CSBEND

A canonical kick sector dipole magnet.

Parameter Name	Units	Type	Default	Description
L	$M$	double	0.0	arc length
ANGLE	$RAD$	double	0.0	bend angle
K1	$1/M^{2}$	double	0.0	geometric quadrupole strength
K2	$1/M^{3}$	double	0.0	geometric sextupole strength
K3	$1/M^{4}$	double	0.0	geometric octupole strength
K4	$1/M^{5}$	double	0.0	geometric decapole strength
E1	$RAD$	double	0.0	entrance edge angle
E2	$RAD$	double	0.0	exit edge angle
TILT	$RAD$	double	0.0	rotation about incoming longitudinal axis
H1	$1/M$	double	0.0	entrance pole-face curvature
H2	$1/M$	double	0.0	exit pole-face curvature
HGAP	$M$	double	0.0	half-gap between poles
FINT		double	0.5	edge-field integral
DX	$M$	double	0.0	misalignment
DY	$M$	double	0.0	misalignment
DZ	$M$	double	0.0	misalignment
FSE		double	0.0	fractional strength error
ETILT		double	0.0	error rotation about incoming longitudinal axis
N_KICKS		long	4	number of kicks
NONLINEAR		long	1	include nonlinear field components?
SYNCH_RAD		long	0	include classical synchrotron radiation?
EDGE1_EFFECTS		long	1	include entrace edge effects?
EDGE2_EFFECTS		long	1	include exit edge effects?
EDGE_ORDER		long	1	order to which to include edge effects
INTEGRATION_ORDER		long	2	integration order (2 or 4)
EDGE1_KICK_LIMIT		double	-1	maximum kick entrance edge can deliver

A canonical kick sector dipole magnet.

Parameter Name	Units	Type	Default	Description
EDGE2_KICK_LIMIT		double	-1	maximum kick exit edge can deliver
KICK_LIMIT_SCALING		long	0	scale maximum edge kick with FSE?
USE_BN		long	0	use b$<$n$>$ instead of K$<$n$>$?
B1	$1/M$	double	0.0	K1 = b1*rho, where rho is bend radius
B2	$1/M^{2}$	double	0.0	K2 = b2*rho
B3	$1/M^{3}$	double	0.0	K3 = b3*rho
B4	$1/M^{4}$	double	0.0	K4 = b4*rho
ISR		long	0	include incoherent synchrotron radiation (scattering)?
SQRT_ORDER		long	0	Order of expansion of square-root in Hamiltonian. 0 means no expansion.

This element provides a symplectic bending magnet with the exact Hamiltonian. For example, it retains all orders in the momentum offset and curvature. The field expansion is available to fourth order.

One pitfall of symplectic integration is the possibility of orbit and path-length errors for the reference orbit if too few kicks are used. This may be an issue for rings. Hence, one must verify that a sufficient number of kicks are being used by looking at the trajectory closure and length of an on-axis particle by tracking. Using INTEGRATION_ORDER=4 is recommended to reduce the number of required kicks.

Normally, one specifies the higher-order components of the field with the K1, K2, K3, and K4 parameters. The field expansion in the midplane is $B_y(x) = B_o * (1 + \sum_{n=1}^4\frac{K_n\rho_o}{n!}x^n)$. By setting the USE_bN flag to a nonzero value, one may instead specify the b1 through b4 parameters, which are defined by the expansion $B_y(x) = B_o * (1 + \sum_{n=1}^4\frac{b_n}{n!}x^n)$. This is convenient if one is varying the dipole radius but wants to work in terms of constant field quality.

Setting NONLINEAR=0 turns off all the terms above K_1 (or b_1) and also turns off effects due to curvature that would normally result in a gradient producing terms of higher order.

Edge effects are included using a first- or second-order matrix. The order is controlled using the EDGE_ORDER parameter, which has a default value of 1. N.B.: if you choose the second-order matrix, it is not symplectic.