A canonical kick sector dipole magnet.
Parallel capable? : yes
GPU capable? : yes
Back-tracking capable? : yes
Parameter Name | Units | Type | Default | Description |
L | M | double | 0.0 | arc length |
ANGLE | RAD | double | 0.0 | bend angle |
K1 | 1∕M2 | double | 0.0 | geometric quadrupole strength |
K2 | 1∕M3 | double | 0.0 | geometric sextupole strength |
K3 | 1∕M4 | double | 0.0 | geometric octupole strength |
K4 | 1∕M5 | double | 0.0 | geometric decapole strength |
K5 | 1∕M6 | double | 0.0 | geometric 12-pole strength |
K6 | 1∕M7 | double | 0.0 | geometric 14-pole strength |
K7 | 1∕M8 | double | 0.0 | geometric 16-pole strength |
K8 | 1∕M9 | double | 0.0 | geometric 18-pole 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 |
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FINT1 | double | -1 | edge-field integral. If negative, use FINT. |
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FINT2 | double | -1 | edge-field integral. If negative, use FINT. |
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DX | M | double | 0.0 | misalignment |
DY | M | double | 0.0 | misalignment |
DZ | M | double | 0.0 | misalignment |
XKICK | RAD | double | 0.0 | horizontal steering angle (approximate) |
YKICK | RAD | double | 0.0 | vertical steering angle (approximate) |
FSE | double | 0.0 | fractional strength error of all components |
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FSE_DIPOLE | double | 0.0 | fractional strength error of dipole component |
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CSBEND continued
A canonical kick sector dipole magnet.
Parameter Name | Units | Type | Default | Description |
FSE_QUADRUPOLE | double | 0.0 | fractional strength error of quadrupole component |
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ETILT | RAD | double | 0.0 | error rotation about incoming longitudinal axis |
N_KICKS | long | 4 | number of kicks |
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ETILT_SIGN | short | 1 | Sign of ETILT relative to TILT. -1 is the old convention prior to 2020.5 |
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NONLINEAR | short | 1 | include nonlinear field components? |
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SYNCH_RAD | short | 0 | include classical, single-particle synchrotron radiation? |
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EDGE1_EFFECTS | short | 1 | If nonzero, determines the method used to include entrance edge effects. |
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EDGE2_EFFECTS | short | 1 | If nonzero, determines the method used to include exit edge effects. |
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EDGE_ORDER | short | 1 | order to which to include edge effects |
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INTEGRATION_ORDER | short | 4 | integration order (2 or 4) |
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EXPAND_HAMILTONIAN | short | 0 | If 1, Hamiltonian is expanded to leading order. |
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EDGE1_KICK_LIMIT | double | -1 | maximum kick entrance edge can deliver |
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EDGE2_KICK_LIMIT | double | -1 | maximum kick exit edge can deliver |
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KICK_LIMIT_SCALING | short | 0 | scale maximum edge kick with FSE? |
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USE_BN | short | 0 | use b<n> instead of K<n>? |
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EXPANSION_ORDER | short | 0 | Order of field expansion. (0=auto) |
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B1 | 1∕M | double | 0.0 | K1 = b1/rho, where rho is bend radius |
B2 | 1∕M2 | double | 0.0 | K2 = b2/rho |
CSBEND continued
A canonical kick sector dipole magnet.
Parameter Name | Units | Type | Default | Description |
B3 | 1∕M3 | double | 0.0 | K3 = b3/rho |
B4 | 1∕M4 | double | 0.0 | K4 = b4/rho |
B5 | 1∕M5 | double | 0.0 | K5 = b5/rho |
B6 | 1∕M6 | double | 0.0 | K6 = b6/rho |
B7 | 1∕M7 | double | 0.0 | K7 = b7/rho |
B8 | 1∕M8 | double | 0.0 | K8 = b8/rho |
XREFERENCE | M | double | 0.0 | reference x for interpretation of fn values |
F1 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F2 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F3 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F4 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F5 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F6 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F7 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
F8 | double | 0.0 | Fractional normal field error
fn=bn*xr |
|
G1 | double | 0.0 | Fractional skew field error. |
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G2 | double | 0.0 | Fractional skew field error. |
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G3 | double | 0.0 | Fractional skew field error. |
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G4 | double | 0.0 | Fractional skew field error. |
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G5 | double | 0.0 | Fractional skew field error. |
|
CSBEND continued
A canonical kick sector dipole magnet.
Parameter Name | Units | Type | Default | Description |
G6 | double | 0.0 | Fractional skew field error. | |
G7 | double | 0.0 | Fractional skew field error. |
|
G8 | double | 0.0 | Fractional skew field error. | |
ISR | short | 0 | include incoherent synchrotron radiation (quantum excitation)? |
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ISR1PART | short | 1 | Include ISR for single-particle beam only if ISR=1 and ISR1PART=1 |
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SQRT_ORDER | short | 0 | Ignored, kept for backward compatibility only. |
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USE_RAD_DIST | short | 0 | If nonzero, overrides SYNCH_RAD and ISR, causing simulation of radiation from distributions, optionally including opening angle. |
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ADD_OPENING_ANGLE | short | 1 | If nonzero, radiation opening angle effects are added if USE_RAD_DIST is nonzero. |
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PHOTON_OUTPUT_FILE | STRING | NULL | output file for photons, if USE_RAD_DIST=1 |
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PHOTON_LOW_ENERGY_CUTOFF | eV | double | 0.0 | Lower limit of photon energy to output. |
REFERENCE_CORRECTION | short | 0 | If nonzero, reference trajectory is subtracted from particle trajectories to compensate for inaccuracy in integration. |
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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. |
|
CSBEND continued
A canonical kick sector dipole magnet.
Parameter Name | Units | Type | Default | Description |
FSE_CORRECTION | short | 0 | If nonzero, FSE is adjusted to compensate for edge effects when EDGE1_EFFECTS or EDGE2_EFFECTS = 2 |
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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 |
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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 eighth 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.
As of version 28.0 and later, the REFERENCE_CORRECTION feature is available to compensate for errors inherent in the numerical integration of the trajectories. In particular, depending on the number of kicks used, as well as the bending radius and angle, an on-axis particle may emerge from the element with a non-zero trajectory and a path-length error. With REFERENCE_CORRECTION set to a non-zero value, these errors are subtracted from the coordinates of all particles. There are some pitfalls to using this feature: first, one may not realize that the number of kicks is too small to provide good results, since the output trajectory of the central particle will always be (nearly) identically zero. Second, in a magnet with a gradient or other field nonuniformities, a particle may emerge centered on the ideal trajectory yet still see the impact of the gradient, sextupole, etc. For these reasons, this feature should be used with caution and only when the residual trajectory is large enough to cause problems.
Higher-order field components
Normally, one specifies the higher-order components of the field with the Kn, with n = 1 through 8.
The field expansion in the midplane is By(x) = Bo * (1 + ∑
n=18xn). By setting the USE_bN flag to a
nonzero value, one may instead specify the bn parameters, which are defined by the expansion
By(x) = Bo * (1 + ∑
n=18
xn). 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.
The EXPANSION_ORDER parameter controls the order of the expansion of the nonlinear fields, so that terms are limited to xi yj with i + j ≤EXPANSION_ORDER. By default, when EXPANSION\_ORDER=0, the expansion order is set automatically, as follows: If the highest non-zero multipole order (specified by Kn, Bn, Fn, or Gn) is n (with n = 1 being quadruople), then the expansion order is set to n + 3. However, the expansion order is never automatically set to less than 4, unless all the multipole terms are zero, in which case the expansion always yields a constant. Since the number of polynomial terms increases like the square of the expansion order, using many multipole terms can significantly increase run time. The maximum value for the expansion order is 10.
Edge angles and edge effects
Some confusion may exist about the edge angles, particularly the signs. For a sector magnet, we have of course E1=E2=0. For a symmetric rectangular magnet, E1=E2=ANGLE/2. If ANGLE is negative, then so are E1 and E2. To understand this, imagine a rectangular magnet with positive ANGLE. If the magnet is flipped over, then ANGLE becomes negative, as does the bending radius ρ. Hence, to keep the focal length of the edge 1∕f = -tanEi∕ρ constant, we must also change the sign of Ei.
Several models are available for edge (or fringe) effects. Which is used depends on the settings of the EDGE_ORDER, EDGE1_EFFECTS, and EDGE2_EFFECTS parameters EDGE1_EFFECTS controls entrance edge effects while EDGE2_EFFECTS controls exit edge effects, as follows:
Radiation effects
Incoherent synchrotron radiation, when requested with ISR=1, normally uses gaussian distributions for the excitation of the electrons. Setting USE_RAD_DIST=1 invokes a more sophisticated algorithm that uses correct statistics for the photon energy and number distributions. In addition, if USE_RAD_DIST=1 one may also set ADD_OPENING_ANGLE=1, which includes the photon angular distribution when computing the effect on the emitting electron.
Adding errors
When adding errors, care should be taken to choose the right parameters. The FSE and ETILT parameters are used for assigning errors to the strength and alignment relative to the ideal values given by ANGLE and TILT. One can also assign errors to ANGLE and TILT, but this has a different meaning: in this case, one is assigning errors to the survey itself. The reference beam path changes, so there is no orbit/trajectory error. The most common thing is to assign errors to FSE and ETILT. Note that when adding errors to FSE, the error is assumed to come from the power supply, which means that multipole strengths also change.
Splitting dipoles
When dipoles are long, it is common to want to split them into several pieces, to get a better look at the interior optics. When doing this, care must be exercised not to change the optics. elegant has some special features that are designed to reduce or manage potential problems. At issue is the need to turn off edge effects between the portions of the same dipole.
First, one can simply use the divide_elements command to set up the splitting. Using this command, elegant takes care of everything.
Second, one can use a series of dipoles with the same name. In this case, elegant automatically turns off interior edge effects. This is true when the dipole elements directly follow one another or are separated by a MARK element.
Third, one can use a series of dipoles with different names. In this case, one must also use the EDGE1_EFFECTS and EDGE2_EFFECTS parameters to turn off interior edge effects.
CSRCSBEND