A straight magnetic field element using offaxis expansion from an onaxis derivative.
Parallel capable? : yes
GPU capable? : no
Backtracking capable? : no
Parameter Name  Units  Type  Default  Description 
L  M  double  0.0  insertion length 
LFIELD  M  double  1  expected length of the field map for verification purposes only. 
FILENAME  NULL  STRING  NULL  name of file containing derivative data 
Z_COLUMN  NULL  STRING  z  name of longitunidal coordinate column in the data file 
FIELD_COLUMN  NULL  STRING  NULL  name of derivative column in the data file 
ORDER  short  1  order of transverse derivative  
EXPANSION_ORDER  short  0  order of expansion in x and y. If zero, determined by data in file. 

STRENGTH  NULL  double  1  factor by which to multiply field 
TILT  RAD  double  0.0  rotation about longitudinal axis 
DX  M  double  0.0  misalignment 
DY  M  double  0.0  misalignment 
DZ  M  double  0.0  misalignment 
BX  T  double  0.0  add BX*STRENGTH to Bx field 
BY  T  double  0.0  add BY*STRENGTH to By field 
Z_INTERVAL  short  1  input z data is sampled at this interval 

Z_SUBDIVISIONS  short  1  Number of subdivisions of z interval to use in integration 

SYNCH_RAD  short  0  if nonzero, include classical, singleparticle synchrotron radiation 

ISR  short  0  if nonzero, include incoherent synchrotron radiation (quantum excitation) 

PARTICLE_OUTPUT_FILE  STRING  NULL  name of file for phasespace and field output. Use for debugging only! 

BOFFAXE continued
A straight magnetic field element using offaxis expansion from an onaxis derivative.
Parameter Name  Units  Type  Default  Description 
GROUP  string  NULL  Optionally used to assign an element to a group, with a userdefined name. Group names will appear in the parameter output file in the column ElementGroup 

This experimental element simulates transport through a 3D magnetic field constructed from an offaxis expansion. At present, it is restricted to nonbending elements and in fact to quadrupoles and sextupoles.
This method of expanding the fields is prone to corruption by noise, to a much greater degree than the generalized gradient expansion used by BGGEXP. However, it uses data that can very readily be obtained from magnetic measurements with a Hall probe. Users are cautioned to take care in deciding how far to trust the expansion.
For quadrupoles, we use the onaxis gradient g(z) and its z derivatives g^{(n)}(z) The scalar potential can be written
 (30) 
From which we find
 (31) 
 (32) 
and
 (33) 
These equations satisfy Maxwell’s curl equation exactly while satisfying the divergence equation to 10^{th} order. A similar expansion is available in the code for sextupoles.
For quadrupoles, at minimum the zdependent gradient B_{1}(z) must be given, while for sextupoles B_{2}(z) is required. B_{n}(z) is specified in the column named by the FIELD_COLUMN parameter. The names for the columns containing z derivatives of B_{n}(z) are constructed from the name of the primary column. Assume for concreteness that FIELD_COLUMN="Gradient". elegant looks for B_{n}^{(1)}(z) in column GradientDeriv and B_{n}^{(m)}(z) for m > 1 in columns GradientDeriv2, GradientDeriv3, etc. Even if the expansion is limited by the ORDER parameter, all gradients will be used for interpolation with respect to z if the Z_SUBDIVISIONS parameter is larger than 1. The expansion is truncated if the needed columns do not exist in the input file.
The needed derivatives can be obtained using the program sddsderiv, e.g.,
(In this example, we use a SavitzkyGolay filter to compute the first three z derivatives of g(z) using a 7^{th} order fit with 7 points ahead of and behind the evaluation location.) The file gradients.sdds would then be given as the value of FILENAME.
Highorder numerical derivative are of course prone to corruption by measurement noise. Examining the derivatives is strongly recommended to ensure this is not an issue.
BRANCH