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

Experiments with magnets (e,eK + ) reaction

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

Paper

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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

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)

Examples of transport matrices R ij

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

Focal lengths and focal planes

Dispersion

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

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

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

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

Parameters

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

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 : 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

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

Split pole magnet (ENGE)

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

Backup

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