To give you some idea how a scanning session with optimization will look like,
an example is discussed in which the transfer tensor for calculation of
momentum aberations is being optimized. In figure 6.1
the dispersive projection of the focal plane is drawn. Imagine that the
spectrometer momentum setting is such that we observe the elastic peak
of 
Ta(e,e'). The ray with momentum p and 
is
indicated by a dashed line. The position where it crosses the first
wire plane is indicated by 
. Rays with the same momentum and an
infinitesimal small 
cross this wire plane at the same spot and
a relation can be established between momentum and x-position in that wire
plane. However, rays entering the spectrometer collimator with the same
momentum but a larger 
will typically cross the wire plane at a
different spot. In other words, the particle momentum can not be deduced
solely from the dispersive position x, unfortunately all the focal plane
vertex parameters (
, 
, 
) are involved.
It is now our task to describe this deviation 
as a function of the
focal plane vertex, the so-called transfer tensor for the momentum aberrations.
Most spectrometer designs are such that the dependence on
is the most important one.
Figure: Explanation of spherical momentum aberations in the
focal plane of a magnetic spectrometer. The dashed line is made by a
ray with momentum p and 
.
Below an example of a kumac-file is given in which the transfer tensor for
the momentum aberations is being optimized. Seven measurements of an elastic
electron scattering peak have been made at different values of 
.
After the assignment of the different input files and definitions of
cut's, histograms and scatter plots are defined. Especially the
/
plots around the seven elastic peak positions are
of interest since they will reveal the momentum aberration as a function of
. This is followed by a command indicating that at the end
of the event-by-event scan an optimization of the momentum transfer
tensor has to be performed.
define/batch on set/file/output c12_full_conv1.hbook set/file/database db_hrs_7x7 set/file/opt_database db_hrs_7x7_opt set/file/detmap tstand_detmap.config set/file/fit fit_full_conv1.inp ********************** Define cuts ************************ define/cut/1d spec_e.y_tra-1 -0.144 0.144 define/cut/1d spece.x_tra-1 -0.749 0.749 define/cut/1d spece.th_tg-1 -0.07 0.07 define/cut/1d spece.ph_tg-1 -0.030 0.030 define/logical vdchole spece.y_tra-1&&spece.x_tra-1 define/logical accept_e spece.th_tg-1&&spece.ph_tg-1 ********************** spectrometer HRS ******************* set/hitbits (+spece.s1) set/auto_window off set/spectrum/bins/x1 560 set/spectrum/window/x1 -0.07 0.07 spectra/save spec_e.th_tg set/spectrum/bins/x1 320 set/spectrum/window/x1 -0.04 0.04 spectra/save spec_e.ph_tg set/spectrum/bins/x1 500 set/spectrum/window/x1 -0.065 0.065 spectra/save spec_e.dp-1 spectra/save spec_e.dp_kin-1 set/spectrum/window/x1 -0.7 0.7 spectra/save spec_e.x_tra-1 set/ntuple 5000 * ***** dp-aberation plots * set/spectrum/window/x2 -0.5 0.5 set/spectrum/window/x1 -0.06 -0.04 spectra/save spec_e.th_tra/spec_e.dp_kin-1 set/spectrum/window/x1 -0.035 -0.0275 spectra/save spec_e.th_tra/spec_e.dp_kin-2 vdc_hole set/spectrum/window/x1 -0.025 -0.0175 spectra/save spec_e.th_tra/spec_e.dp_kin-3 vdc_hole set/spectrum/window/x1 -0.015 0.015 spectra/save spec_e.th_tra/spec_e.dp_kin-4 vdc_hole set/spectrum/window/x1 0.015 0.0225 spectra/save spec_e.th_tra/spec_e.dp_kin-5 vdc_hole set/spectrum/window/x1 0.0225 0.030 spectra/save spec_e.th_tra/spec_e.dp_kin-6 vdc_hole set/spectrum/window/x1 0.040 0.060 spectra/save spec_e.th_tra/spec_e.dp_kin-7 vdc_hole * ***** optimize momentum resolution in electron spectrometer * calibrate/optimize spec_e.dp_kin * ********************* scanning and output ***************** set/file/header hdr_c12_dpm5.prm file/scan ../monte_car/data_full_conv1_dpm5 MAX=1000 FIRST=1 set/file/header hdr_c12_dpm4.prm file/scan ../monte_car/data_full_conv1_dpm4 MAX=1000 FIRST=1 set/file/header hdr_c12_dpm3.prm file/scan ../monte_car/data_full_conv1_dpm3 MAX=1000 FIRST=1 set/file/header hdr_c12.prm file/scan ../monte_car/data_full_conv1 MAX=1000 FIRST=1 set/file/header hdr_c12_dpp3.prm file/scan ../monte_car/data_full_conv1_dpp3 MAX=1000 FIRST=1 set/file/header hdr_c12_dpp4.prm file/scan ../monte_car/data_full_conv1_dpp4 MAX=1000 FIRST=1 set/file/header hdr_c12_dpp5.prm file/scan ../monte_car/data_full_conv1_dpp5 MAX=1000 FIRST=1 CHOPT=-o * spectra/write quit
Which parts of the tensor should be optimized is indicated in the database,
see appendix B. The first number in each line of the tensor
elements indicates whether it is kept fixed or is being fitted.
A summary of the fitting is listed in a file which name is deduced from
the file name fit_input, f.i. momentum_aber.inp produces
momentum_aber.res.
In figure 3 the result of such an optimization is shown.
On the left side the scatter plot 
/
is shown for
elastic 
Ta(e,e') scattering without any aberration corrections.
On the right is shown the same data but now after correction for momentum
aberations.
Figure: Two scatter plots showing 
versus dp/p for
elastic 
Ta(e,e') scattering. In the one on the left side, no
aberration corrections have been performed on the calculated momentum.
The plot on the right is the result of an optimization as the example
shown in this section.