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FERMILAB-Conf-01/421 December 2002
Accelerator Physics and Technology Limitations to Ultimate Energy
and Luminosity in Very Large Hadron Colliders
P. Bauer, P. Limon, S. Peggs, M. Syphers, N. Solyak
The following presents a study of the accelerator physics and technology limitations to
ultimate energy and luminosity in very large hadron colliders (VLHCs). The main accelerator
physics limitations to ultimate energy and luminosity in future energy frontier hadron
colliders are synchrotron radiation (SR) power, proton-collision debris power in the
interaction regions (IR), number of events-per-crossing, stored energy per beam and beam-
stability [1]. Quantitative estimates of these limits were made and translated into scaling
laws that could be inscribed into the particle energy versus machine size plane to delimit
the boundaries for possible VLHCs. Eventually, accelerator simulations were performed to
obtain the maximum achievable luminosities within these boundaries. Although this study
aimed at investigating a general VLHC, it was unavoidable to refer in some instances to the
recently studied, [2], 200 TeV center-of-mass energy VLHC stage-2 design (VLHC-2). A more
thorough rendering of this work can be found in [3].
1. Limitations, Scaling Laws and Maximum Luminosities
Table I contains a specification of the assumed limiting parameters of a VLHC for
the purpose of this study. In most cases the numbers are believed to push at the cutting
edge of accelerator technology, some are those of the recently studied VLHC-2. The 10
W/m/beam peak SR power limit, though double that of the VLHC-2 study, corresponds
to the ultimate power level that we believe can be handled by a beam-screen installed in
a 40 mm aperture magnet, with a 20 mm beam stay-clear area [4]. The maximum stored
beam energy was (arbitrarily) set to 10 GJ, which is double that in the VLHC-2 study. The
beam-stability parameters represent the instabilities expected to be the most dominant
in VLHCs [5], namely those of the transverse type such as the resistive wall instability,
Laslett tune-shift and the fast head tail instability (TMCI). Unlike the case of the VLHC-2
study which has higher stability margins, the limiting beam-stability parameters were
specified to be at the stability thresholds, assuming that counter-measures (feedback
systems, ..etc.) would be in place to provide stable beams. The radiation damping time
condition excludes machines that are not SR dominated. SR damping is the only way
Table I: Limiting Parameters of a VLHC.
Parameter Limit
Peak synchrotronradiation power (Wi//beam) 10
P eak IR debris power (kW/beam) 50
Maximum number of events per crossing 60
Maximum beam-beam tune-shift parameter 0.008
Maximum peak beam stored energy(GJ) 10
Ratio of radiation damping and luminositylifetime -peak 0.5
Resistive wall instability rise-time (turns) 1
Initial bunch intensity gven byTMCI criterion NTiCI
Maximum Lasletttune-shift 0.2
Minimum luminosity 103 cm'2s 2
known today to achieve high luminosity. However, the beam stability limitations and the
minimum SR condition are "soft". The VLHC-1 design in the study is an example of a
machine that is prone to beam-instability and without radiation damping. Note,
however, that the peak luminosity in this VLHC-1 is 103' cnfs'. In order to permit a
straight-forward formulation of scaling laws representing the limiting parameters of
Table I, some parameters had to be fixed, all of which are listed in Table Il. Almost all of
them are similar to those in the VLHC-2 study, except for the bunch-spacing time and
3*, for which more aggressive values were chosen. The simulations assumed round
beams. The scaling laws were formulated in terms of the energy per beam, the arc bending radius and theM403
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al., P. Bauer et. Accelerator physics and technology limitations to ultimate energy and luminosity in very large hadron colliders, article, December 5, 2002; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc734205/m1/1/: accessed April 26, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.