1. HLAB MEETING -- Paper -- T.Gogami 30Apr2013

2. Experiments with magnets (e,eK + ) reaction

3. Dispersive plane Transfer matrix R 12, R 16 Emittance Beam envelope [ ] Transport Appendix K.L.Brown and F.Rothacker

4. Paper

5. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

6. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

7. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

8. Design requirements 1.Correct beam transport properties 2.To reduce the – Weight – Cost – Power

9. Dipole, Quadrupole, Sextupole B y (x) = a + bx + cx 2 + The field of the magnet as a multpole expansion about the central trajectory Dipole term Quadrupole term Sextupole term

10. Dipole elements R 0 = mv/qB 0 Object Image Particle of higher momentum Dipole term Quadrupole term Sextupole term

11. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

12. Field-path integral Field-path integral B 0 R 0 1 rad

13. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

14. A quadropole element A)By a separate quadrupole magnet B)By a rotated input or output in a bending magnet C)By a transverse field gradient in a bending magnet

15. A quadropole element A)By a separate quadrupole magnet B)By a rotated input or output in a bending magnet C)By a transverse field gradient in a bending magnet Extra cost

16. Rotated pole edge (1) Imaging in the dispersive plane Optical focusing power

17. Rotated pole edge (2) Imaging in the non-dispersive plane

18. Rotated pole edge (3) Optical focusing power Dispersive plane Non-dispersive plane

19. Transverse field gradient (1) Focusing power Transverse field gradient is zero (Pure dipole field) Transverse field gradient is not zero

20. Transverse field gradient (2) Total focusing power ( Dipole + transverse field gradient )

21. A)A pure dipole filed Focusing in the dispersive plane B)A transverse field gradient characterized by n – Focusing in both plane – Sum of the focusing powers is constant 1/f x + 1/f y = (1-n)/(R 0 2 )ds – n/R 0 2 = ds/R 0 2 C)If n=1/2 Dispersive and non-dispersive focusing power: ds/2R 0 2 D)If n < 0 – Dispersive plane focusing power : strong and positive – Non-dispersive plane focusing power : negative Transverse field gradient (3)

22. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

23. Matrix formalism (first order) x 1 = x x 2 = θ = p x /p z (CT) x 3 = y x 4 = φ = p y /p z (CT) x 5 = l = z – z(CT) x 6 = δ = (p z – p z (CT))/p z (CT)

24. Examples of transport matrices R ij

25. Imaging R 12 = 0 – x-image at s with magnification R 11 R 34 = 0 – y-image at s with magnification R 33

26. Focal lengths and focal planes

27. Dispersion

28. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

29. Phase ellipse and Beam envelope x θ Phase ellipse Beam emittance x z Beam Envelope s = 0 beam size (beam waist)

30. Output beam matrix Initial Beam matrix After a magnet system with an R-matrix (R ij ) Output beam ellipse

31. Contents Introduction Field-path integrals First order imaging Matrix formalism Beam envelope and phase ellipse Second order aberrations and sextupole elements Practical magnet design

32. Parameters

33. Practical magnet design Key constrains An advantage B 0 R0R0 Focal length

34. Strong focusing technique NOVA NV-10 ion implanter Bend : 70 degrees Gap : 5 cm Bending radius : 53.8 cm Pole gap field : 8 kG Particle : 80 keV antimony Weight : 2000 lb Pole edge rotation : 35 degrees Field index : -1.152 x-defocus y-focus x-focus y-defocus x : DFD y : FDF Uniform field bending magnet Weight : 4000 lb Pole gap field : 16 kG Coil power : substantially higher

35. SPL with field clamp + ENGE New magnetic field map Committed to the svn

36. Split pole magnet (ENGE)

37. Matrix tuning (E05-115) Before After FWHM ~ 4 MeV/c 2

38. Backup

39. Transverse field gradient (2) Total focusing power ( Dipole + transverse field gradient )