Spectrometer Optics

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Spectrometer Optics

• John J. LeRose

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The Basics
Charged particles moving through static magnetic
fields.
Magnetic Rigidity
Local radius of curvature
Bend Angle
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TRANSPORT formalism
References K.L. Brown, D.C. Carey, C. Iselin
and F. Rothacker, Designing Charged Particle Beam
Transport Systems, CERN 80-04 (1980) K.L. Brown,
SLAC Report-75 (http//www.slac.stanford.edu/cgi-w
rap/getdoc/slac-r-075.pdf) ...
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All trajectories are characterized by their
difference from a reference trajectory
The Central Trajectory
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General Solution of the equation of motion
Each component can be expressed as a Taylor
series around the Central Ray
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The first order transfer matrix
For static magnetic systems with midplane
symmetry
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Some examples
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Matrix for a string of elements is the product of
the individual matrices
Drift L1
Drift L2
Quad L
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(No Transcript)
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Focal Plane
y
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Multipoles
Dipoles
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The equation of motion
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The solution

• 1st order terms drive the higher order terms.
• Higher order field components dont contribute to
  lower order matrix elements.

Coupling to magnetic elements (kn) can be
determined by differentiating
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Going back to focal plane rotation
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Generalized Transfer Tensor and its inverse
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Tools
TRANSPORT Goes up to 3rd order. Multiplies
successive matrices (tensors). Allows the user
to select magnetic parameters to be varied and
properties to be achieved. Good place to start.
COSY Goes up to arbitrary order. (not sure what
this means) Evaluates the transfer tensor for
each element. Multiplies successive matrices
(tensors). (I think) Very powerful, but
difficult. The novice user should be very
careful. (My opinion!)
Raytracing Codes (SNAKE, RAYTRACE, and GEANT)
Integrates the equation of motion particle by
particle through the magnetic system Should be as
good as the magnetic field description. Slow (but
with todays computing power not really a
limitation anymore). Matrices/Tensors are
inferred from the results of the tracings. (e.g.
fit with MUDIFI)