Beam-beam studies for the Tevatron Page: 2 of 12
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Half crossing Angle
Figure 2: The relative decrease in luminosity and the head-
on tune shift parameter as a function of the half crossing an-
gle in the 450 plane.
Once the crossing angles are introduced with more than
one hundred bunches in each beam, several beam dynamics
issues become imnportant. Some of them are listed here:
* Single beam issues
Dynamic and physical aperture resulting after off-axis
excursion in IR quads. At the first parasitic interac-
tion which occurs within the quadrupole Q2, the beam
size is about 2mm. Assuming that a minimum of 4Q
separation is necessary, they will be apart by about
8mm. Coupled with the large beam size, this orbit rel-
atively far from the quadrupole axis will make both
beams more sensitive to the nonlinear fields of the
triplet quadrupoles. In addition, orbit perturbations
could lead to larger beam loss due to the tighter phys-
ical aperture in these quadrupoles.
* Beam-beam issues
- Long range interactions at collision. The long-
range interactions distort the tune footprint sig-
nificantly. For example, the zero amplitude tune
shift can lie within the interior of the footprint
and there can be folds within the footprint. In
such cases the tuneshifts at large amplitudes may
be greater than at smaller amplitudes. The im-
pact of these folds on the stability needs to be
investigated. From studies on the SSC and the
LHC , it is known that the amplitude in phase
space where diffusive motion begins is smaller
than the separation between the beams if all the
long-range kicks occur at the same phase. This
diffusive amplitude rdiff can be expressed as
rdiff reP -A
where reP is the average separation between the
beams and A a NpcNP where Npc is the
number of parasitic collisions and NP is the in-
tensity of the strong bunch. In the Tevatron the
long-range kicks occur at different phases so this
expression may not be directly applicable. Nev-
ertheless if there are enough such interactions
where the tails of the beams overlap, diffusive
motion and eventually particle loss may start at
amplitudes less than the average separation.
- Crossing angle induced synchro-betatron reso-
nances. The strength of these resonances is of-
ten characterized by the Piwinski parameter X
as /_l. The typical requirement is that this pa-
rameter should be much less than one for these
resonances to have negligible effect. This would
favour shortening the bunch length. However
resonance strengths cannot increase monotoni-
cally with X because at large crossing angles the
overlap between the beams decreases and the
strength of the beam-beam force and the reso-
nances decrease. Nevertheless, a detailed study
of these resonances and how they combine with
the long-range interactions to affect growth of
particle amplitudes needs to be done.
- Bunch to bunch variations in orbit. A separator
scheme to ensure that collisions of most bunches
are well centered will be essential. Dipole kicks
due to the long-range beam-beam collisions will
also produce significant variations in orbits from
bunch to bunch.
- PACMAN bunches. Bunches which are the fur-
thest away from the center of a train might be in a
different tune region and therefore more suscep-
tible to losses.
- Long-range interactions at injection and during
the ramp. As the beams are ramped to top energy,
the separation helix changes and the separation
is very small at some locations. This could be a
problem when there are nearly two hundred in-
teractions. However, the beams are larger during
the ramp so beam-beam kicks are smaller.
Figure 3 shows the sequence of collisions for different
bunches in a train. The head of the train will meet the head
of the opposing train at the IP and all subsequent long-range
encounters with the other train will be downstream of the IP.
A bunch in the center of the train will experience half of its
long-range encounters upstream of the IP and the remain-
ing encounters downstream of the IP. The last bunch in the
train will have all long-range encounters upstream of the IP.
Figure 4 shows the anti-symmetric optics around the IP. As
a consequence of the anti-symmetry, there is no reflection
symmetry about the center of the train and the strength of
the beam-beam kicks is different for each bunch. In Run Ila
where there will be three trains of 12 bunches each, there
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Sen, Tanaji. Beam-beam studies for the Tevatron, article, June 13, 2000; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc710905/m1/2/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.