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## ALPH

An alpha magnet implemented as a matrix, up to 3rd order. PART is used to split the magnet into halves. XSn and DPn allow momentum filtration at the midpoint.
Parallel capable? : yes
 Parameter Name Units Type Default Description XMAX double 0.0 size of alpha XS1 double 0.0 inner scraper position relative to XMAX XS2 double 0.0 outer scraper position relative to XMAX DP1 double -1 inner scraper fractional momentum deviation DP2 double 1 outer scraper fractional momentum deviation XPUCK double -1 position of scraper puck WIDTHPUCK double 0.0 size of scraper puck DX double 0.0 misalignment DY double 0.0 misalignment DZ double 0.0 misalignment TILT double 0.0 rotation about incoming longitudinal axis PART long 0 0=full, 1=first half, 2=second half ORDER long 0 matrix order [1,3] GROUP string NULL Optionally used to assign an element to a group, with a user-defined name. Group names will appear in the parameter output file in the column ElementGroup

This element provides a matrix-based implementation of an alpha magnet [5]. Matrices up to third order are available [4].

The parameter XMAX determines the size of the alpha, which is related to the gradient in the magnet and the central momentum by

 (9)

The path length of the central particle is .

Because an alpha magnet has large dispersion at the midplane, it is often used for momentum filtration in addition to bunch compression. The dispersion at the center is given by the simple relation

 (10)

To use an alpha magnet for momentum filtration in elegant, one must split the alpha magnet into two pieces. One may then either use the scraper features of the ALPH element or other elements such as SCRAPER or RCOL.

To split an alpha magnet, one uses the PART parameter. E.g.,

! First half, with momentum filter between -5% and +2.5%
AL1: ALPH,XMAX=0.11,PART=1,DP1=-0.05,DP2=0.025
! Second half
AL2: ALPH,XMAX=0.11,PART=2
AL:  LINE=(AL1,AL2)


As just illustrated, the parameters DP1 and DP2 may be used to filter the momentum by providing fractional momentum deviation limits. These are implemented in a physical fashion by computing the corresopnding horizontal position deviations and imposing these as limits on the particle coordinates. One may also do this directly using the XS1 and XS2 parameters, which specify maximum acceptable deviations from the nominal horizontal position. XS1 is the allowed deviation on the low-energy side while XS2 is the allowed deviation on the high-energy side.

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Robert Soliday 2013-05-28