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ACCELERATOR PHYSICS ISSUES OF
A VERY LARGE HADRON COLLIDER
W. Chou, Fermilab,* P.O. Box 500, Batavia, IL 60510, USA
Abstract II. SELECTED ISSUESA Very Large Hadron Collider (VLHC) was proposed for
the post-LHC future.[1] This paper gives a quick survey of
a number of accelerator physics issues based on the infor-
mation obtained from a parameter spreadsheet SSP.[2] The
main technical challenges to build such a machine appear to
be: the large number of events per crossing (in hundreds),
enormous beam stored energy (equivalent to tens tons of
TNT), ground motion (which is particularly harmful when
the synchrotron frequency is in the sub-Hertz range), small
dynamic aperture (due to long filling time), fast growth of
the resistive wall instability (in a fraction of one turn), low
threshold of the single bunch transverse instability (due to
big machine size), strong synchrotron radiation (at a level
close to the LEP) and short radiation damage lifetime, etc.
Possible solutions to some of these problems will also be
discussed.
I. INTRODUCTION
The VLHC is really very large in the low field approach.
Although a coherent parameter list is yet to be developed,
this paper will base its discussions on the following assumed
"Level 0" specifications:Energy per beam E
Luminosity G
Collision
No. Detector
Circumference100 TeV
1 x 1035 cm-2s-1
p-p
1
106 metersBecause the interaction cross section is approximately pro-
portional to 1/M2, where M is the equivalent parton beam
energy, the luminosity should go as E2. Anything below
1035 may be difficult to justify for a 100 TeV machine.
The physics of p-p and p-p is similar at multi-TeV region.
But p-p is easier to reach high luminosity. Besides, p may
be just too expensive to fill up a megameter ring.
Starting from these top level parameters, one can gener-
ate their derivatives by running a spreadsheet. One such
program is the SSP. It was originally written for the for-
mer project SSC, but can easily be modified to serve the
VLHC. The next section will discuss a number of acceler-
ator physics issues based on the output of this program.
*Operated by Universities Research Association Inc. under Con-
tract No. DE-AC02-76CH03000 with the U.S. Department of Energy.A. Events per crossing
The number of events per crossing has a Poisson distri-
bution. The average number n is:n U ies
(1)
in which Uinel is the inelastic pp cross section, and Sb the
bunch spacing. The value of o-inel at 200 TeV center-of-
mass energy is unknown. If the scaling law in the lower
energy regions is employed, it could be estimated at about
150 mb. Thus, the only knob to reduce n is by reducing Sb,
i.e., increasing the number of bunches. But even at a 16
ns bunch spacing, the number of events per crossing could
still reach about 300! This must be a serious challenge to
the detector design.
B. Beam stored energy
This is one of the primary concerns. For G = 1035, Sb =
16 ns, #* = 0.3 m, and eN(95%) = 24r, the current is about
0.6 A per beam. The stored energy of the two beams would
be about 400 GJ, which is equivalent to 90 tons of TNT!
Any accidental beam loss could be a catastrophe.
C. Ground motion
This is another primary concern for a machine of this
size. It has two effects:
1. Relative movement of the magnets:
This may be caused by tides, seismic effects, ground
water level changes, etc., which could lead to mis-
alignment and mis-steering and result in an aperture
problem.
2. Resonance with the synchrotron frequency:
The small slip factor (3 x 10-6) and low revolution
frequency (300 Hz) lead to a very low synchrotron fre-
quency (fraction of 1 Hz). This would make it vul-
nerable to external perturbations, such as the ground
motion, which has large components in this low fre-
quency range.
D. Filling time and dynamic aperture
Assuming two rings in the Tevatron tunnel as the in-
jector, each capable to deliver 2.5 TeV protons (using 10
Tesla dipoles), cycle time 200 seconds. Then the filling
time would be over 9 hours!
Such a long filling time would pose a threat to the dy-
namic aperture at injection. The big dynamic range of the
beam energy (from 2.5 to 100 TeV, a factor of 40) would
imply that the field quality at injection could not be very
good. Assume the error field be similar to that of the SSC
magnets. Then, scaled from the SSC simulation results,
the dynamic aperture would shrink to less than 1 a-!
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Chou, W. Acccelerator Physics Issues of a Very Large Hadron Collider, article, June 1, 1997; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc711989/m1/3/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.