The use of gradient sector magnets in Chasman-Green lattice (abstract)

The design of the next generation synchrotron radiation ring is based on a low-emittance storage ring with large numbers of zero-dispersion straight-section for insertion devices. As a candidate, the Chasman-Green lattice is likely to be the most promising to be investigated. In this paper, field gradients and edges which are not perpendicular to the optic axis are proposed to introduce the bending magnets for a low-emittance Chasman-Green lattice. The horizontal beam emittance of a large ring is generally expressed as1 (1) εx=Cqγθ3F(ψ)/Jx, where Cq=3.83×10−13 m, γ=Lorentz factor of the stored beam, θ=bending angle of a dipole magnet, F(ψ)=emittance form factor as a function of the betatron phase advance per half cell ψ, Jx=partition number of the horizontal betatron oscillation. The form factor F(ψ) depends on the lattice structure and is expressed for the symmetrical cell as (2) F(ψ)=(1/ρθ3)(1/ρθ) ∫ρθ0(γη2 +2αηη′+βη′2)ds, where H=γη2+2αηη′+βη′2 is the Courant–Snyder dispersion invariant, ρ is the magnetic radius, α, β, γ are Twiss parameters and η, η′ are the dispersion function and the derivative with s the integral ranges over a bending magnet. We calculate, for examples, F(ψ) for a single lens approximation of equal focal length with ρ=25 and θ=π/32 radian. For the gradient magnet, the gradient parameter K is taken to be −0.05(1/m2) for example, where K is defined as (3) K=(1−n)/2, n=−(ρ/B)(dB/dx). The absolute value of K is restricted to be small to guarantee the damping of energy oscillation. For a nonperpendicular edge, the angle between the edge normal and the beam axis is chosen to be −0.255 radian, for example. The sign conversion is in the usual manner.2 The form factor F(ψ) is calculated as a function of Ψ for the two examples. Another factor to effect the emittance is the partition number Jx as seen in Eq. (1). J x can be written as (4) Jx=1−Kρ2θ2/3, in the first-order calculation. A negative K has little effect to decrease the emittance in cooperation with F(ψ). The horizontal beam emittance is shown to be decreased by the reduction of the factor in two examples in cooperation with the increase of the horizontal damping partition number of the betatron oscillation.