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Hahn-Meitner-Institut Berlin

KH. Hahn-Meitner-Institut Berlin. Hahn-Meitner-Institut Berlin. Larmor phase corrections in neutron resonance spin-echo: curved dispersion surfaces. NMI3 General Meeting - Joint Research Activity Polarized Neutron Techniques, Task 2-A. Klaus Habicht Hahn-Meitner-Institut Berlin.

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Hahn-Meitner-Institut Berlin

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  1. KH

  2. Hahn-Meitner-Institut Berlin Hahn-Meitner-Institut Berlin Larmor phase corrections in neutron resonance spin-echo: curved dispersion surfaces NMI3 General Meeting - Joint Research ActivityPolarized Neutron Techniques, Task 2-A Klaus Habicht Hahn-Meitner-Institut Berlin • Motivation: curvature limited resolution in single x-tal spectroscopy • Analytical calculations: • Larmor phase with curved dispersion surfaces • Simplified case: out-of-scattering plane curvature of the dispersion relation • Cross-term problem: partial correction • Monte-Carlo simulations: current sheets in NRSE • Test experiments: current sheets in NRSE • Summary / Future activity RAL, 26. September 2005 Klaus Habicht, habicht@hmi.de

  3. Motivation: curvature limited resolution in single x-tal spectroscopy Depolarization effects in N(R)SE-TAS lifetime measurements of single x-tal excitations: • beam divergence • sample mosaicity (transverse excitations) • curvature of the dispersion surface state of the art: effects can be calculated for inelastic, dispersive signals; data correction: divide experimental data by calculated resolution function K. Habicht et al., J. Appl. Cryst.36, 1307 (2003), Physica B 350 E803-E806 (2004) Goal: match planes of constant Larmor phase to curved dispersion surfaces of single crystal excitations Benefit: enhanced resolution for line width measurements

  4. Analytical calculations: Larmor phase with curved dispersion energy qperp qpar How is curvature of the dispersion surface included in the Larmor phase ? Polarization scattering function TAS transmission probability Larmor phase beam divergence second order expansion of the Larmor phase second order expansion of the dispersion relation curvature terms

  5. Analytical calculations: out-of-scattering-plane curvature Consider curvature in the z-direction only motivation: vertical TAS resolution usually coarse vertical terms separate from in-plane resolution (easy to calculate)  reasonable goal to correct for curvature in 1 dimension only Curvature terms in Larmor phase Beam divergence in Larmor phase TAS transmission function (Cooper Nathans) cross terms !

  6. Analytical calculations: out-of-scattering-plane curvature Consider curvature in the z-direction only motivation: vertical TAS resolution usually coarse vertical terms separate from in-plane resolution (easy to calculate)  reasonable goal to correct for curvature in 1 dimension only Curvature terms in Larmor phase Beam divergence in Larmor phase TAS transmission function (Cooper Nathans) cross terms ! Transformation to real space coordinates

  7. Analytical calculations: cross-term problem natural approach: compensate second order terms by correction elements which provide additional phases proportional to quadratic space coordinates (e.g. 1D Fresnel coils ) F. Mezei, Lecture Notes in Physics (1979); M. Monkenbusch, NIM A, 287 (1990) 465, NIM A 399 (1997) 301, NIM A 437 (1999) 455 first spectrometer arm sample second spectrometer arm in small sample limit (correct in second order) Larmor phase additional phase from correction elements complete correction with Fresnel coils is not possible ! has no solution!

  8. Analytical calculations: partial correction no correction correction in first arm correction in second arm correction in both arms favors divergence correction in both arms ! favors correction in arm 1 or 2 favors correction in arm 2 ! perfect correction by correction in arm 2 ! matching of curvature and instrumental resolution terms do not correct divergence in both arms !

  9. Monte Carlo simulations: current sheets in NRSE Fresnel-coil correction-scheme applicable to NSE (TASSE), longitudinal NRSE What about NRSE ?  correction elements in longitudinal guide field, Monkenbusch‘s parabolic coils digression: simplest case - Mezei tilt coils ( ‘ figure 8 coils ‘ ) numerical calculations for tilt coils in zero field magnetic field calculations using Radia (ESRF) calculation of polarization as a function of space and divergence using VITESS (K. Lieutenant, G.Zsigmond, S. Manochine, HMI) 33 cm setup: z y x direction of currents z J P NSE situation: strong longitudinal field along z; Bz , By components neglected y neutron flight path z x 23.8 mm y

  10. Monte Carlo simulations: current sheets in NRSE 33 cm setup: NRSE: after the first RF-coil polarization isotopically distributed in x-y plane after transmission of two elements: strong spatially dependent polarization (depolarization effect in zero field) z y x z P J y j x

  11. Monte Carlo simulations: current sheets in NRSE p-flip, B || y 33 cm setup: after transmission of two elements with p flip: spatial dependence of polarization removed! z y x z P J y j x

  12. Monte Carlo simulations: current sheets in NRSE 33 cm setup: P0 || y z y x z P J y p-flip, B || y p-flip, B || y p-flip, B || y j x phase is spatially independent but depends linearly on divergence ! same precession angle j for incident polarization P0 || x

  13. Test experiments: current sheets in NRSE z y x p-flip, H || y Direct beam experiments using the NRSE option at the cold triple axis instrument V2 BENSC, HMI each point is obtained from full NRSE scan Setup 1: NRSE bootstrap coils after transmission of one element: strong spatially dependent polarization (depolarization effect in zero field) as expected after transmission of two elements and p-flip : Polarization recovered as predicted

  14. Test experiments: current sheets in NRSE z y x p-flip, H || y p-flip, H || y p-flip, H || y Direct beam experiments using the NRSE option at the cold triple axis instrument V2 BENSC, HMI Setup 2: q2 observed effective tilt angles suggest that Larmor phase can be controlled to some extent with current sheets even in NRSE

  15. Summary / Future Activity • Analytical calculations: • 6 Fresnel correction scheme does not eliminate all second order terms due to curvature, • in general only partial correction possible • in most situations divergence correction in one spectrometer armonly preferred over complete divergence correction in both arms • Monte-Carlo simulations: • suggest current sheets can work in NRSE • Test experiments: • operation of current sheets in NRSE is possible without complete beam depolarization • Application of genetic algorithm (in cooperation with P. Bentley): • current activity on implementation for RESCAL (TAS parameter optimization) • Future activity: • optimization of experimental parameters for correction elements using genetic algorithm • experimental tests with non-linear current distributions

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