Synchrotron Frequency Spread Research Articles

Mitigation of intensity limitation in the CERN SPS using a double RF system

The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC). Multi-bunch instabilities limit the intensity of the beam that can be accelerated to 450 GeV in the SPS and transferred to the LHC. Without mitigation measures, the threshold of bunch intensity of the longitudinal instability is three times below the nominal bunch intensity of the LHC beam. The High Luminosity LHC project (HL-LHC), which requires a doubling of the nominal bunch intensity, relies on improvement of beam stability in the SPS. A fourth harmonic RF system allows, presently, to stabilize the beam up to nominal LHC intensity. It increases the synchrotron frequency spread inside the bunch, providing more efficient Landau damping of beam instability. However, nonlinearities of the synchrotron frequency distribution inside the bunch pose a limitation on bunch length. This paper explores possible intensity increase in the SPS by studying the effect on beam stability of the voltage ratio between two RF systems. The results are substantiated by beam measurements and particle-tracking simulations. An optimized voltage program of the second RF system during the cycle has been tested in operation and beam stability and the quality have been successfully improved.

Improving Touschek lifetime and synchrotron frequency spread by passive harmonic cavity in the storage ring of SSRF

Beam lifetime of a synchrotron is dominated by Touschek scattering. In the beamline Phase II project of Shanghai synchrotron radiation facility, a passive third harmonic cavity is to be installed for bunch lengthening and instability suppressing. In this paper, the beam dynamics of the cavity is investigated. The parameters of passive operation are optimized to cancel the slope of RF voltage and lengthen the bunches. The Touschek lifetime increases are estimated for optimum and non-optimum voltage flattening. A tolerance of the operation is studied in case that there is a shift on detuning angle. The effect caused by reduction in harmonic voltage generated by lengthened bunch distribution is also estimated using iteration method. An increase in synchrotron frequency spread due to nonlinearity of the voltage giving to the bunch is found by using tracking simulation. This spread can help in damping coupled bunch instability through Landau damping.

Calculations for shortening the bunch length in storage rings using a harmonic cavity

Using the Hefei Light Source phase II project (HLS- II) as an example, a theoretical analysis of shortening the bunch lengths using a higher harmonic cavity (HHC) is given. The threshold voltage of an active HHC and the threshold tuning angle of a passive HHC are first analysed. The optimum tuning angle for the constant detuning scenario and the optimum harmonic voltage for the constant voltage scenario are presented. The calculated results show that the reduced bunch length is about half that of the nominal bunch. The bunch lengths vary from 11 mm at 0.1 A to 7 mm at 0.4 A for the constant detuning scenario, while the bunch lengths are around 7 mm over the beam current range for the constant voltage scenario. In addition, the synchrotron frequency spread is increased. It indicates that HHC may be used to reduce the bunch length and increase the Landau damping of synchrotron oscillations in a storage ring.

Equilibrium bunch density distribution with passive harmonic cavities in a storage ring

The MAX IV storage rings, currently under construction in Lund, Sweden, will use third harmonic cavities operated passively to lengthen the bunches and alleviate collective instabilities. These cavities are an essential ingredient in the MAX IV design concept and are required for achieving the final design goals in terms of stored current, beam emittance, and beam lifetime---such performance challenges are in fact common to all recent ultralow emittance storage ring designs and harmonic cavities are currently under consideration in several laboratories. In this paper, we report on parametric studies comparing different harmonic cavity settings in terms of the resulting bunch length, peak bunch density, and incoherent synchrotron frequency spread for the MAX IV 3 GeV ring. The equilibrium longitudinal bunch density distribution was calculated by establishing a self-consistent equation for the bunch form factor, describing the bunch shape. The calculations are fully self-consistent in the sense that not only the amplitude but also the phase of the waves excited by the beam in the harmonic cavity were assumed to be a function of the bunch shape, which allowed us to explore a wide parameter range not restricted to the region close to the conditions for which the first and second derivatives of the total rf voltage are zero at the synchronous phase. Our results indicate that up to a factor 5 increase in rms bunch length is achievable with a purely passive system for the MAX IV 3 GeV ring while keeping a relatively large harmonic cavity detuning, thus limiting the unavoidable Robinson antidamping rate from the fundamental mode of a passively operated harmonic cavity to values below the synchrotron radiation damping rate. The paper is complemented by results of measurements performed in the MAX III storage ring, which showed good agreement with calculations following the fully self-consistent approach.

Synchrotron frequency spread independence of bunched-beam stochastic cooling at the Fermilab Recycler

It is generally accepted that longitudinal stochastic cooling of bunched beams is not possible without a synchrotron frequency spread. Experiments in the Recycler storage ring (Fermilab) demonstrate the opposite: with an antiproton bunch in a parabolic potential well (no synchrotron frequency spread), the cooling was almost as efficient as in a trapezoidal potential well (with a relative synchrotron frequency spread of {approx} 100%). A possible explanation is that, at Recycler parameters, diffusion processes are sufficient to provide particle mixing.

Methods for suppressing the longitudinal instability of a bunched beam with the help of landau damping

Two methods which have been proposed for increasing the synchrotron frequency spread and consequently stabilizing the longitudinal instability of a bunched beam in a synchrotron include the reduction of the amplitude of the accelerating field to a level ensuring almost complete filling of the separatrix by the bunch and the insertion of an additional accelerating system operating on the highest harmonic of the fundamental frequency of acceleration. In this paper the efficiencies of these methods are compared for the case when the impedance of the accelerator chamber is determined by a narrow-band resonator whose transmission bandwidth is much smaller than the bunch repetition frequency.

Nonlinear perturbation approach to bunch lengthening and blow-up of energy spread

An analytical method is formulated in the nonlinear regime for longitudinal instabilities of a bunched beam in particle accelerators. In the present perturbation approach to the Vlasov equation, the average distribution function of particles which is stationary in the linear theory, is adiabatically changed by the nonlinear term of the second-order in perturbed quantities. A set of two differential equations for the bunch length (or the energy spread) and the perturbation amplitude is given in the absence or presence of the synchrotron frequency spread. Bunch lengthening in electron beams and the overshoot phenomenon in the bunch blow-up in proton beams are investigated systematically.

Longitudinal stability limit for electron bunches in a double RF system

Combination of main and higher harmonic RF cavities, the so called double RF system, produces a zero slope of the RF waveform and realizes a biquadratic RF potential in the synchrotron phase space. The system yields a longer bunch and a very large synchrotron frequency spread. In this paper, a dispersion relation is derived for longitudinal instabilities of electron bunches in the biquadratic RF potential by using the canonical formulation of Suzuki. It is numerically shown that the stability limit is greatly increased by Landau damping.

Stochastic Cooling of Bunched Beams

Numerical simulation studies are presented for transverse and longitudinal stochastic cooling of bunched particle beams. Radio frequency buckets of various shapes (e.g. rectangular, parabolic well, single sinusoidal waveform) are used to investigate the enhancement of phase space cooling by nonlinearities of synchrotron motion. The connection between the notions of Landau damping for instabilities and mixing for stochastic cooling are discussed. In particular, the need for synchrotron frequency spread for both Landau damping and good mixing is seen to be comparable for bunched beams.

Stabilité des oscillations longitudinales d'un faisceau groupe se propageant dans une chambre a vide d'impedance reactive

The longitudinal space-charge force is assumed to vary like the derivative of the longitudinal beam density. Solutions of the linearized Vlasov equation are then given as an expansion of normal modes for the longitudinal phase-space density of a bunched beam. For a given bunch intensity, the method allows calculation of the required synchrotron frequency spread inside a parabolic bunch, in order to stabilize the beam against coherent oscillations by Landau-damping.