ILMATRIX

Parameter Name	Units	Type	Default	Description
L		double	0.0	Length (used for position and time-of-flight computation)
NUX		double	0.0	Horizontal tune
NUY		double	0.0	Vertical tune
NUX1M		double	0.0	First chromatic derivative of the horizontal tune
NUY1M		double	0.0	First chromatic derivative of the vertical tune
NUX2M		double	0.0	Second chromatic derivative of the horizontal tune
NUY2M		double	0.0	Second chromatic derivative of the vertical tune
NUX3M		double	0.0	Third chromatic derivative of the horizontal tune
NUY3M		double	0.0	Third chromatic derivative of the vertical tune
NUX1AX		double	0.0	First amplitude derivative of the horizontal tune wrt Ax
NUY1AX		double	0.0	First amplitude derivative of the vertical tune wrt Ax
NUX1AY		double	0.0	First amplitude derivative of the horizontal tune wrt Ay
NUY1AY		double	0.0	First amplitude derivative of the vertical tune wrt Ay
BETAX		double	0.0	On-momentum horizontal beta function
BETAY		double	0.0	On-momentum vertical beta function
BETAX1M		double	0.0	First chromatic derivative of horizontal beta function
BETAY1M		double	0.0	First chromatic derivative of vertical beta function
ALPHAX		double	0.0	On-momentum horizontal alpha function

An Individualized Linear Matrix for each particle for fast symplectic tracking with chromatic and amplitude-dependent effects

Parameter Name	Units	Type	Default	Description
ALPHAY		double	0.0	On-momentum vertical alpha function
ALPHAX1M		double	0.0	First chromatic derivative of horizontal alpha function
ALPHAY1M		double	0.0	First chromatic derivative of vertical alpha function
ETAX		double	0.0	On-momentum horizontal eta function
ETAPX		double	0.0	On-momentum horizontal eta' function
ETAY		double	0.0	On-momentum vertical eta function
ETAPY		double	0.0	On-momentum vertical eta' function
ETAX1		double	0.0	First chromatic derivative of horizontal eta function
ETAPX1		double	0.0	First chromatic derivative of horizontal eta' function
ETAY1		double	0.0	First chromatic derivative of vertical eta function
ETAPY1		double	0.0	First chromatic derivative of vertical eta' function
ALPHAC		double	0.0	First-order momentum compaction factor
ALPHAC2		double	0.0	Second-order momentum compaction factor

This element allows fast, symplectic tracking of transport through a periodic cell with chromatic and amplitude-dependent tunes, beta functions, and dispersion. This is done by computing a linear matrix for every particle. The linear matrix is composed from Twiss parameters, tunes, dispersion, etc., supplied by the user. The user can also supply selected chromatic and amplitude derivatives of these quantities, which are used to compute the individual particle's beta functions, tune, dispersion, etc., which in turn allows computing the individual particle's linear matrix.

Using this element is very similar to using linear chromatic matrix tracking via the setup_linear_chromatic_tracking command. The advantage is that using ILMATRIX, one can split a ring into segments and place, for example, impedance elements between the segments.

This element was inspired by requests from Y. Chae (APS).