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Electromagnetic Devices and Electromagnetic Devices and OpticsOptics- PHY743 -- PHY743 -
Devices are based on the electrodynamics' character of moving charged particles in presence of electro-magnetic fields – Especially magnetic field
Basic principle is originated from Lorentz force
F = q[E + (v B)/c]
Electric force in the direction of E – Acceleration Magnetic force normal to both v and B – Circular
motion
The characters can be described by “Optics”
The characters defined the variety of “Elements”
Circular motion of charged particle in uniform B field
Magnetic DipoleMagnetic Dipole
Uniform B Field Pointing Out of
Paper
Circular Motion:
=
33.356 pB
– Radius in meterP – Momentum in GeV/cB – Field in Tesla (kGauss)
is a function of momentum
p
p
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Momentum Dispersion by Magnetic Dipole
Function of Magnetic Dipole:◦ Change charged particles’ trajectory orientation◦ Disperse trajectory orientation according to
momentum
Magnetic Dipole – Magnetic Dipole – Cont.Cont.
Optics: Prism
Wavelength Dispersion
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Magnetic Dipole
pp
p+p
p -pp
Momentum Dispersion
Basic Structure of a Dipole
Magnetic Dipole – Magnetic Dipole – Cont.Cont.
“H” Dipole
“C” DipoleYork Iron
(High )
Electric Coil
Magnetic Flux
Magnetic
Flux Uniform Field
Region• Large uniform field area• Suitable for large particle trajectory profile - Spectrometer
• Small uniform field area but small size• Suitable for small particle trajectory profile – Beam Line Element or Special application
Effective Field Boundary (EFB)
Magnetic Dipole – Magnetic Dipole – Cont.Cont.
By/B0
Z/G
By – Normal fieldB0 – Total field strengthZ – Trajectory distanceG – Gap of the opening
1.0
Uniform Field
Region
None-uniform field - “Fringe Field
Distribution” F.F.D.
I = BydZ
ByZ = BydZ
EFBActual Pole
Iron Boundary
Boundary shaping outlined by EFB line and detailed F.F.D. are important parameters for design and optical description of a dipole
Bx and Bz are mot zero in fringe field
region
Important Optical Parameters for a Dipole
◦B0 and L (path length)
◦ and These are first order parameters
◦ and ◦Shaping of EFB’s◦Fringe field descriptionThese are second and higher order parameters
Magnetic Dipole – Magnetic Dipole – Cont.Cont.
B0
Basic Structure of a Quadrupole◦ York iron with 4 inner circular
symmetric poles
◦ Four sets of connected coils
◦ Field flux flows oppositely:
Up-Down and Left-Right◦ B = 0 at r = 0, Bmax at r = R
Magnetic QuadrupoleMagnetic Quadrupole
R
R
Bmax (Tip
Field)
0
B(r)(For Illustration
only)
Profile of Charged Particles w/ the Same Momentum
It works just like an optical lens
Quadrupole magnet – Magnetic Lens
Magnetic Quadrupole – Magnetic Quadrupole – Cont.Cont.
PointSource
PointImage
Optical Lens
Symbol of Focusing Lens
Horizontal (or Vertical) Plane
Vertical (or Horizontal) Plane
Quadrupole focuses the charged particles. Multipoles and quadrupoles are needed to focus the
particles in full phase space
Magnetic Multipoles have the same concept as Quadrupole except number of poles
They are:◦ Hexapole (Axial Symmetry – 2nd order in optics)◦ Octapole (Point Symmetry – 3rd order in optics)◦ Decapole (Axial Symmetry – 4th order in optics)◦ Dodecapole (Point Symmetry – 5th order in optics)
Hardware Hexapole
Magnetic MultipolesMagnetic Multipoles
York Iron
Coils
Pole Face
Imperfect Quadrupole produces Multipole fieldsReference to perfect
QuadrupoleAxial asymmetry of pole spacingPoint asymmetry of pole spacing
Others defects: Combined asymmetries, imperfect individual pole location and rotation, and imperfect pole face curvatures. These are unavoidable.
Quadrupoles are used for beam line and spectrometer to confine or focus the beam profile since Dipole changes the profile size due to incident angle and momentum spreads
Hexapoles are used commonly in beam line to control the beam profile at hardware level
Multipole Fields from spectrometer Quadrupoles are commonly described or corrected in the “Optics” description
Optical Parameters for Quadrupole and Multipoles:
◦ Tip field strength – Bmax, radius R, and effective length L (1st order)
◦ Strength of Multipole field contents (2nd and higher orders)◦ Fringe field distribution description (2nd and higher orders)
Magnetic Multipoles – Magnetic Multipoles – Cont.Cont.
Used to separate particles w/ the same momentum, i.e. purify the secondary beam content
Basic Structure:
Location and size of the slit selects the particles Optical Parameters: Effective path length – L and Ex (first order)
Gap and width of electrodes and fringe field (Higher orders)
Electric Separator – Velocity Electric Separator – Velocity SeparatorSeparator
Vacuum Chamber
Window
HV (+250kV)
HV (-250kV)
Uniform E field: F = qE = ma Mass Slit
(Move Up-Down)
Heavier
Particle
Lighter Particl
e
Commonly used for collision physics or large acceptance reactional or decay physics
Basics structure (Assuming for reactional or decay physics):
Optical parameters: Length of solenoid Diameter of solenoid Asymptotic magnetic field of solenoid, i.e. B = 0.4IN/L
SolenoidsSolenoids
x x x x x x x x x x x x x x x x x
. . . . . . . . . . . . .
. . . . . .
Cylindrical York Iron
End Cap York
Electric Cylindrical Coil Uniform Axial B Field
Detector
Region
Target
Momentum of Detected Particle
Transverse momentum is
measured by the r Longitudinal
momentum is measured by TOF
Example: The Hadron Hall at J-Example: The Hadron Hall at J-PARCPARC
Put All The Elements Together for Hadronic Beam LinesPut All The Elements Together for Hadronic Beam Lines
50 GeV/c proton beam to primary production target
Secondary lines for +, K+, or p beam
Secondary lines for -, K-, or p beam
Beam line dipoles Dipole spectrometer Quadru-/multi-poles Separators/Mass Slits
Example: Continuous Electron Beam Accelerator Facility (CEBAF)
AB
CCH
NorthLinac
+400MeV
SouthLinac
+400MeV
InjectorWest Arc
East Arc
Example: Continuous Electron Beam Accelerator Facility (CEBAF)
499 MHz, = 120
Optical fiber-
based, RF-pulsed
drive lasers
ARC’s and Hall A/C lines require a series of beam line dipoles to separate passes and reorient the beam direction
Many quadrupoles and multipoles are required to confine the beam profile, remittance, achromatic in momentum at target
Example: Hall C at Jlab (CEBAF)Example: Hall C at Jlab (CEBAF)
SOS
HMS
Quadra-Poles
and DipolesThey form specialized magnetic optical instruments
that analyze the momentum of the scattered charged particles from the experimental target
Coordinate Matrices◦ At target: Xt = (xt, x’t, yt, y’t, 0, p), xt = yt = 0 for point
“target”
◦ At focal plane: Xfp = (xfp, x’fp, yfp, y’fp, L, p), measured at focal plane
◦ x’ and y’ are the angles in dispersion and non-dispersion planes◦ p is momentum in % with respect to the central momentum
Transportation Matrices – Representing the Optical Character of the Spectrometer System◦ M – Forward optical matrix from target to focal plane◦ M-1 – Backward optical matrix from focal plane to target
Matrix Representation of Optical Transportation and Reconstruction◦ Forward: Xfp = M Xt Backward: Xt = M-1 Xfp
◦ p can be found when M (or M-1) and the rest elements in Xt, and Xfp matrices are known, i.e.
Matrix Representation of Magnetic Matrix Representation of Magnetic OpticsOptics
Using Spectrometer at CEBAF as ExampleUsing Spectrometer at CEBAF as Example
p = F(known coordinates) where F is also written in matrixAt CEBAF: x’t = F’(known coordinates and p); y’t = F”(known
coordinates and p)Reconstruction matrices, F, F’, and F”, are all derived from M or M-1
By Polynomial expansion, M is written in series of orders in which the 1st order matrix represents the basic optical nature of a specifically designed spectrometer.
1st order matrix M(6x6): Using 1,2,3,4,5,6 for x, x’, y, y’, L, p
Each element represents an “Amplification” or a “Correlation” from individual Xt to Xfp coordinates
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
MM
11
R11, R12, R13, R14, R15, R16R21, R22, R23, R24, R25, R26R31, R32, R33, R34, R35, R36R41, R42, R43, R44, R45, R46R51, R52, R53, R54, R55, R56R61, R62, R63, R64, R65, R66
Xt
Xfp
Example: ◦ R11 and R33 are xfp/xt and yfp/yt ratios, i.e. image
(or spot size) “Amplifications”
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
Object size (xt)
Illustrated by a simple single lens optics
f
Image size (xfp)
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
Example – Cont.: ◦ R12 and R34 are xfp/x’t and yfp/y’t, i.e.
“Correlation” dependence of image or spot size at FP to the incident angular acceptance x’t and y’t.
Illustrated by a simple single lens optics
f
Point Object
Two different angles: x’t ~ 0 and x’t at maximum
Crossing z over a z
Causing an enlarged and smeared image size xfp and xfp- x’t correlation
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
Example – Cont.: ◦ Element R16 (p/xt) represents the enlarged image size due
to momentum accaptance or “bite”.◦ D/M = R11/R16 defines an important character for a
spectrometer: Momentum Dispersion in unit of cm/%. In principle, the larger D/M the better momentum resolution for a spectrometer.
Illustrated by a simple single lens optics
f
Point Object
Rays with different
“Wavelength”, i.e.
“Momentum”
Rays with lowest
momentum
Rays with highest
momentum
1st order focal plane
Image size due to “Wavelength” or
Momentum acceptance
FP
General considerations of a specific optical system◦ Optimize all first order parameters, including all drift
spaces to achieve specific optical features for a system◦ D/M for required momentum resolution of a spectrometer◦ To achieve Point-to-point focusing, minimize R12 and
R34, i.e. no angular and size correlations: Better momentum resolution.
◦ To achieve Point to Parallel focusing, minimize R22 and R44, i.e. no angular and angular correlations: Better angular acceptance but poor 1st order focusing.
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
p = 0
p = +
p = -
p = +
p = -
General considerations of a specific optical system – Cont.◦ Mixed: Point-to-Point in x but Point-to-Parallel in y. Enhance
resolution by good D/M and x focusing but increase angular acceptance from y’.
◦ Achromatic optics for beam line: R16 0 (or D/M 0)To minimize the beam size and dispersion to connect optical
systems or send beam on experimental target.
◦ Issues to be considered for a spectrometer: Momentum resolution Momentum and angular acceptances Total path length Focal plane size Total spin precession for polarized particle
Matrix Representation of Magnetic Optics Matrix Representation of Magnetic Optics – – Cont.Cont.
x
z
R12 0
yR44 0
First order optics defines the intrinsic and general features of an optical system (a spectrometer or a sub-section of beam line). It is an ideal approximation that analogs to the small lens approximation of optics.
Higher order optics come from non-ideal features of a system, thus represent the “realities”. Inclusion of higher order matrices in M is to reproduce the “Real Optics” of a “Realistic” system. Therefore, it is extremely important and crucial to evaluate and obtain the realistic higher order optics in order for the system to work or achieve the design goal.
The sources contributed to higher order optics:◦ Fringe field effect from each electro-magnetic element◦ Dipole EFB boundary shape and non-parallel of dipoles◦ Asymmetries from symmetric elements◦ Alignment errors and relative rotations between elements◦ Precision of field setting◦ Field interference between elements
Higher Order of Electro-magnetic OpticsHigher Order of Electro-magnetic Optics
Higher order matrix elements:◦ 2nd order: Ri|jk, i, j, k = 1 – 6, e.g. Rx’|x’y’=R2|24
Total of ~63/2 elements◦ 3rd order: Ri|jkl, i, j, k, l = 1 – 6, e.g. Rx’|x’yy’=
R2|234 Total of ~64/22 elements
◦ 4th order: Total of ~65/23 elements◦ …
Number of orders needed: 6 – 10 for accuracyNumber of elements: Often more than
thousand
Higher Order of Electro-magnetic Optics Higher Order of Electro-magnetic Optics – – Cont.Cont.
Magnetic devices and systems are similar as optical components and systems, such as
Quadra-poles Lens and Dipole Prism, …
Magnetic devices and systems can be designed and used based on magnetic optics. Commonly used optics software are:
Transport – Up to third orders, used for basic design, obtain matrix Turtle – Use matrix to evaluate profiles to optimize acceptance Raytrace – Describe field up to fifth orders, use field map to
evaluate “realistic” optics COSY – Combined all above, include higher orders and obtain
matrix
Accurate optical matrix is essential for designing and using the magnetic systems – beam line and spectrometer
Summary of Magnetic OpticsSummary of Magnetic Optics
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