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In order to compute the Projected Emittance either in x- or in y-direction with a series of
measured beam profiles (non-destructive beam data collection)
there are several methods well suitable for doing it with two more or less known computer codes.
- Computing the 86% Projected Emittance with Graphic Transport:
- From the measured beam profile data collected along the beam line the Sigma-widths have to be computed.
The given Fortran Listing shows how this may be done. The 2*Sigma
values together with the actual quadrupole settings have to be entered in a special Transport input file in order
to perform an Envelope Fit for the actual optics of the beam line.
In a similar manner the 86% Projected Emittance may be found by measuring one or more beam profiles
after a varied set of one or more quadrupoles (with different settings) and by performing a
Multiple Envelope Fit with this set of 2*Sigma data.
- If enough profile data are available, then even information about the momentum spread and the dispersion
trajectory may be extracted with the help of an envelope fit procedure.
A Simultaneous Fit of two 590 MeV proton beam optics is a typical
example for this advanced technique. A necessary condition is that for both sets of quadrupole lens
settings the beam has to be transportable with reasonable low losses along the beam line. Furthermore,
the 2 settings have to differ enough in values for the quadrupole settings and in the measured
profile widths at the corresponding locations.
- The projected emittances in x and y may be read out with the
Ellipse Display routine of the Transport framework,
which draws the beam ellipses in (x/x') and (y/y') and shows among several parameters also
Epsx and Epsy which represent the respective projected emittances. Beam ellipses
and projected emittance in (longitudinal) z-direction are also available if required.
- In order to learn more about projected emittance, beam ellipses etc. in connection with Transport, the SIN-report
Representation of Beam Ellipses for Transport Calculations by Werner Joho is recommended. In this report
all aspects concerning beam ellipses are discussed by an expert.
- Computing the projected emittace by reconstructing the measured beam profiles with a
Maximum Entropy Beam Tomography (MENT) algorithm:
In order to get this procedure working you need to measure at least 3 profiles either in x- or in y-direction.
Their phase advance angles should typically differ from profile to profile by about 60 degrees (3 profiles) or 30 degrees
(5 profiles). At one profile location the phase-angle should be zero (waist, most narrow beam width).
An 86%-value may also be extracted from this method and compared with the projected emittance value
computed with the Transport envelope fit method. More info is given in a
1982 SIN Annual Report about MENT or partially in a
2000 PSI Annual Report. The
downloadable MENT-packages contain several input files with profile data taken from several proton
beam lines at PSI.
Note: By applying both computation methods to the same profile data for gaining the corresponding 86%
projected emittance values, the two values usually agree quite well. But sometimes with imperfect profile
data the 2 values may differ by up to a factor of 2. Then the value extracted with Beam Tomography (MENT) has the tendency
to be larger than the value extracted with Graphic Transport.
Last updated by
Urs Rohrer on 1-Mar-2006
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