Computation and numerical simulation of focused undulator radiation for optical stochastic cooling

Abstract

Optical stochastic cooling (OSC) is a promising technique for the cooling of dense particle beams. Its operation at optical frequencies enables obtaining a much larger bandwidth compared to the wellknown microwave-based stochastic cooling. In the OSC undulator radiation generated by a particle in an upstream "pickup" undulator is amplified and focused at the location of a downstream "kicker" undulator. Inside the kicker, a particle interacts with its own radiation field from the pickup. The resulting interaction produces a longitudinal kick with its value depending on the particles momentum which, when correctly phased, yields to longitudinal cooling. The horizontal cooling is achieved by introducing a coupling between longitudinal and horizontal degrees of freedom. Vertical cooling is achieved by coupling between horizontal and vertical motions in the ring. In this paper, we present formulae for computation of the corrective kick and validate them against numerical simulations performed using a wave-optics computer program.

The design of Optical Stochastic Cooling for IOTA

“…Only the first harmonic of the radiation interacts resonantly with the particle in the kicker undulator 8 . Therefore, we keep only the first harmonic of radiation in further calculations:…”

Optical stochastic cooling with an arc bypass in the Cornell Electron Storage Ring

“…The parameters of the arc bypasses are given in Table I and The PU and KU are helical undulators comprised of 14 periods of length 28 cm, yielding an undulator parameter K ¼ 4.51 and a zero-angle wavelength of 780 nm. Using the formula for the theoretical kick amplitude ΔE found in [14] we obtain a value of 420 meV in the absence of amplification. For this value we have assumed a lossless light transport system consisting of a telescope that provides 1-to-1 imaging along the lengths of the PU and KU, and a normalized angular acceptance γθ m ¼ 3.5, where θ m is the angle subtended by the telescope.…”

“…where M 5;n are elements of the 6 × 6 transfer matrix from PU to KU centers, ΔE is the kick amplitude which is determined by the undulator parameters, particle beam energy, light optics design and OA gain [13,14], while k l ≡ 2π=λ l , where λ l is the zero-angle wavelength of the undulator radiation. The path length from PU to KU through the OSC bypass will depend on the betatron and synchrotron phases and amplitudes of the particle at the PU, as well as the matrix elements M 5;n .…”

Measurements of undulator radiation power noise and comparison with $\textit{ab initio}$ calculations

“…We are considering using our fluctuations measurement apparatus, or an improved variation of it, as a tool for the diagnostics of the Optical Stochastic Cooling (OSC) experiment in IOTA [45][46][47]. In this experiment, the beam emittance will be even smaller and the existing diagnostic tools may not have sufficient resolution.…”