Nominal longitudinal parameters for the LHC beam in the CERN SPS

Abstract

A proton beam with the basic structure defined by the the LHC requirements, was first available for injection into the SPS in 1998. At the end of 2002, following a significant beam-studies and RF hardware upgrade programme, a beam having both the nominal LHC intensity and the correct longitudinal parameters was obtained at top energy for the first time. This beam, characterised by high local density, must satisfy strict requirements on bunch length, longitudinal emittance and bunch to bunch phase modulation for extraction to the LHC, where only very limited particle losses are acceptable. The problems to be solved came mainly from the high beam loading and microwave and coupled bunch instabilities which led both to beam losses and to unacceptably large longitudinal emittance on the flat top. In this paper the steps taken to arrive at these nominal beam parameters are presented. Large Hadron Collider Project NOMINAL LONGITUDINAL PARAMETERS FOR THE LHC BEAM IN THE CERN SPSP. Baudrenghien, T. Bohl, T. Linnecar, E. Shaposhnikova and J. Tuckmantel, CERN, Geneva, Switzerland Abstract A proton beam with the basic structure defined by the the LHC requirements, was first available for injection into the SPS in 1998. At the end of 2002, following a significant beam-studies and RF hardware upgrade programme, a beam having both the nominal LHC intensity and the correct longitudinal parameters was obtained at top energy for the first time. This beam, characterised by high local density, must satisfy strict requirements on bunch length, longitudinal emittance and bunch to bunch phase modulation for extraction to the LHC, where only very limited particle losses are acceptable. The problems to be solved came mainly from the high beam loading and microwave and coupled bunch instabilities which led both to beam losses and to unacceptably large longitudinal emittance on the flat top. In this paper the steps taken to arrive at these nominal beam parameters are presented.

The magnetic field produced by a protons beam with the three-axial Gauss distribution

“…Formulae (5-7) were substituted suitably to (11)(12)(13) together with (8-10) and (3, 4, 2, 1). As the final result following formulae were received:…”

The magnetic and electric field produced by a proton bunch from the LHC and project of the chamber for investigations in these fields

“…Each bunch has a length of l while the charge density in the bunch is described by the Gauss distribution as having a maximum in the centre [9][10][11]. The transversal dimensions of the bunch are measured in tens of µm.…”

The LHC proton beam in the cern SPS: an update

“…This can be cured for nominal intensity if the emittance is intentionally increased above 0.5 eVs and the 800 MHz is used for Landau damping. As a result, the final emittance has been measured in the range 0.52-0.56 eVs, well below the initial target (< 0.7 eVs) [10].…”

“…Indeed the impedance reduction program was completed [1], [8], each of the four 200 MHz Travelling Wave Cavities were equipped with a feedforward and feedback pair [9] and the 800 MHz system was back in operation, ready to provide extra Landau damping. The steps taken are described in detail in [10].…”

“…The longitudinal damping system needed to cure a low frequency (<2 MHz) dipole mode coupled-bunch instability on the flat bottom [10] is also used to damp the phase and energy error at the injection of the second, third and fourth batch. This is essential to keep the emittance constant for all bunches.…”