|TILT||double||0.0||rotation about longitudinal axis|
|FSE||double||0.0||fractional strength error|
|HKICK||double||0.0||horizontal correction kick|
|VKICK||double||0.0||vertical correction kick|
|HCALIBRATION||double||1||calibration factor for horizontal correction kick|
|VCALIBRATION||double||1||calibration factor for vertical correction kick|
||use for horizontal steering?|
||use for vertical steering?|
|EDGE1_EFFECTS||long||1||include entrance edge effects?|
|EDGE2_EFFECTS||long||1||include exit edge effects?|
|FRINGE_TYPE||STRING||fixed-strength||type of fringe: "inset", "fixed-strength", or "integrals"|
|FFRINGE||double||0.0||For non-integrals mode, fraction of length occupied by linear fringe region|
|I0P||double||0.0||i0+ fringe integral|
|I1P||double||0.0||i1+ fringe integral|
|I2P||double||0.0||i2+ fringe integral|
|I3P||double||0.0||i3+ fringe integral|
|LAMBDA2P||double||0.0||lambda2+ fringe integral|
|I0M||double||0.0||i0- fringe integral|
|I1M||double||0.0||i1- fringe integral|
|I2M||double||0.0||i2- fringe integral|
|I3M||double||0.0||i3- fringe integral|
A quadrupole implemented as a matrix, up to 3rd order.
|LAMBDA2M||double||0.0||lambda2- fringe integral|
||If non-zero, converts the quadrupole into a radially-focusing lens|
|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 simulates a quadrupole using a matrix of first, second, or third order.
By default, the element has hard edges and constant field within the
defined length, L. However, this element supports two different methods of implementing fringe fields.
Which method is used is determined by the
The first method is based on a third-order matrix formalism and the assumption of
linear fringe fields. To invoke this method, one specifies ``inset'' or
``fixed-strength'' for the
FRINGE_TYPE parameter and then provides
a non-zero value for FFRINGE. If FFRINGE is zero (the default), then the magnet
is hard-edged regardless of the setting of
FRINGE_TYPE. If FFRINGE is positive, then the magnet has
linear fringe fields of length FFRINGE*L/2 at each end. That
is, the total length of fringe field from both ends combined is FFRINGE*L.
Depending on the value of FRINGE_TYPE, the fringe fields are modeled as contained within the length L (``inset'' type) or extending symmetrically outside the length L (``fixed-strength'' type).
For ``inset'' type fringe fields, the length of the ``hard core'' part of the quadrupole is L*(1-FFRINGE). For ``fixed-strength'' type fringe fields, the length of the hard core is L*(1-FFRINGE/2). In the latter case, the fringe gradient reaches 50% of the hard core value at the nominal boundaries of the magnet. This means that the integrated strength of the magnet does not change as the FFRINGE parameter is varied. This is not the case with ``inset'' type fringe fields.
A more recent implementation of fringe field effects is based on integrals and is invoked
FRINGE_TYPE to ``integrals''. However, this method provides a first-order matrix only.
This is based on publications of D. Zhuo et al.  and J. Irwin et
al. , as well as unpublished work of C. X. Wang (ANL). The fringe field is characterized by
10 integrals given in equations 19, 20, and 21 of . However, the values input into elegant
should be normalized by or , as appropriate.
For the exit-side fringe field, let be the center of the magnet, be the location of the nominal end of the magnet (for a hard-edge model), and let be a point well outside the magnet. Using to represent the hard edge model and the actual field profile, we define the normalized difference as . (Thus, , using the notation of Zhou et al.)
The integrals to be input to elegant are defined as
Normally, the effects are dominated by and .