KQUAD

A canonical kick quadrupole, which differs from the MULT element with ORDER=1 in that it can be used for tune correction.
Parallel capable? : yes

Parameter Name	Units	Type	Default	Description
L	$M$	double	0.0	length
K1	$1/M^{2}$	double	0.0	geometric strength
TILT	$RAD$	double	0.0	rotation about longitudinal axis
BORE	$M$	double	0.0	bore radius
B	$T$	double	0.0	pole tip field (used if bore nonzero)
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
HKICK	$RAD$	double	0.0	horizontal correction kick
VKICK	$RAD$	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 correction?
VSTEERING		long	0	use for vertical correction?
N_KICKS		long	4	number of kicks
SYNCH_RAD		long	0	include classical synchrotron radiation?
SYSTEMATIC_MULTIPOLES		STRING	NULL	input file for systematic multipoles
RANDOM_MULTIPOLES		STRING	NULL	input file for random multipoles
STEERING_MULTIPOLES		STRING	NULL	input file for multipole content of steering kicks
INTEGRATION_ORDER		long	4	integration order (2 or 4)
SQRT_ORDER		long	0	Order of expansion of square-root in Hamiltonian. 0 means no expansion.
ISR		long	0	include incoherent synchrotron radiation (scattering)?

A canonical kick quadrupole, which differs from the MULT element with ORDER=1 in that it can be used for tune correction.

Parameter Name	Units	Type	Default	Description
ISR1PART		long	1	Include ISR for single-particle beam only if ISR=1 and ISR1PART=1
EDGE1_EFFECTS		long	0	include entrance edge effects?
EDGE2_EFFECTS		long	0	include exit edge effects?
I0P	$M$	double	0.0	i0+ fringe integral
I1P	$M^{2}$	double	0.0	i1+ fringe integral
I2P	$M^{3}$	double	0.0	i2+ fringe integral
I3P	$M^{4}$	double	0.0	i3+ fringe integral
LAMBDA2P	$M^{3}$	double	0.0	lambda2+ fringe integral
I0M	$M$	double	0.0	i0- fringe integral
I1M	$M^{2}$	double	0.0	i1- fringe integral
I2M	$M^{3}$	double	0.0	i2- fringe integral
I3M	$M^{4}$	double	0.0	i3- fringe integral
LAMBDA2M	$M^{3}$	double	0.0	lambda2- fringe integral
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 kick method based on symplectic integration. The user specifies the number of kicks and the order of the integration. For computation of twiss parameters and response matrices, this element is treated like a standard thick-lens quadrupole; i.e., the number of kicks and the integration order become irrelevant.

Specification of systematic and random multipole errors is supported through the SYSTEMATIC_MULTIPOLES and RANDOM_MULTIPOLES fields. These fields give the names of SDDS files that supply the multipole data. The files are expected to contain a single page of data with the following elements:

1. Floating point parameter referenceRadius giving the reference radius for the multipole data.
2. An integer column named order giving the order of the multipole. The order is defined as $(N_{poles}-2)/2$, so a quadrupole has order 1, a sextupole has order 2, and so on.
3. Floating point columns an and bn giving the values for the normal and skew multipole strengths, respectively. These are defined as a fraction of the main field strength measured at the reference radius, R: $a_n = \frac{K_n r^n / n!}{K_m r^m / m!}$, where $m=1$ is the order of the main field and $n$ is the order of the error multipole. A similar relationship holds for the skew multipoles. For random multipoles, the values are interpreted as rms values for the distribution.

Specification of systematic higher multipoles due to steering fields is supported through the STEERING_MULTIPOLES field. This field gives the name of an SDDS file that supplies the multipole data. The file is expected to contain a single page of data with the following elements:

1. Floating point parameter referenceRadius giving the reference radius for the multipole data.
2. An integer column named order giving the order of the multipole. The order is defined as $(N_{poles}-2)/2$. The order must be an even number because of the quadrupole symmetry.
3. Floating point column an giving the values for the normal multipole strengths, which are driven by the horizontal steering field. an is specifies the multipole strength as a fraction of the steering field strength measured at the reference radius, R: $a_n = \frac{K_n r^n / n!}{K_m r^m / m!}$, where $m=0$ is the order of the steering field and $n$ is the order of the error multipole. The bn values are deduced from the an values, specifically, $b_n = a_n*(-1)^{n/2}$.

The dominant systematic multipole term in the steering field is a sextupole. Note that elegant presently does not include such sextupole contributions in the computation of the chromaticity via the twiss_output command. However, these chromatic effects will be seen in tracking.

Apertures specified via an upstream MAXAMP element or an aperture_input command will be imposed inside this element, with the following rules/limitations:

• If apertures from both sources are present, the smallest is used.
• The apertures are assumed to be rectangular, even if the ELLIPTICAL qualifier is set for MAXAMP.

Fringe field effects are 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 $K_1$ or $K_1^2$, as appropriate.

For the exit-side fringe field, let $s_1$ be the center of the magnet, $s_0$ be the location of the nominal end of the magnet (for a hard-edge model), and let $s_2$ be a point well outside the magnet. Using $K_{1,he}(s)$ to represent the hard edge model and $K_1(s)$ the actual field profile, we define the normalized difference as $\tilde{k}(s) = (K_1(s) - K_{1,he}(s))/K_1(s_1)$. (Thus, $\tilde{k}(s) = \tilde{K}(s)/K_0$, using the notation of Zhou et al.)

The integrals to be input to elegant are defined as

$$i_0^- = \int_{s_1}^{s_0} \tilde{k}(s) ds i_0^+ = \int_{s_0}^{s_2} \tilde{k}(s) ds$$ (14)

$$i_1^- = \int_{s_1}^{s_0} \tilde{k}(s) (s-s_0) ds i_1^+ = \int_{s_0}^{s_2} \tilde{k}(s) (s-s_0) ds$$ (15)

$$i_2^- = \int_{s_1}^{s_0} \tilde{k}(s) (s-s_0)^2 ds i_2^+ = \int_{s_0}^{s_2} \tilde{k}(s) (s-s_0)^2 ds$$ (16)

$$i_3^- = \int_{s_1}^{s_0} \tilde{k}(s) (s-s_0)^3 ds i_3^+ = \int_{s_0}^{s_2} \tilde{k}(s) (s-s_0)^3 ds$$ (17)

$$\lambda_2^- = \int_{s_1}^{s_0} ds \int_s^{s_0} ds\prime \tilde{k}(s) \tilde{k}(s\prime) (s\prime-s) \lambda_2^+ = \int_{s_0}^{s_2} ds \int_s^{s_0} ds\prime \tilde{k}(s) \tilde{k}(s\prime) (s\prime-s)$$ (18)

Normally, the effects are dominated by $i_1^-$ and $i_1^+$.

The EDGE1_EFFECTS and EDGE2_EFFECTS parameters can be used to turn fringe field effects on and off, but also to control the order of the implementation. If the value is 1, linear fringe effects are included.