Electromagnetic Devices and Optics - PHY743 -

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Electromagnetic Devices and Optics- 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 qE (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

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Magnetic Dipole

• Circular motion of charged particle in uniform B
  field

Circular Motion

• Radius in meter
• P Momentum in GeV/c
• B Field in Tesla (kGauss)

?
?
? is a function of momentum p
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Magnetic Dipole Cont.

• Momentum Dispersion by Magnetic Dipole
• Function of Magnetic Dipole
• Change charged particles trajectory orientation
• Disperse trajectory orientation according to
  momentum

Magnetic Dipole
Optics Prism
Wavelength Dispersion
Momentum Dispersion
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Magnetic Dipole Cont.

• Basic Structure of a Dipole

H Dipole

• Small uniform field area but small size
• Suitable for small particle trajectory
• profile Beam Line Element or
• Special application

• Large uniform field area
• Suitable for large particle trajectory
• profile - Spectrometer

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Magnetic Dipole Cont.

• Effective Field Boundary (EFB)

Bx and Bz are mot zero in fringe field region
I ?BydZ
Boundary shaping outlined by EFB line and
detailed F.F.D. are important parameters for
design and optical description of a dipole
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Magnetic Dipole Cont.

• Important Optical Parameters for a Dipole
• B0 and L (path length)
• ? and ?
• These are first order parameters
• ? and ?
• Shaping of EFBs
• Fringe field description
• These are second and higher order parameters

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Magnetic Quadrupole

• 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

R
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Magnetic Quadrupole Cont.

• It works just like an optical lens
• Quadrupole magnet Magnetic Lens

Quadrupole focuses the charged particles.
Multipoles and quadrupoles are needed to focus
the particles in full phase space
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Magnetic Multipoles

• 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

Others defects Combined asymmetries, imperfect
individual pole location and rotation, and
imperfect pole face curvatures. These are
unavoidable.
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Magnetic Multipoles Cont.

• 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)

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Electric Separator Velocity Separator

• 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)

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Solenoids

• 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
  0.4?IN/L

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Example The Hadron Hall at J-PARCPut All The
Elements Together for Hadronic Beam Lines
Secondary lines for ?, K, or p beam
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Example Continuous Electron Beam Accelerator
Facility (CEBAF)
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Example Continuous Electron Beam Accelerator
Facility (CEBAF)

• ARCs 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

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Example Hall C at Jlab (CEBAF)
HMS
SOS
They form specialized magnetic optical
instruments that analyze the momentum of the
scattered charged particles from the experimental
target
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Matrix Representation of Magnetic OpticsUsing
Spectrometer at CEBAF as Example

• Coordinate Matrices
• At target Xt (xt, xt, yt, yt, 0, ?p), xt
  yt 0 for point target
• At focal plane Xfp (xfp, xfp, yfp, yfp, 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.

?p F(known coordinates) where F is also
written in matrix
At CEBAF xt F(known coordinates and ?p)
yt F(known coordinates and ?p)
Reconstruction matrices, F, F, and F, are all
derived from M or M-1
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Matrix Representation of Magnetic Optics Cont.

• 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

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Matrix Representation of Magnetic Optics Cont.

• Example
• R11 and R33 are xfp/xt and yfp/yt ratios, i.e.
  image (or spot size) Amplifications

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Matrix Representation of Magnetic Optics Cont.

• Example Cont.
• R12 and R34 are xfp/xt and yfp/yt, i.e.
  Correlation dependence of image or spot size at
  FP to the incident angular acceptance xt and
  yt.

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Matrix Representation of Magnetic Optics 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.

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Matrix Representation of Magnetic Optics Cont.

• 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.

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Matrix Representation of Magnetic Optics Cont.

• 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

R44 ? 0
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Higher Order of Electro-magnetic Optics

• 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

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Higher Order of Electro-magnetic Optics Cont.

• Higher order matrix elements
• 2nd order Rijk, i, j, k 1 6, e.g.
  RxxyR224
• Total of 63/2 elements
• 3rd order Rijkl, i, j, k, l 1 6, e.g.
  Rxxyy R2234
• Total of 64/22 elements
• 4th order Total of 65/23 elements
• Number of orders needed 6 10 for accuracy
• Number of elements Often more than thousand

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Summary of Magnetic Optics

• 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