1 / 37

Dynamical Polarization of neutron beams

Dynamical Polarization of neutron beams. G. Badurek, C. Hartl, E. Jericha Atominstitut, Vienna University of Technology. Dynamical Polarization of Neutron Beams. Idea & Motivation. Conventional neutron polarizers Waste >50% of incident beam intensity.

alaula
Download Presentation

Dynamical Polarization of neutron beams

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Dynamical Polarizationof neutron beams G. Badurek, C. Hartl, E. Jericha Atominstitut, Vienna University of Technology

  2. Dynamical Polarization of Neutron Beams Idea & Motivation • Conventionalneutron polarizers Waste >50% of incident beam intensity. • Gedankenexperiment:What, if we turn the unwanted spin component into the „right“ direction?use 100% of intensity

  3. Dynamical Polarization of Neutron Beams Concept • No interaction with matter • Flip„wrong“ spins • Accept atiny energy shift(~10-5) • In principleloss-free:100% transmission100% polarization First Proposal: Badurek, Rauch, Zeilinger Z. Phys. B 38 (1980) 303

  4. Dynamical Polarization of Neutron Beams Energy Change Spin-dependent engergy shift: • Spin flipeffectspotential energy only • 2 xkinetic energychange (same direction)at themagnet borders

  5. z x -y Spin Precession Region Transition regionbefore and behind the spin precession region causes anadiabatic spin rotationinto and from the x-direction. Two /2-turnersat entrance and exit of the precession region: • 1st spin turnerstartsspin rotation (turns spin into (z-y)-plane) • 2nd spin turnerstopsspin rotation (turns spin back into x-direction)

  6. Polychromatic Pulsed Beam Polarization • Polarizepolychromaticneutron beams • Pulsedsource required • TOFpathbefore polarizer mapswavelength  time • Monoenergeticpolarization conditionfor each wavelength time-dependent operation

  7. Monte-Carlo Simulation: Concept • 3-dim.classical spin rotation • Simple field geometry • Continuousmonochromatic(static) or pulsedpolychromatic(time dependent) setup • Process „neutron events“ (t, x, v, P) step by step • Calculation exact where possible • RF flipper,, DC flipperand2nd/2 turner:„Krüger arrangement“

  8. Monte-Carlo Simulation: Geometry

  9. Neutron Centre of Mass Motion

  10. Neutron Spin Motion: Classical Description

  11. Neutron Spin Motion: Quantum Mechanics

  12. z y x D t0 t1 = t0+D·v Neutron Spin Motion inside a “Krüger-arrangement“ parameters: RF field frequency Effective Larmor frequency vector:

  13. z y x D t0 t1 = t0+D·v Neutron Spin Motion inside a “Krüger-arrangement“ Equation of motion: S  S‘(t) : P(t)=G(t)·P’(t) In the primed system the rotation axis lies statically in the x’-axis! Solution:

  14. 1 0.5 0 -0.5 -1 1 0.5 0 -0.5 -1 -1 -0.5 0 0.5 1 1 Neutron Spin Motion inside a “Krüger-arrangement“ Movement of the polarization vector‘s tip Example parameters (resonance case):

  15. RF-Flipper

  16. Rotating p/2 Spin-Turner

  17. Typical Result of Monte-Carlo Simulation

  18. Dynamical Polarization of Neutron Beams Typical Result of Monte-Carlo Simulation Source Pulse Duration Incident flight path: 60 m Splitting Field: 4 10 T Precession Length: 1 m

  19. Tensorial Neutron Tomography of magnetic samples G. Badurek, E. Jericha, H. Leeb, R. Szeywerth Atominstitut, Vienna University of Technology

  20. Tensorial Neutron Tomography Idea & Motivation • Determination of magnetic structures in bulk ferromagnetic materials Unique reconstruction by tomographic methods. • Path-ordering effects in neutron spin rotationDevelopment of novel reconstruction alogrithms.

  21. Tensorial Neutron Tomography Concept Perfect crystal neutron interferometer Set-up for neutron interferometric spinor tomography. • Combination of neutron depolarization concepts and neutron interferometry.

  22. Spin rotation operator Quality of the reconstruction

  23. Reconstruction quality – traditional methods 1 G. Badurek et al., Physica B 335 (2003) 114

  24. Reconstruction quality – traditional methods 2 reasonable reconstruction up to 2 µm pixel sizes

  25. Summary of novel reconstruction algorithms • Elimination procedure • Separation procedure • (Sums of separated logarithms) • Modified algebraic reconstruction technique • ART with path ordering • ART with converging projections • Taylor series expansion

  26. Elimination procedureneutrons with multiple velocities • Elimination of path ordering effects using experimental data of multiple different velocities reconstruction via traditional ART or FBP

  27. Reconstruction quality – multiple wavelengths good results up to pixel sizes of 5-6 µm

  28. Multiple wavelengths – influence of noise pixel size 3 µm problem: uncertainties in each term and large g-factors for neighbouring velocities

  29. Separation procedureseparation of line integrals andpath ordering effects L ... contains line integral without path ordering K ... contains all path ordering effects U ... determined by experiment solved by iteration L(0) taken from a model describing the sample quality of the reconstruction essentially determined by the applicability of the model

  30. Separation procedure - iteration by inverse Radon transformation traditional methods (ART or FBP) taking full path ordering into account the measurement enters here good results up to pixel sizes of ~ 4 µm

  31. Reconstruction quality – separation procedure a) individual projections from the angular range 0 – 2p b) averaged quantities from the projections q & q+p

  32. Modified ARTtaking path ordering into account • ART performs the inverse Radon transformation by solving a system of linear equations for discretized pixel structures • Path-ordered integrals also have to be written as linear equations to apply ART → linear approximation (with B(i) being the reconstruction for the current iteration):

  33. Iteration procedure for the modified ART • Solving this system of linear equations changes the standard ART algorithm just in one way: pseudo-projections are no longer line integrals but path-ordered integrals. • The algorithm looks like this: • Result: full convergence for 4-5 µm for a 20x20 pixel structure, slightly better than prior methods with possible advantages concerning limited angle data

  34. Modified ART 2assure convergence of the projections aim - convergence correction for a specific pixel proportional to the neutron path length across this pixel iteration procedure initial condition

  35. Modified ART – method 2 in case of convergence no convergence skip this projection for reconstruction • full convergence up to 5 µm for a 20x20 pixel structure • advantages for incomplete data sets • relatively robust against uncertainties from counting statistics and pixel deformations

  36. Modified ART 3linearization by Taylor series expansion magnetic field distribution n-th iteration series expansion coefficients iteration procedure

  37. Reconstruction quality – modified ART a) results for the modified ART b) results for modified ART method 2 c) results for modified ART method 3 10 iterations for each method only

More Related