Beam Instabilities in Very Large Hadron Collider

The Very Large Hadron Collider (VLHC) is a superconducting proton-proton collider with approximately 100 TeV cm and approximately 10 s−1cm−2 luminosity [1]. Currently, beam dynamics in this future accelerator is the subject of intensive studies within the framework of the US-wide VLHC R&D program. This presentation summarizes recent developments in the field. Besides general discussion on relevant VLHC parameters, we consider various beam instabilities and ways to avoid them. Finally, we outline possibilities for theoretical and experimental R&D. 1 COLLIDER PARAMETERS At the energies contemplated, protons and anti-protons behave almost indistinguishably and the VLHC is foreseen as a pp collider. The 150 GeV rapid cycling Fermilab Main Injector produces a beam with the required quality to feed the 3 TeV VLHC Booster accelerator, followed by 50+50 TeV VLHC. The 3 TeV Booster has to be capable of cycling rapidly to fill the VLHC in a reasonable time. The parameters for the machine are not yet all fixed. The amount of freedom varies a lot from parameter to parameter. For example, the beam energy Eb = 50 TeV and the collider luminosity L = 10 s−1cm−2 are fixed a priori by physics considerations [2]. The dipole magnetic field B ≈ 2 T in the case of the low-field (LF) option, andB = 10−14 T for the high-field (HF) option are approximately fixed. Freedom in the dipole field is limited by the choice of magnet technology. Closely related to B, and also technology dependent, is the beam pipe aperture. It varies very little for LF around a = 9 mm (half gap) and varies somewhat more for HF a = 10...20 mm (radius). In the case of HF, the beam aperture is reduced from the physical coil aperture by the necessity of a synchrotron radiation beam screen. The choice of a significantly affects the magnet cost. Another approximately fixed parameter is the bunch spacing. The first order assumption is lbb = 18.9 ns which is the period of the 53 MHz RF system of the Fermilab Main Injector. Larger lbb would increase the number of inelastic interactions/crossing nint ∝ tbb and would give a larger head-on beam-beam tune shift parameter ξ ∝ √ tbb. Both are undesirable, but the total beam power decreases (Pstored ∝ 1/ √ tbb). LHC has tbb ≈ 25 ns. Present day detector triggering technology appears to disfavor bunch spacing of 10 ns or less. Another detector-related requirement is to keep the number of interactions per unit length low (i.e. less than 0.20.3 int/mm would allow vertex recognition). This leads to the desire to have a longer luminous region, and therefore, bunch length. The latter could be as long as σs = 5...10cm rms. One has also to consider the beta-function at the interaction point as an approximately fixed parameter. These considerations limit the minimum value of β∗ to about 15 cm while the maximum value of about 50 cm is determined by the need for high luminosity. Table 1: Zeroth order VLHC parameter list Parameter, units Low-field High-field Proton Energy, Ep, TeV 50 50 Luminosity, L, s−1cm−2 10 10 Injection Energy, Einj, TeV 3 3 Dipole field , B, T 2.0 11.6 Circumference, C , km 520 95 Rev. frequency, f0, Hz 577 3156 Bunch spacing, lbb, ns 18.9 18.9 No. bunches, Nb 9200