1 / 14

Analytical & Exact calcs. of EDM B-fields

Analytical & Exact calcs. of EDM B-fields. Analytical studies (simple expansions) To understand limitations to field uniformity May allow simple optimization of field profile Exact studies: Evaluate average gradients over fiducial volume

kalani
Download Presentation

Analytical & Exact calcs. of EDM B-fields

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. Analytical & Exact calcs. of EDM B-fields • Analytical studies (simple expansions) • To understand limitations to field uniformity • May allow simple optimization of field profile • Exact studies: • Evaluate average gradients over fiducial volume • relevant for Geometric phase contributions to false EDM

  2. y y x x z z Analytical Studies • Evaluate leading-order contributions to main sources of field non-uniformity • Considered two geometries: Open Cosq coil Pure Cosq coil

  3. B-field 1st order expansion • Main field has first-order quadratic dependence on direction due to symmetry • Bx(x) = B0(1 + axx2) – geo. phase contribution • Bx(y) = B0(1 + ayy2) – (not studied yet) • Bx(z) = B0(1 + azz2) – largest non-uniformity

  4. L R y z x Bx(z) study • Field due to “barrel” + “endcap” wires eg: qn

  5. Bx(z) = B0[1 + (abz +aez )z2] • For R>>L ,abz ~ - ½ aez • Now add cylindrical open Ferromagnetic shield • creates mirror currents for barrel wires • this doubles abz givingaez ~ -abz • thus Bx(z) gradient cancelled to 1st order • Sign of gradient depends on details of cancellation • Consistent with measured coil

  6. Bx(x) Study (R=35cm, L=300cm) • Simple expression for Bx(x) for pair of loops • Btotx(x) = B0S (1 + anx x2) • Can try to cancel atotx with single additional loop pair • Also find atotx is minimized for particular value of nloops axtot = 5.3 x 10-6

  7. Pure Cosq coil Open Square Cosq coil y y x x z z Exact calcs. of EDM B-fields • Biot-Savart for straight filaments • Full 3-d profile of B-field • Evaluate <|dBx/dx|> over fiducial volume • Considered two geometries

  8. Comparison with prototype

  9. Fiducial Volume 10 cm 50 cm 7.5 cm 10 cm

  10. False EDM from Geometric phase • Pendlebury et al PRA 70 032102 (04) • Lamoreaux and Golub nucl-ex/0407005 • Geometric phase contribution to false EDM’s depends strongly on radial fields perpendicular to B0 • These result from dBx/dx in our exp. x

  11. Geometric phase contributions • Gradients + vxE field gives dnf • Magnetometers (199Hg & 3He) pick up phase at different rate due to higher velocities • Can be reduced by frequent collisions with buffer gas or phonons (if ) • Neutron can also receive false EDM

  12. Using Pendlebury et al estimates and our basic field profile: • 20 turns of cosq coils without ferromagnetic shield (R=35cm L=300cm) • <dBx/dx> = 0.1 nT/m with B0 = 1 mG • Gives dfn ~ 5 x 10-26 e-cm • But…

  13. With B0 = 10 mG and 42 turns of open (square) cosq coil (R = 61cm, L= L=392 cm – Jan’s ref.) get: • <|dBx/dx|> = 0.15 nT/m • Gives dfn ~ 8 x 10-28 e-cm Note: New Sussex-ILL exp. plans to use • 25 mG • Claims <|dBx/dx|> = 0.1 nT/m “after trimming • Gives dfn ~ 8 x 10-29 e-cm

  14. To Do • Optimize “trimming” of field • Additional coils to minimize <|dBx/dx|> • Check optimum R vs L • Ferromagnetic enclosure with various penetrations

More Related