10.46 KQUAD—A canonical kick quadrupole.

A canonical kick quadrupole.
Parallel capable? : yes
GPU capable? : yes
Back-tracking capable? : yes






Parameter Name UnitsType Default

Description






L M double 0.0

length






K1 1∕M2double 0.0

geometric strength






TILT RADdouble 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






N_KICKS long 4

number of kicks (rounded up to next multipole of 4 if INTEGRATION_ORDER=4)






HKICK RADdouble 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 short 0

use for horizontal correction?






VSTEERING short 0

use for vertical correction?






SYNCH_RAD short 0

include classical, single-particle synchrotron radiation?






SYSTEMATIC_MULTIPOLES STRINGNULL

input file for systematic multipoles






EDGE_MULTIPOLES STRINGNULL

input file for systematic edge multipoles






RANDOM_MULTIPOLES STRINGNULL

input file for random multipoles






STEERING_MULTIPOLES STRINGNULL

input file for multipole content of steering kicks






SYSTEMATIC_MULTIPOLE_FACTOR double 1

Factor by which to multiply systematic and edge multipoles






KQUAD continued

A canonical kick quadrupole.






Parameter Name UnitsType Default

Description






RANDOM_MULTIPOLE_FACTOR double1

Factor by which to multiply random multipoles






STEERING_MULTIPOLE_FACTOR double1

Factor by which to multiply steering multipoles






MIN_NORMAL_ORDER short -1

If nonnegative, minimum order of systematic and random normal multipoles to use from data files.






MIN_SKEW_ORDER short -1

If nonnegative, minimum order of systematic and random skew multipoles to use from data files.






MAX_NORMAL_ORDER short -1

If nonnegative, maximum order of systematic and random normal multipoles to use from data files.






MAX_SKEW_ORDER short -1

If nonnegative, maximum order of systematic and random skew multipoles to use from data files.






INTEGRATION_ORDER short 4

integration order (2 or 4)






SQRT_ORDER short 0

Ignored, kept for backward compatibility only.






ISR short 0

include incoherent synchrotron radiation (quantum excitation)?






ISR1PART short 1

Include ISR for single-particle beam only if ISR=1 and ISR1PART=1






EDGE1_EFFECTS short 0

include entrance edge effects?






EDGE2_EFFECTS short 0

include exit edge effects?






LEFFECTIVE M double0.0

Effective length. Ignored if non-positive.






I0P M double0.0

i0+ fringe integral






I1P M2 double0.0

i1+ fringe integral






KQUAD continued

A canonical kick quadrupole.






Parameter Name UnitsType Default

Description






I2P M3 double0.0

i2+ fringe integral






I3P M4 double0.0

i3+ fringe integral






LAMBDA2P M3 double0.0

lambda2+ fringe integral






I0M M double0.0

i0- fringe integral






I1M M2 double0.0

i1- fringe integral






I2M M3 double0.0

i2- fringe integral






I3M M4 double0.0

i3- fringe integral






LAMBDA2M M3 double0.0

lambda2- fringe integral






EDGE1_LINEAR short 1

Use to selectively turn off linear part if EDGE1_EFFECTS nonzero.






EDGE2_LINEAR short 1

Use to selectively turn off linear part if EDGE2_EFFECTS nonzero.






EDGE1_NONLINEAR_FACTOR double1

Use to selectively scale nonlinear entrance edge effects if EDGE1_EFFECTS>1






EDGE2_NONLINEAR_FACTOR double1

Use to selectively scale nonlinear exit edge effects if EDGE2_EFFECTS>1






RADIAL short 0

If non-zero, converts the quadrupole into a radially-focusing lens






EXPAND_HAMILTONIAN short 0

If 1, Hamiltonian is expanded to leading order.






TRACKING_MATRIX short 0

If nonzero, gives order of tracking-based matrix up to third order to be used for twiss parameters etc. If zero, 2nd-order analytical matrix is used.






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, EDGE_MULTIPOLES, and RANDOM_MULTIPOLES fields. These specify, respectively, fixed multipole strengths for the body of the element, fixed multipole strengths for the edges of the element, and random multipole strengths for the body of the element. 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 (Npoles - 2)2, so a quadrupole has order 1, a sextupole has order 2, and so on.
  3. Floating point columns normal and skew giving the values for the normal and skew multipole strengths, respectively. (N.B.: previous versions used the names an and bn, respectively. This is still accepted but deprecated) These are defined as a fraction of the main field strength measured at the reference radius, R: fn =      n
KKmnRRm--∕n∕!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 multipole fractional strengths. 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 (Npoles - 2)2. The order must be an even number because of the quadrupole symmetry.
  3. Floating point column normal giving the values for the normal multipole strengths, which are driven by the horizontal steering field. (N.B.: previous versions used the name an for this data. This is still accepted but deprecated) normal is specifies the multipole strength as a fraction fn of the steering field strength measured at the reference radius, R: fn =     n
KKnmRRm-∕∕nm!!, where m = 0 is the order of the steering field and n is the order of the error multipole. The skew values (for vertical steering) are deduced from the normal values, specifically, gn = fn * (-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.

As of version 29.2, this element incorporates the ability to have different values for the insertion and effective lengths. This is invoked when LEFFECTIVE is positive. In this case, the L parameter is understood to be the physical insertion length. Using LEFFECTIVE is a convenient way to incorporate the fact that the effective length may differ from the physical length and even vary with excitation, without having to modify the drift spaces on either side of the quadrupole element.

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 K1 or K12, as appropriate.

For the exit-side fringe field, let s1 be the center of the magnet, s0 be the location of the nominal end of the magnet (for a hard-edge model), and let s2 be a point well outside the magnet. Using K1,he(s) to represent the hard edge model and K1(s) the actual field profile, we define the normalized difference as ˜k(s) = (K1(s) - K1,he(s))∕K1(s1). (Thus, ˜k(s) = K˜(s)∕K0, using the notation of Zhou et al.)

The integrals to be input to elegant are defined as

                        ∫ s0              ∫ s2
                   i- =     ˜k(s)ds   i+ =     ˜k (s)ds                         (60)
                    0    s1           0    s0
             -   ∫ s0                 +   ∫ s2
            i1 =     ˜k(s)(s - s0)ds   i1 =     ˜k (s)(s- s0)ds                  (61)
                ∫ ss10                      ∫s0s2
           i- =     ˜k(s)(s - s0)2ds   i+ =     ˜k (s)(s- s0)2ds                 (62)
            2    s1                   2    s0
            -   ∫ s0           3      +   ∫ s2           3
           i3 =     ˜k(s)(s - s0) ds   i3 =     ˜k (s)(s- s0) ds                 (63)
      ∫ s0  ∫ s0 s1                        s∫0s2  ∫ s2
λ - =     ds    ds′˜k(s)˜k(s′)(s′ - s)  λ+  =     ds    ds′˜k(s)˜k(s′)(s′ - s)     (64)
  2    s1    s                         2    s0    s

Normally, the effects are dominated by i1- and i1+. The script computeQuadFringeIntegrals, packaged with elegant, allows computing these integrals and the effective length if provided with data giving the gradient vs s.

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. If the value is 2, leading-order (cubic) nonlinear effects are included. If the value is 3 or higher, higher order effects are included.

KQUSE