J. Gao

BUNCH LENGTHENING AND ENERGY SPREAD INCREASING IN ELECTRON STORAGE RINGS

Abstract A theory of bunch lengthening and energy spread increasing in electron storage rings is established by introducing the concept of collective random excitations. Analytical formulae are established to calculate the equilibrium bunch length and energy spread in the whole current range. Some experimental results are compared with those predicted by the theory and the results compare quite well.

Analytical estimation of the dynamic apertures of circular accelerators

Abstract By considering delta function sextupole, octupole, and decapole perturbations and using difference action-angle variable equations, we find some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2 m pole in general); and their combined effects are derived based on the Chirikov criterion of the onset of stochastic motions. Comparisons with numerical simulations are made, and the agreement is quite satisfactory.

Analytical determination of the coupling coefficient of waveguide cavity coupling systems

Abstract By applying the perturbation method, we show in a general way how to determine the coupling coefficient of a waveguide cavity coupling system and as a special example we derive the analytical expressions of the coupling coefficient for a waveguide cavity coupling system. The term “cavity” in this paper stands for the cavity in both standing and travelling wave structures.

Analytical estimation of the beam–beam interaction limited dynamic apertures and lifetimes in e+e− circular colliders

Abstract Physically speaking, the delta function like beam–beam nonlinear forces at interaction points act as a sum of delta function nonlinear multipoles. By applying the general theory established by J. Gao (Nucl. Instr. and Meth. A 451 (2000) 545), in this paper we examine analytically the beam–beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam–beam limited beam lifetimes and the beam–beam tune shifts are established, which show clearly why experimentally one has always a maximum beam–beam tune shift, ξ y ,max , around 0.045 for e + e − circular colliders, and why one can use round beams to double this value approximately. Comparisons with some machine parameters are given.

On the single bunch longitudinal collective effects in electron storage rings

After giving an analytical expression for the single bunch short range wake potential of a storage ring, we have discussed separately the roles of linear and nonlinear terms of the Taylor expansion of the wake potential on the bunch longitudinal motion. The equations describing bunch lengthening and increase in energy spread are established. Applications to different operating machines are made.

An empirical equation for bunch lengthening in electron storage rings

Abstract In this paper we propose an empirical equation for the bunch lengthening in electron storage rings, where the unique dominating quantity concerning the impedance of a ring is its total longitudinal loss factor, K ||,0 tot , for one turn. The comparisons are made between the analytical and experimental results, and the agreements are extremely well.

Analytical estimates of halo current loss rates in space charge dominated beams

Abstract In this paper, we investigate the dynamical behaviours of a continuous intense charged particle beam in a transport system. It is assumed that fermion particles, such as electron and proton, in the beam follow Fermi–Dirac statistics in the equilibrium state. The halo particles executing stochastic motions due to the envelope oscillation induced nonlinear resonances are investigated. Analytical formulae for the halo current and halo current loss rate on the beam pipe wall are established.

Analytical estimation of the effects of crossing angle on the luminosity of an e+e− circular collider

Abstract Based on the theory established in Nucl. Instr. and Meth. A 463 (2001) 50, in this note we investigate the effects of the crossing angle on the luminosity of an e + e − circular collider. Analytical expression for the luminosity reduction factor is established and compared with simulation result.

3D investigations of the 35 MV tandem Vivitron

Abstract Trying to understand the sparking on the metal bars which connect the discrete electrodes on the same radial position, the 3D program Antigone [1] has been used to model the Vivitron structure (which includes terminal electrode, tank, discrete electrodes (DE), and, of course, metal bars) and to find out the electric field distributions on the surface of the electrodes. 3D calculation shows that the maximum electric field happens on the metal bars instead of the edges of the discrete electrodes so in disagreement with the initial machine design expectation. According to the numerical simulations, 20 MV appears as the limit for the terminal voltage with the present machine structure. Improvements on the metal bars seem necessary if nominal voltage is still envisaged.

On the scaling law of single bunch transverse instability threshold current vs. the chromaticity in electron storage rings

Abstract Based on the single bunch transverse instability theory established by Gao (Nucl. Instr. and Meth. A 416 (1998) 186), it is shown that the functional relation between the instability threshold bunch current and the chromaticity of the machine is I th ∝ ξ c d , with d ≈1.3 and d ≈2.3 at potential well and microwave instability dominated bunch lengthening regimes, respectively. These scaling laws are confirmed by the experimental results from ESRF.