Wiggler mapping

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

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 symplectic. This is "runge_kutta" tracking

Comparison of custom, taylor, and runge_kutta 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_22_dlr0208 1-july-2002
- Vector fields data table w7-20_22_fid.table
- Fit parameters are dlr0208.in.
- Peak field is 2.1T.
- plot
7 pole wiggler w7-20_26_0210_003900 9-august-2002
- Vector fields data table w7-20_26_fid.table
- Fit parameters are dlr0210_003900.in
- Peak field is 2.1T.
- Near zero kick at x=0
- plot (PS) angle out vs displacement in
- plot (PS) displacement out vs displacement in
- plot (PS)y(x) angle out vs x(y) displacement in
7 pole wiggler w7-20_26_0211_001500 1-august-2002
- Vector fields data table w7-20_26_fid.table
- Fit parameters are w7-20_26_0211_001500.in
- Peak field is 2.1T.
- Near zero kick at x=0
- plot angle out vs displacement in
7 pole wiggler w7-20_26_0221_07500 9-august-2002
- Vector fields data table w7-20_26_fid.table
- Fit parameters are w7-20_26_0221_07500.in
- Peak field is 2.1T.
- Near zero kick at x=0
- plot (PS) angle out vs displacement in
- plot (PS) displacement out vs displacement in
- plot (PS) y(x) angle out vs x(y) displacement in
- plot angle out vs displacement in. This plot includes symplectic integration. (added 6-september-2002)
7 pole wiggler w7-20_26_t38 10-september-2002
- Vector fields data table w7-20_26_fid.table
- Fit parameters are w7-20_26_t38.bmad_coefs
- Peak field is 2.1T.
- Near zero kick at x=0
- plot (PS) angle out vs displacement in
- plot (PS) displacement out vs displacement in
- plot (PS) y(x) angle out vs x(y) displacement in
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)
- plot (PS) angle out vs displacement in (symplectic integration with 100 steps)
7 pole wiggler w7-20_37_135_0711_005000 November 18, 2002
- Vector fields data table w7-20_37_135_fid.table
- Fit parameters are w7-20_37_135_0711_005000.in
- Peak field is 1.9T
- Near zero kick at x=0
- plot angle out vs displacement in
7 pole 1.7T w7_20_28_110_0408_001500 8-july-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0408_015500.in
- Peak field is 1.7T
- Order 5 taylor coefficients are computed with 150 steps
- plot
7 pole 1.7T w7_20_28_110_0408_001500 8-july-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0408_015500.in
- Peak field is 1.7T
- Order 5 taylor coefficients are computed with 250 steps
- plot
7 pole 1.7T w7_20_28_110_0408_001500 8-july-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0408_015500.in
- Peak field is 1.7T
- Order 7 taylor coefficients are computed with 150 steps
- plot angle out vs displacement in
- plot displacement out vs displacement in
7 pole 1.7T w7_20_28_110_0411_005800 8-july-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0411_005800.in
- Peak field is 1.7T
- Order 5 taylor coefficients are computed with 250 steps
- plot angle out vs displacement in
7 pole 1.7T w7_20_28_110_0411_005800 24-july-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0411_005800.in
- Peak field is 1.7T
- Order 7 taylor coefficients are computed with 150 steps
- plot angle out vs displacement in
7 pole 1.7T w7_20_28_110_0423_003500 6-august-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0423_003500.in
- Peak field is 1.7T
- Order 5 taylor coefficients are computed with 150 steps
- plot angle out vs displacement in
- plot displacement out vs displacement in
7 pole 1.7T w7_20_28_110_0423_003500 6-august-2002
- Vector fields data table is w7-20_28_110_fid.table
- fit parameters are w7-20_28_110_0423_003500.in
- Peak field is 1.7T
- Order 7 taylor coefficients are computed with 150 steps
- plot angle out vs displacement in
- plot displacement out vs displacement in
8pole wiggler w8-20_25_121_0631_014200 24-nov-2004
- Vector fields data table is w8-20_25_121_fid.table
- fit parameters are w8-20_25_121_0631_014200.in
- Peak field is 1.9 T
- plot angle out vs displacement in, taylor order 3, symp_lie, symp_map, taylor, 11/24/2004
- plot and ps angle out vs displacement in, taylor order 3, symp_lie, symp_map, rk_custom, 11/30/2004
8pole wiggler w8-20_37_144_0333_005200 5-dec-2002
- Vector fields data table is w8-20_37_144_fid.table
- fit parameters are w8-20_37_144_0333_005200.in
- Peak field is 2.1 T
- plot angle out vs displacement in
- png and ps angle out vs displacement in including seventh order taylor about zero
- png Taylor order 1
8pole wiggler w8-20_10_dlr0310 1-july-2002
- Vector fields data table is w8-20_10_fid.table
- fit parameters are dlr0310.in
- Peak field is 2.3T
- plot angle out vs displacement in
- plot displacement out vs displacement in
8 pole 2.1T w8_20_10_0316_006900 22-july-2002
- Vector fields data table is w8-20_10_fid.table
- fit parameters are w8-20_10_0316_006900.in
- Taylor order 3
- Peak field is 2.3T
- plot angle out vs displacement in
8 pole 2.3T w8_20_10_0316_006900 9-august-2002
- Vector fields data table is w8-20_10_fid.table
- fit parameters are w8-20_10_0316_006900.in
- Taylor order 5
- Peak field is 2.1T
- plot angle out vs displacement in
- plot displacement out vs displacement in
- plot (PS ) y(x) angle out vs x(y) displacement in
8 pole 1.7T w8_20_10_114_dlr0503_001600 3-july-2002
- Vector fields data table is w8-20_10_114_fid.table
- fit parameters are dlr0503_001600
- Peak field is 1.7T
- plot
8 pole 1.7T w8_20_12_114_dlr0509_004000 8-july-2002
- Vector fields data table is w8-20_12_114_fid.table
- fit parameters are w8-20_12_114_0509_004000.in
- Peak field is 1.7T
- plot angle out vs displacement in
- plot displacement out vs displacement in
8 pole 2.1T w8_20_20_161_0621_009500 26-august-2002
- Vector fields data table is w8-20_20_161_fid.table
- fit parameters are w8-20_20_161_0621_009500.in
- Taylor order 5
- Peak field is 2.1T
- plot (PS )angle out vs displacement in
- plot (PS )displacement out vs displacement in
- plot (PS ) y(x) angle out vs x(y) displacement in
- plot (PS ) angle out vs displacement in. This plot includes symplectic integration. (6-september-2002)
- plot y(x) angle out vs x(y) displacement in This plot includes symplectic integration.(6-september-2002)
- plot displacement out vs displacement in This plot includes symplectic integration. (6-september-2002)