Non integer harmonic number acceleration of lead ions in the CERN SPS

Abstract

The project to accelerate lead ions in the CERN complex has been successfully completed and physics has begun. In the SPS, the final machine in the chain, the ions are accelerated from an energy of 5.1 GeV/nucleon to 160 GeV/nucleon using the existing 200 MHz travellingwave cavities. The change in revolution frequency during acceleration is much larger than can be accepted by the untuned cavities when operated at constant harmonic number. A technique has been developed to overcome this limitation which takes advantage of the filling time of this type of cavity which is shorter than one turn. Fast amplitude and frequency modulation of the RF waveform allows the cavities to operate at a constant, optimum frequency during the passage of a batch of particles in the structure. This frequency is not a multiple of the revolution frequency and therefore during the gaps between batches the phase of the composite RF waveform is changed to maintain synchronism from turn to turn as the beam accelerates. The technique and hardware are described in detail together with the first operational experience.

10.2172/15011779

“…The longitudinal beam distribution then picks up a head-tail phase and instability may arise [16]. In fact, longitudinal head-tail instability had been observed at the CERN SPS [17] and it was also seen at the Fermilab Tevatron.…”

Some issues on the RF system in the 3 GeV Fermilab pre-booster

“…We follow closely the approach by Boussard [7]. Let the bunch spacing be h b rf buckets or T b in time.…”

Introduction to collective instabilities----longitudinal and transverse

“…Near the resonant frequency ω r /(2π), the longitudinal and transverse impedances can be derived from a RLC-parallel circuit: Another example is the longitudinal impedance for a length of the resistive beam pipe: 18) where b is the radius of the cylindrical beam pipe, σ c the conductivity of the pipe wall, 19) the skin depth at frequency ω/(2π), and µ r the relative magnetic permeability of the pipe wall. The transverse impedance is 20) and is related to the longitudinal impedance by…”

“…The longitudinal beam distribution then picks up a head-tail phase and instability may arise [21]. In fact, longitudinal head-tail instability had been observed at the CERN SPS [20] and it was also seen at the Fermilab Tevatron.…”