
About Transport Envelope Fits 

The computer program Transport is very useful because it has some powerful
fit capabilities, which are usually applied when designing new beam lines. For
these cases the starting conditions (e.g. phase space, waist positions)
are assumed being known. Thus the fields and gradients of different
magnetic elements are varied in order to get the beam through the beam line by
fulfilling the designer's boundary conditions.
On an existing beam line with some profile monitors
(eventually harps or beam scanners)
Transport may also be used in a kind of opposite
manner by helping to find out the initial beam conditions (which are usually
unknown or changing from day to day) leading to the measured profile data.
In practice this is done by using the measured beam halfwidths as constraints
and by freeing the appropriate vary codes of the initial beam. If there are
3 or more measured widths per direction, then also the correlation coefficients
(r12 and r34) may be freed. The actual field values (conversion from hardware
DAC value via look up table) for the gradients
of the quadrupole lenses have also to be inserted at the appropriate places.
At the Proton ACS of PSI, measuring the profile widths and insertion of all values is done
since many years automatically with a special computer program (e.g. ENV.COM).
There is also the possibility to measure the beam profiles with several settings
of quadrupoles on the same beam line with the same initial beam conditions and
then performing a simultaneous multi envelope fit.
Why doing an envelope fit at all ? There are several reasons for it:
The better the fit, the more confidant you are to know the parameters of your
beam line. A good fit is a kind of a consistency test. Eventually some wrong
assumptions have to be corrected. (*
Inter and extrapolation between the measured points are acceptable. You do
not have to rely on manually drawn curves, which often are wrong.
It is the simplest way to measure the 87 % projected emittances of the beam
without the interference of a slit system and without reducing the beam
intensity. Another method to measure the emittance of a beam in a nondestructive
manner is the Maximum Entropy Beam Tomography, which gives
interesting possibilities to compare results.
If you know the initial beam conditions, you have the possibility to use
these parameters in a following fit to modify quadrupole settings in order to
adjust waist positions and beam sizes along the beam line. Usually, these newly computed
settings could be tried out online with even the full powered beam staying on. If done so,
a new envelope fit then shows, if the changed settings had the desired effect. If
needed this process may be iterated several times.
Here is a Transport sample input file:
/Sample Envelope Fit/
0
15. 1.0 /MM/ .1 ;
15. 6.0 /PM/ .1 ;
1. 1.5 8.5 1.0 17.0 0. 0. 1.17 /BEAM/ ; (Guess of initial BEAM parameters)
(12. 0.1 0. 0. 0. 0. 0.1 /CORR/ ;) (Correlations r12 and r34 => waist position)
3. 5. ;
5. 0.6 5.4812 125. /Q1/ ; (5.4812 = inserted field value)
3. .5;
5. 0.6 4.9299 125. /Q2/ ; (4.9299 = inserted field value)
3. 4.5 ;
10. 1. 1. 40. .1 /X1/ ; (40.0 = measured xvalue)
10. 3. 3. 5. .1 /Y2/ ; (5.0 = measured yvalue)
3. 5. ;
10. 1. 1. 20. .1 /X3/ ; (20.0 = measured xvalue)
10. 3. 3. 60. .1 /Y4/ ; (60.0 = measured yvalue)
3. 2. ;
SENTINEL
/*PLOT*/
1
1.111100 /BEAM/; (vary x,x',y and y'of BEAM)
(12.100001 /CORR/;) (vary r12 and r34 of CORR)
10. /X1/ ; (constraint)
10. /Y2/ ; (constraint)
10. /X3/ ; (constraint)
10. /Y4/ ; (constraint)
SENTINEL
SENTINEL
In order to visualize these special fit constraints, you have to set the two
parameters 'xMeasurements' and 'yMeasurements' in the 'Display Parameters'
dialog box into the "on" position (MEASX=1.0 and MEASY=1.0 in FOR004.DAT). In
the Graphic Transport display these constraints then appear as little "T"s.
Very often the program does not find a solution to the problem and the fit is
therefore diverging or sticking to the initial values. The reason for this
behavior may be different from case to case and sometimes it is very time
consuming to find a solution to the problem. Very often the guess of the
initial parameters have to be changed for being successful.
Be always aware that fitting with Transport is an art, which demands some
understanding of the physics of the beam line under consideration and the
functioning of the Transport code as well. If you feed the code with unphysical
input, then it may crash with an arithmetic trap (division by zero etc.).
Because of the complexity of the problems to be solved no special algorithms have
been built into the code to prevent such events from happening.
Even with space charge effects being present, the Transport envelope fit may well be
working. This is mainly due to the stochastic fit procedure, which does not require, that the
derivatives of the transfermatrices of all elements along the beam line have to be known.
How well this fit may work has been presented in an article at the
16th International Conference of Cyclotrons and
Their Applications 2001 (Figure 1).
Two more examples for demonstrating the usefulness of Transport envelope fits are given here:
Simultaneous Envelope Fit of two 590 MeV Proton Beam Optics and
TRANSPORT input file of envelope fit for isotope production.
Two hints for improving the quality of envelope fits:

For beam lines with large aperture quadrupoles the fringing field effects should be included
in the transport input file. An example of how to accomplish this is given in the
Compendium of Transport Enhancements (Chapter 1).
Experience with PSI secondary beam lines has shown, that quadrupole settings extracted from model
calculations including fringing field corrections are usually closer to settings found by experimental
tuning for maximum beam transmission than those modelsettings without fringing field corrections.

Experience at PSI has also shown that magnetic quadrupoles with mirror plates acting as field clamps give better
envelope fit results, because the fringing fields of neighboring quadrupoles do practically not overlap.
Therefore the effective lengths (computed from the field gradient along the axis of a single quadrupole)
of the hard edge model used in transport remain independent of the neighboring quadrupole's field value settings.
*)
There is even an additional and better way to check the correctness of all
involved parameters by measuring horizontal and vertical displacements while
deviating the beam offaxis with steering and bending magnets and performing a
beam centroid shift fit with the acquired data
(utilizing the charged particle beam as a "surveying tool").
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Last updated by
Urs Rohrer on 27Feb2006
