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Simulations of neutron spin manipulation and transport for the LANL neutron EDM experiment

Doug Wong. Simulations of neutron spin manipulation and transport for the LANL neutron EDM experiment. nEDM searches and Baryon Asymmetry. A probe of CP violation Baryon asymmetry (Sakharov requirements) - Baryon number violation - Departure from thermodynamic equilibrium

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Simulations of neutron spin manipulation and transport for the LANL neutron EDM experiment

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

  2. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 10-26e cm, the LanlnEDM search is aiming for 10-27 e cm CP Violation and Strangeness

  3. FRIB Topical Program: Hadronic EDMs – Doug Wong nEDM search at LANL • Room temperature nEDMapparatus • 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) R.W.P Jr. 2018 Plaster 2018

  4. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 LanlnEDM TPR 2018

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

  6. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong Ramsey’s method: Making a fringe On resonance Also off resonance Off resonance 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. 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 Note: this is just for demonstration purposes, the animation skips lots of precession time, and the ramsey fringe was made with different parameters

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

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

  12. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 E5-2680 v3 CPUs and four 480 GB solid-state drives

  14. FRIB Topical Program: Hadronic EDMs – Doug Wong • 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 https://github.com/wschreyer/PENTrack

  15. FRIB Topical Program: Hadronic EDMs – Doug Wong Ramsey method: PENTrack vs numerical SE solution B0= 1 uT(w0= 183.247 rad/s) BL= 4 nT(wL= 0.732989) Precession = 180s π/2 pulse time = 4.286 sec (for an optimized ramseyfringe, wL = π/tpulse) gyromagnetic ratio of the neutron 1.832 471 72 x 10^8 rad s^-1 T^-1 Result from integrating Schrodinger equation

  16. FRIB Topical Program: Hadronic EDMs – Doug Wong 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= 183.247 rad/s) BL= 4 nT(wL= 0.732989) Precession = 180s π/2 pulse time = 4.286 sec Height of precession chamber = 0.1 m dB0/dz = 1e-7 [T/m] (1000 neutrons, bin size = 0.1)

  17. FRIB Topical Program: Hadronic EDMs – Doug Wong T2 • Basic method: Plot <Sx> vs t, which should tend towards 0 as spins decouple • B0 = 1 uT.Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m • Neutron energy: Uniform distribution 0 - 200 nEv • Number of neutrons simulated: 5000 dB/dZ = 1e-8 [T/m] dB/dZ = 1e-7 [T/m]

  18. FRIB Topical Program: Hadronic EDMs – Doug Wong T2 • Fit with exp(-(t - c) / T2 ) * sin(w*t + phi) • B0 = 1 uT.Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m • Neutron energy: Uniform distribution 0 - 200 nEv • Number of neutrons simulated: 5000 dB/dZ = 1e-8 [T/m] dB/dZ = 1e-7 [T/m] dB/dZ = 1e-8 [T/m]

  19. FRIB Topical Program: Hadronic EDMs – Doug Wong T2 • Can also get out of the rotating frame by using <Sx>^2 + <Sy>^2 • Fit exp(-(t - c) / T2 ) • B0 = 1 uT.Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m • Neutron energy: Uniform distribution 0 - 200 nEv • Number of neutrons simulated: 5000 dB/dZ = 1e-8 [T/m] dB/dZ = 1e-7 [T/m]

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

  21. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong December 2019 field mapping Non-adiabaticity parameter k B0 coil Wall 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 Center of MSR transport coils transport coils B0 coil Wall Center of MSR B0 coil Wall transport coils

  24. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 B0 coil Wall transport coils

  25. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong B0 coil design and new MSR

  28. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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) LanlnEDM TPR 2018

  30. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong UCN Transmission: No window Energy spectrum can be guessed from ramping curve

  32. FRIB Topical Program: Hadronic EDMs – Doug Wong UCN Transmission: With window Takeyasu Ito 

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

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

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

  36. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong False nEDM sources

  38. FRIB Topical Program: Hadronic EDMs – Doug Wong 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. FRIB Topical Program: Hadronic EDMs – Doug Wong 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 blochsiegert 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. FRIB Topical Program: Hadronic EDMs – Doug Wong Comagnetometer and neutron COM difference

  41. FRIB Topical Program: Hadronic EDMs – Doug Wong Summary • To better characterize the value of αin 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

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