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Spectrometer Optics

Spectrometer Optics. John J. LeRose. a. The Basics. Charged particles moving through static magnetic fields. Magnetic Rigidity. Local radius of curvature. Bend Angle. Arbitrary Trajectory. Reference Trajectory. y. x. r 0. Magnetic Midplane. TRANSPORT formalism. References:

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Spectrometer Optics

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  1. Spectrometer Optics John J. LeRose

  2. a The Basics Charged particles moving through static magnetic fields. Magnetic Rigidity Local radius of curvature Bend Angle

  3. Arbitrary Trajectory Reference Trajectory y x r0 Magnetic Midplane 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-wrap/getdoc/slac-r-075.pdf) …...

  4. x x x z x z y z l = length difference between trajectory and the reference trajectory All trajectories are characterizedby their difference from a reference trajectory* *”The Central Trajectory”

  5. General Solution of the equation of motion: Each component can be expressed as a Taylor series around the Central Ray:

  6. The first order transfer matrix: For static magnetic systems with midplane symmetry:

  7. Generalized Transfer Tensor and its inverse:

  8. Calibrations for normal running • In general one wants to determine the tensor elements, Dijkl, Tijkl, Pijkl, Yijkl • Start from the last best known values • Previous run • Calculated from SNAKE output (new tunes) • Use your favorite polynomial fitting routine • Collect calibration data: • The extent of the calibration data taken depends on how well you need to measure things • Elastic scattering with and without sieve • Delta scans • “Optics” target (segmented in y0) • Optimize the tensors • Pointing survey is also a good idea

  9. Sample Sieve Slit Spectrum

  10. 12C(e,e’) @ 6° and 2 GeV 10-4 (FWHM) all peaks

  11. The End Thanks!

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