Wiggler mapping for 6 wiggler lattice design
Wiggler tracking
For wigglers where a detailed field map is available, such as those computed
with Vector Fields or Mermaid, we have developed three tracking techniques.
The most straightforward is to simply integrate through the tabulated field
values given by the finite element code. This necessarily requires some
interpolation between the grid points and is slow. The output of the FE code,
and the interpolated values are not necessarily consistent with Maxwell's equations
and may in general be rather coarse. As a result, the computed dependence
of kick on displacement is not smooth. And the tracking is not symplectic.
We refer to this as "custom" tracking
Alternatively, we fit a linear combination of analytic functions to the
tabulated values. The functions all satisfy Maxwell and the tracking
is symplectic. Having found the functional form of the fields we can
- Use symplectic integration to track through the analytic form of the field.
The result is symplectic but the calculation is time consuming. This is "symplectic" tracking
- Calculate a taylor series expansion of the phase space map. We can
then track using the taylor coefficients. Although there is some overhead
computing the coefficients, the taylor tracking is very fast and symplectic
to whatever order is desired. This is "taylor" tracking
- Alternatively we can simply integrate through the analytic
form of the fields. The tracking is not symplectic. This is "runge_kutta" tracking
Comparison of custom, symplectic (symp), taylor, and runge_kutta (rk) tracking
X' vs X at y=-20mm,0, and +20mm and Y' vs Y at x=-30mm,0, and +30mm is shown in the
plot for the 3 tracking methods.
- 7 pole wiggler w7-20_37_0237_002800 30-october-2002
- Vector fields data table w7-20_37_fid.table
- Fit parameters are w7-20_37_0237_002800.in
- Peak field is 2.1T.
- Near zero kick at x=0
- plot (PS) angle out vs displacement in (symplectic integration with 250 steps)
- For each of the four tracking methods, there are 6 data files for the
7 pole wigglers labelled as follows
- Files: x'_out vs x_in with y_in = 0 end with "0mm_y.dat"
- Files: x'_out vs x_in with y_in = 20mm end with "20mm_y.dat"
- Files: x'_out vs x_in with y_in = -20 end with "-20mm_y.dat"
- Files: y'_out vs y_in with x_in = 0 end with "0mm_x.dat"
- Files: y'_out vs y_in with x_in = 30mm end with "30mm_y.dat"
- Files: y'_out vs y_in with x_in = -30 end with "-30mm_y.dat"
- plot (PS) angle out vs displacement in (symplectic integration with 100 steps)
- 8pole wiggler w8-20_37_144_0333_005200 5-dec-2002
- Vector fields data table is w8-20_37_144_fid.table
- fit with 134 terms. fit parameters are w8-20_37_144_0333_005200.in
- Peak field is 2.1 T
- plot angle out vs displacement in
- For each of the four tracking methods, there are 6 data files for the
8 pole wigglers labelled in the same way as described above.
- png
and ps angle out vs displacement in including seventh order taylor about zero
- 8pole wiggler w8_t74_g27 (same field table as above) 4-apr-2003
- Vector fields data table is w8-20_37_144_fid.table
- fit with 74 terms. fit parameters are w8_t74_g27.in
- png
and ps angle out vs displacement in including seventh order taylor about zero
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