Crystalline beams Page: 4 of 5
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Figure 3. Limits (in l/vp at which an ordered beam
can withstand bending shear as a function of the
linear particle density A. A beam with a single shell
would be in the vicinity of X = 1-2. The points with
error bars represent the results of simulation.
slightly modify these conditions [5]. When the shear is
overcome, and if strong longitudinal cooling is applied, the
beam separates into a set of strings that slip past each
other, and are ordered in a triangular pattern with respect
to each other as shown in figure 4. Such ordering is
characteristic of sheared colloids, but it is not clear
whether the cooling in a beam could ever be sufficientlyp. 4
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4
X:
1k
* is
0
t
4 i
I.
1 r
It
*4
Figure 4. The projection onto a perpendicular plane
of particles in a simulated beam beyond the shear
limit with continuous cooling.strong to produce such a system. Ideally, one would like to
have a beam cooled to a constant angular velocity, where
only the fluctuations in discrete bending elements would
cause a much smaller problem of shear oscillations. The
stability of such systems has been explored in simulations
for relatively modest beams 15].gam
1,
0.1
I I
- +-. SMALL STORAGE RMNS
.~.---f
s is c F
IWeOrdering in Bunched Beams
In a storage ring it is also possible to cool a bunched
beam. This is a case of a three-dimensional confinement
similar to ion traps, but with the longitudinal confining
force much less than the transverse ones. The fact that the
bunching is applied in perhaps only one place in the ring
matters even less than the periodicity of the transverse
focusing lattice, because the relevant time scale is much
longer: the period for synchrotron oscillations. A cold
beam bunch is a very elongated spheroid in the cold
hydrodynamic limit. Simulations show that for discrete
particles the beam will be multi-shelled in the center of a
bunch, as before, gradually thinning out, and eventually
ending in one-dimensional strings at the ends as shown in
figure 5.
Figure 5. Simulation of a beam bunch, roughly 20
cm long and 0.2 mm in radius.
IV. EXPERIMENTAL PROGRESS AND
FUTURE PROSPECTS
Considerable progress has been made in recent years
in the cooling of beams in small storage rings. With laser
cooling, work at the TSR in Heidelberg [6] has reached
longitudinal temperatures in the fractional Kelvin regime,
work at ASTRID in Arhus in the milliKelvin regime [7]
which is in the crystalline regime, however the transverse
temperatures are not known. The suppression of Schottky
noise has been observed for continuous beams at
ASTRID [8] and the space-charge limit in the length of
cooled bunched beam has also been seen [9], along with
related work with electron cooling at Indiana [10]. The
transverse temperature and thus the three-dimensional
ordering are not firmly established, some simulations
indicate that the longitudinal-transverse coupling is strong
for the space-charge limited beams that have apparently
been achieved, and then the transverse temperature could
be similar to the longitudinal one. However better
diagnostics on the transverse properties of the beam are
needed and with these more quantitative measurements
will become possible.
*This work was supported by the U.S. Department of
Energy, Nuclear Physics Division, under contract
W-31-109-ENG-38.
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Schiffer, J.P. Crystalline beams, article, June 1, 1995; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc621779/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.