
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
UCN Transmission: No window
PPM Field
Neutron transmission
B = 0 T
N- + N+
B = 5 T N+
Energy spectrum can be guessed from ramping curve

32. UCN Transmission: With window
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
UCN Transmission: With window
PPM Field
Neutron transmission
B = 0 T
(N- + N+) f
B = 5 T N+
Takeyasu Ito 

33. PPM ramping simulation (a work in progress)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
PPM ramping simulation (a work in progress)
High field seekers
No PPM window (B = 0 T)
Low field seekers
Mixed spin states

34. PPM ramping simulation (a work in progress)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
PPM ramping simulation (a work in progress)
High field seekers
No PPM window (B = 2 T)
Low field seekers
Mixed spin states

35. PPM ramping simulation (a work in progress)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
PPM ramping simulation (a work in progress)
High field seekers
No PPM window (B = 5 T)
Low field seekers
Mixed spin states

36. PPM ramping simulation (a work in progress)
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
PPM ramping simulation (a work in progress)
An easy way to validate these results: in the upcoming run cycle, perform a ramp with the spin flipper on, in order to count low field seekers
Low field seekers
Mixed spin states

37. False nEDM sources FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
False nEDM sources

38. Geometric Phase: Bloch Siegert shift
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Geometric Phase: Bloch Siegert shift
A linear RF = two circular RFs with equal frequency but opposite directions of rotation (sin is odd, cos is even)
 N. F. Ramsey, Phys. Rev. 100, 1191–1194 (1955)

39. Geometric Phase FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Geometric Phase
False EDM from gradient in chamber and the v x E effect
Say there is some gradient along both xy and z
Bloch siegert shift
Maxwell eq.
and by cylindrical symmetry
Assume constant B0z gradient, integrating gives
Now plug B0xy and into bloch siegert shift formula up top
Frequency shift correlates to false EDM
linear E term gives false EDM if you reverse the E field!
Plugging in values gives something on the order of 10^-27 e cm!

40. Comagnetometer and neutron COM difference
FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Comagnetometer and neutron COM difference

41. FRIB Topical Program: Hadronic EDMs – Doug Wong
August 23, 2019
Summary
To better characterize the value of α in the figure of merit, we must understand
Initial polarization
Spin transport into the precession cell
Spin decoherence/depolarization in the precession cell
Spin transport out of the precession cell into the spin analyzer
Spin analyzer efficiency
To improve the accuracy of our simulations, we have planned B field mappings and transport/storage tests in the upcoming run cycle
Understanding of the 1/√ N factor requires simulation and measurement of the neutron energy spectrum
As simulations approach a full transport/Ramsey/dump sequence, false nEDM signals such as geometric phase must also be considered