EMITTANCE COMPENSATION FOR MAGNETIZED BEAMS Page: 4 of 6
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EMITTANCE COMPENSATION FOR MAGNETIZED BEAMS
Jdrg Kewisch, Xiangyun Chang, Brookhaven National Laboratory
Upton, NY 11973, U.S.A.
Emittance compensation is a well established technique
 for minimizing the emittance of an electron beam from
a RF photo-cathode gun. Longitudinal slices of a bunch
have a small emittance, but due to the longitudinal charge
distribution of the bunch and time dependent RF fields
they are not focused in the same way, so that the direction
of their phase ellipses diverges in phase space and the
projected emittance is much larger. Emittance
compensation reverses the divergence. At the location
where the slopes of the phase ellipses coincide the beam
is accelerated, so that the space charge forces are reduced.
A recipe for emittance compensation is given in .
For magnetized beams (where the angular momentum
is non-zero) such emittance compensation is not sufficient
because variations in the slice radius lead to variations in
the angular speed and therefore to an increase of
emittance in the rotating frame. We describe a method and
tools for a compensation that includes the beam
A magnetized beam is a beam with an angular
momentum is non-zero. Such beams are useful for the
generation of flat electron beam, as are needed for the
International Linear Collider, and in an electron cooler,
where the electron temperature inside a solenoid must be
minimized. According to Busch's theorem the
magnetization is (outside solenoid fields) a constant of
motion, i.e. an existing unmagnetized bunch cannot be
magnetized. It must be born that way inside a longitudinal
A RF Photo-cathode electron gun is an efficient device
to produce low emittance bunched electron beams. The
electrons are produced by a pulsed laser beam, which
eliminates the beam choppers used for bunched beams
from DC electron guns. The disadvantage of the RF gun is
that particles in different longitudinal positions of the
bunch do not see the same external and internal fields as
they would in a DC gun. This leads to an apparent
emittance blow up. However, the information of how the
bunch was deformed is still available and the process of
emittance compensation, devised by Serafini and
Rosenzweig , makes it possible to reverse the
emittance blow-up to a large degree.
For this purpose it is useful to cut the bunch into
longitudinal slices and consider their motion. When a
slice leaves the cathode it occupies a horizontal line in the
x-x' phase space. The length of this line is given by the
spot size of the laser and the thickness comes from the
* Work performed under the auspices of the U.S Department of Energy
transverse temperature of the electrons leaving the
As the bunch progresses through the electron gun the
lines rotate in phase space with different speed, depending
on the local current density (space charge) and the time
dependence of the RF fields. The projection of all lines
will then produce a butterfly shape.
The beam is then focused by a solenoid. Because of the
space charge defocusing the position of envelope waist of
each slice depends quadratically on the convergence and it
is possible to minimize the spread of the waist positions
by adjusting the solenoid strength. At the waist the beam
is accelerated to higher energies where the space charge
forces become less important. The phase space lines may
have changed their length, but they are all approximately
horizontal which minimizes the projected emittance.
For a magnetized beam the emittance compensation is
not that simple. The phase space of a slice leaving the
cathode is also a line. This line turns into an ellipse when
the slice leaves the gun solenoid and experiences the
solenoid fringe field. Of course the emittance of the slice
does not change, since the application of another solenoid
will reproduce the initial area in phase space. Here r is the
radius of the slice and the index 0 is used for the field and
radius on the cathode.
Equation 1 shows that the appropriate solenoid field
depends on how much the slice changed the radius. If the
slices of the bunch expand at different rate then a single
field strength can not recover the emittances of all slices.
The magnetization is creating a different kind of
emittance blow-up of the projected emittance. Magnetized
emittance compensation must therefore try to line up the
radius expansion as well as the slopes of the envelopes.
The well known  differential equation for the slice
,, ' , 7 eB r
r"+ 2 r'+ 2 r+ r
2# 27 2# 27 2m c#7Y
- - C + +Y / j r 3
Here r is the radius of the beam,
= E / me+, 8 = v / c , e, is the normalized
thermal emittance and M =< /y(x - y'- y x')>. B is the
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KEWISCH,J. & CHANG, X. EMITTANCE COMPENSATION FOR MAGNETIZED BEAMS, article, June 25, 2007; United States. (https://digital.library.unt.edu/ark:/67531/metadc888127/m1/4/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.