Parallel capable? : yes

Parameter Name | Units | Type | Default | Description |

L | double | 0.0 | length | |

K1 | double | 0.0 | geometric strength | |

TILT | double | 0.0 | rotation about longitudinal axis | |

DX | double | 0.0 | misalignment | |

DY | double | 0.0 | misalignment | |

DZ | double | 0.0 | misalignment | |

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 | |

HSTEERING | long | `0` |
use for horizontal steering? | |

VSTEERING | long | `0` |
use for vertical steering? | |

ORDER | long | `0` |
matrix order | |

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.

Parameter Name | Units | Type | Default | Description |

LAMBDA2M | double | 0.0 | lambda2- fringe integral | |

RADIAL | long | `0` |
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 `FRINGE_TYPE`

parameter.

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
by setting `FRINGE_TYPE`

to ``integrals''. However, this method provides a first-order matrix only.
This is based on publications of D. Zhuo *et al.* [34] and J. Irwin *et
al.* [35], 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 [34]. 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

(62) | |||

(63) | |||

(64) | |||

(65) | |||

(66) |

Normally, the effects are dominated by and .