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HLAB MEETING -- Paper --. T.Gogami 30Apr2013. Experiments with magnets. ( e,e’K + ) reaction. Dispersive plane Transfer matrix R 12 , R 16 Emittance Beam envelope ・・・. 詳細な計算 [ 参照 ] Transport Appendix K.L.Brown and F.Rothacker. Paper. Contents. Introduction Field-path integrals
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HLAB MEETING-- Paper -- T.Gogami 30Apr2013
Experiments with magnets (e,e’K+) reaction
Dispersive plane • Transfer matrix • R12 , R16 • Emittance • Beam envelope • ・・・ 詳細な計算 [参照] Transport Appendix K.L.Brown and F.Rothacker
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 • Correct beam transport properties • To reduce the • Weight • Cost • Power
Dipole, Quadrupole, Sextupole By(x) = a + bx + cx2 + ・・・・ The field of the magnet as a multpole expansion about the central trajectory Sextupole term Dipole term Quadrupole term
Dipole elements R0 = mv/qB0 Dipole term Quadrupoleterm Sextupoleterm Particle of higher momentum Image Object
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 B0R0 1 rad [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 • By a separate quadrupole magnet • By a rotated input or output in a bending magnet • By a transverse field gradient in a bending magnet
A quadropole element • By a separate quadrupole magnet • By a rotated input or output in a bending magnet • By a transverse field gradient in a bending magnet Extra cost
Rotated pole edge (1) ( Frequently used to generate first order imaging ) Imaging in the dispersive plane Optical focusing power
Rotated pole edge (2) ( Frequently used to generate first order imaging ) Imaging in the non-dispersive plane (Rot B = 0 )
Rotated pole edge (3) ( Frequently used to generate first order imaging ) Optical focusing power Dispersive plane Non-dispersive plane
Transverse field gradient (1) Transverse field gradient is zero (Pure dipole field) Focusing power Transverse field gradient is not zero Field index
Transverse field gradient (2) Total focusing power ( Dipole + transverse field gradient ) Field index
Transverse field gradient (3) Field index • A pure dipole filed Focusing in the dispersive plane • A transverse field gradient characterized by n • Focusing in both plane • Sum of the focusing powers is constant 1/fx + 1/fy = (1-n)/(R02)ds – n/R02 = ds/R02 • If n=1/2 Dispersive and non-dispersive focusing power: ds/2R02 • If n < 0 • Dispersive plane focusing power : strong and positive • Non-dispersive plane focusing power : negative
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) x1 = x x2 = θ = px/pz(CT) x3 = y x4 = φ = py/pz(CT) x5 = l = z – z(CT) x6 = δ = (pz – pz(CT))/pz(CT)
Imaging • R12 = 0 • x-image at s with magnification R11 • R34 = 0 • y-image at s with magnification R33
Focal lengths and focal planes • x-plane • y-plane
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 Phase ellipse Beam Envelope θ x x z 1/2 s = 0 beam size (beam waist) Beam emittance
Output beam matrix Initial Beam matrix • Initial beam ellipse • R-matrix After a magnet system with an R-matrix (Rij) Output beam ellipse • Final beam matrix • Final 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
Practical magnet design Key constrains • Bending power • Pole gap • Coil power • Magnet weight : Coil weight : Steel weight An advantage B0 R0 Focal length
“Strong focusing” technique Large pole edge rotation + Large field index 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 • Uniform field bending magnet • Weight : 4000 lb • Pole gap field : 16 kG • Coil power : substantially higher x : DFD y : FDF x-defocus y-focus x-focus y-defocus
SPL with field clamp + ENGE New magnetic field map Committed to the svn
Matrix tuning (E05-115) Before FWHM ~ 4 MeV/c2 After
Transverse field gradient (2) Total focusing power ( Dipole + transverse field gradient ) Simple harmonic motion Simple harmonic motion Field index