An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam motion in a synchrotron. By observing this coherent motion, the optical parameters can be directly measured at the beam position monitor locations. The driven oscillation induced by an AC dipole will generate a phase space ellipse which differs from that of the free oscillation. If not properly accounted for, this difference can lead to a misinterpretation of the actual optical parameters, for instance, of 6% or more in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the linear optics parameters is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. Beam position data taken under the influence of an AC dipole, with this new interpretation in mind, can lead to more precise measurements of the normal Courant-Snyder parameters. This new parameterization of the driven motion is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.
The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be treated perturbatively, the latter requires a robust approach adapted to strongly coupled optics and a parametrization of the linear optics must be performed to explore beam dynamics in such peculiar lattices. This paper reviews the main concepts commonly put forth to describe coupled optics and clarifies the proposed parametrization formalisms. The links b…
The betatron tune, which is defined as the number of transverse oscillations in one turn of a ring accelerator, is one of the most important parameters. An undesired betatron tune increases the amplitude of the transverse oscillation so that many particles are lost from the ring sooner than designed. Since a betatron tune is controlled by the magnetic fields in the ring, the ripple of the magnet current directly displaces the betatron tune from its designated value. We have developed a system that corrects the betatron tune displacement using the measured magnet current at the J-PARC (Japan Pr…
Betatron oscillation is a commonly known phenomenon in laser or beam driven plasma wakefield accelerators. In the conventional model, the plasma wake provides a linear focusing force to a relativistic electron, and the electron oscillates in one transverse direction with the betatron frequency proportional to $1/\sqrtγ$, where $γ$ is the Lorentz factor of the electron. In this work, we extend this model to three-dimensional by considering the oscillation in two transverse and one longitudinal directions. The long-term equations, with motion in the betatron time scale averaged out, are obtained…
Tune identification - i.e. attribution of the spectral peak to a particular normal mode of oscillations - can present a significant difficulty in the presence of strong transverse coupling when the normal mode with a lower damping rate dominates spectra of Turn-by-Turn oscillations in both planes. The introduced earlier phased sum algorithm helped to recover the weaker normal mode signal from the noise, but by itself proved to be insufficient for automatic peak identification in the case of close phase advance distribution in both planes. To resolve this difficulty we modified the algorithm by…
A novel coupling of the transverse betatron motion to the longitudinal microwave instability is studied. Besides the radial coherent dipole mode space charge field, simulation and theoretical studies in this paper show that the longitudinal coherent dipole mode space charge field due to centroid wiggles also plays an important role in the isochronous regime, it induces betatron oscillation frequencies in temporal evolutions of spectra of longitudinal charge densities, radial centroid offsets and coherent energy deviations of local centroids.
We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring. The transversal betatron oscillation formula of the bunch is also given. The latter is the generalization of the Farley's pitch correction \cite{Farley}, including radial oscillation as well as vertical one. Some useful formulae for muon storage ring are discussed in appendix.
In a lepton storage ring of very high energy (e.g. in the $e^+e^-$ Higgs factory) synchrotron radiation from quadrupoles constrains transverse dynamic aperture even in the absence of any magnetic nonlinearities. This was observed in tracking for LEP and the Future Circular $e^+e^-$ Collider (FCC-ee). Here we describe a new mechanism of instability created by modulation of the particle energy at the double betatron frequency by synchrotron radiation in the quadrupoles. Energy modulation varies transverse focusing strength at the same frequency and creates a parametric resonance of the betatron …
Ultrafast high-brightness X-ray pulses have proven invaluable for a broad range of research. Such pulses are typically generated via synchrotron emission from relativistic electron bunches using large-scale facilities. Recently, significantly more compact X-ray sources based on laser-wakefield accelerated (LWFA) electron beams have been demonstrated. In particular, laser-driven sources, where the radiation is generated by transverse oscillations of electrons within the plasma accelerator structure (so-called betatron oscillations) can generate highly-brilliant ultrashort X-ray pulses using a c…
The measurement of the betatron tunes in a circular accelerator is of paramount importance due to their impact on beam dynamics. The resolution of the these measurements, when using turn by turn (TbT) data from beam position monitors (BPMs), is greatly limited by the available number of turns in the signal. Due to decoherence from finite chromaticity and/or amplitude detuning, the transverse betatron oscillations appear to be damped in the TbT signal. On the other hand, an adequate number of samples is needed, if precise and accurate tune measurements are desired. In this paper, a method is pr…
In the cavitation regime of plasma-based accelerators, a population of high-energy electrons tailing the driver can undergo betatron motion. The motion results in X-ray emission, but the brilliance and photon energy are limited by the electrons' initial transverse coordinate. To overcome this, we exploit parametrically unstable betatron motion in a cavitated, axially modulated plasma. Theory and simulations are presented showing that the unstable oscillations increase both the total X-ray energy and average photon energy.
The effects of electron clouds on positively-charged beams have been an active area of research in recent years at particle accelerators around the world. Transverse beam-size blow-up due to electron clouds has been observed in some machines, and is considered to be a major limiting factor in the development of higher-current, higher-luminosity electron-positron colliders. The leading proposed mechanism for beam blow-up is the excitation of a fast head-tail instability due to short-range wakes within the electron cloud. We present here observations of betatron oscillation sidebands in bunch-by…
Specific velocities of particles circulating in a storage ring can lead to betatron resonances at which static perturbations of the particles' orbit yield large transverse (betatron) oscillations. We have observed betatron resonances in an ultracold-atom storage ring by direct observation of betatron motion. These resonances caused a near-elimination of the longitudinal dispersion of atomic beams propagating at resonant velocities, an effect which can improve the performance of atom interferometric devices. Both the resonant velocities and the strength of the resonances were varied by delibera…
Synchrotron radiation of relativistic electrons in storage rings naturally leads to the process of damping of betatron oscillations. Damping time and transverse beam emittance can be reduced by wigglers or undulators while the beam parameters are still well defined by the common radiation integrals, based on the properties of synchrotron radiation. However, the quantum excitation of betatron oscillations in principle can be considerably reduced if an electron radiation occurs due to the Thomson scattering in the periodic electromagnetic field. After a brief introduction we compare radiation pr…
In an ideal accelerator, the single-particle dynamics can be decoupled into transverse motion -- the betatron oscillations -- and longitudinal motion -- the synchrotron oscillations. Chromatic and dispersive effects introduce a coupling between these dynamics, the so-called synchro-betatron coupling. We present an analysis of the fully coupled dynamics over a single synchrotron oscillation that leads to an averaged invariant with synchro-betatron coupling in a generic lattice. We apply this analysis to two problems: first, a toy lattice where the computations are analytically tractable, then a…
A new scheme for the two-dimensional cooling of ion beams in storage rings is suggested in which ions interact with a counterpropagating broad-band laser beam. The interaction region in the direction of the ion movement is much less then the wavelength of the ion betatron oscillations. The laser beam in the orbit plane has sharp flat edge directed to the ion beam and the width of the laser beam of the order of the ion beam width. Laser beam radial position is being displaced with some velocity at first from inside and then from outside to the ion beam and decreases both betatron and synchrotro…
The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful renormalization group method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the Henon map is also presented. This calculation represents the first successful application of a renormalization gr…
This work demonstrates that two systematic errors, coherent betatron oscillations (CBO) and muon losses can be reduced through application of radio frequency (RF) electric fields, which ultimately increases the sensitivity of the muon $g-2$ experiments. As the ensemble of polarized muons goes around a weak focusing storage ring, their spin precesses, and when they decay through the weak interaction, $μ^+ \rightarrow e^+ ν_e \bar{ν_μ}$, the decay positrons are detected by electromagnetic calorimeters. In addition to the expected exponential decay in the positron time spectrum, the weak decay as…
Turn-By-Turn (TBT) betatron oscillation data is a very powerful tool in studying machine optics. Hundreds and thousands of turns of free oscillations are taken in just few tens of milliseconds. With beam covering all positions and angles at every location TBT data can be used to diagnose focusing errors almost instantly. This paper describes a new approach that observes focusing error collectively over all available TBT data to find the optimized quadrupole strength, one location at a time. Example will be shown and other issues will be discussed.
A system for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations in the Tevatron is described. It is based on the signal from a single beam-position monitor located in a region of the ring with large amplitude functions. The signal is digitized over a large number of turns and Fourier-analyzed offline with a dedicated algorithm. To enhance the signal, band-limited noise is applied to the beam for about 1 s. This excitation does not adversely affect the circulating beams even at high luminosities. The device has a response time of a few seconds, a frequency resolu…
Though a straight drift-quadrupole system can not be made an achromat, there exists an example of a bend-free drift-quadrupole system which can transport certain incoming beam ellipses without introducing first-order chromatic distortions. In this paper we show that such a possibility is not a rare special case, but a general property. For every drift-quadrupole system there exists an unique set of Twiss parameters, which will be transported through that system without first order chromatic distortions. Moreover, we prove that at the same time these Twiss parameters minimize the absolute value…
By tailoring the wavefront of the laser pulse used in a laser-wakefield accelerator, we show that the properties of the x-rays produced due to the electron beam's betatron oscillations in the plasma can be controlled. By creating a wavefront with coma, we find that the critical energy of the synchrotron-like x-ray spectrum can be significantly increased. The coma does not substantially change the energy of the electron beam, but does increase its divergence and produces an energy-dependent exit angle, indicating that changes in the x-ray spectrum are due to an increase in the electron beam's o…
A system was developed for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations based on the signal from a single beam-position monitor (BPM) located in a region of the ring with large amplitude functions. The signal is digitized over a large number of turns and Fourier-analyzed offline with a dedicated algorithm. To enhance the signal, the beam is excited with band-limited noise for about one second, and this was shown not to significantly affect the circulating beams even at high luminosity. The system is used to measure betatron tunes of individual bunches and …
In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as canonical McMillan map. Both of them are simplest symmetric McMillan maps with only one intrinsic parameter, the trace of the Jacobian at the fixed point. While these dynamical systems have numerous of applications and are used in many areas of math and physics, some of their dynamical properties have not been described yet. We fulfill the gap and provide complete description of all stable trajectories including para…
Cavity-based x-ray free-electron lasers (CBXFEL) will allow use of optical cavity feedback to support generation of fully coherent x-rays of high brilliance and stability by electrons in undulators. CBXFEL optical cavities comprise Bragg-reflecting flat crystal mirrors, which ensure x-rays circulation on a closed orbit, and x-ray refractive lenses, which stabilize the orbit and refocus the x-rays back on the electrons in the undulator. Depending on the cavity design, there are tens of degrees of freedom of the optical elements, which can never be perfectly aligned. Here, we study signatures of…
