Nonlinear theory of transverse beam echoes

Abstract

Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough. The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.

Accelerator Physics Center at Fermilab : History and Accomplishments (2007-2018)

“…Seminal results were obtain in studies of Integrable non-linear optics (A.Valishev, et al), coherent beam stability (A.Burov, V.Balbekov, K.Y.Ng, et al), Landau damping with electron lenses and space-charge (V.Shiltsev, Yu.Alexahin, et al), beam phase-space manipulations (P.Piot, et al), beam-beam effects (Yu.Alexahin, T.Sen, A.Valishev et al), electron lenses for beam-beam and space-charge compensation and collimation (V.Shiltsev, G.Stancari, et al). See References [4,6,7,8,15,25,29,30,37,46,47,51,54,62,96,98,121,122,132,135,145,157,171,185,194,195] in Appendix E. II.11. Beam physics considerations for far-future colliders: carried out by several APC scientists and covered selected topics of efficient wakefield acceleration, technology and cost challenges of the colliders, channeling acceleration in crystals and carbon nanotubes, etc.…”

Fields and characteristic impedances of dipole and quadrupole cylindrical stripline kickers

“…Stripline kickers (dipole and quadrupole) are often preferred because of their relative simplicity and fast response time. An application of interest where both types of kickers are needed is the generation of beam echoes [3,4,5,6,7]. Detailed designs are usually done with electromagnetic codes which solve for the fields using a variety of numerical schemes, see e.g.…”

Echoes in a Single Quantum Kerr-nonlinear Oscillator

“…Over the years, echoes have been discovered in various physical systems, such as systems consisting of many interacting/non-interacting particles, or single quantum particles. Examples of echoes in many-particle systems include photon echoes [3,4], neutron spin echo [5], cyclotron echoes [6], plasma-wave echoes [7], cold atom echoes in optical traps [8][9][10], echoes in particle accelerators [11][12][13][14], echoes in free-electron lasers [15], and echoes in laser-kicked molecules [16][17][18]. In addition, echoes have been observed in single quantum systems, such as atoms interacting with a quantized mode of electromagnetic radiation [19,20], and in single vibrationally excited molecules [21].…”