A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be related to the beta function and the number of zeros the beta function goes through per turn. The solutions of the equations of motion are found in terms of th...

The described in [1] nonlinear eld components of CESR elements have been included in model structure. Then using program MAD [2] the single beam dynamics was explored. The calculated variation of betatron tunes versus orbit position and the excitation of the nonlinear betatron resonances found with tracking are in good agreement with measurements. The elements given the main contribution into t...

X-ray phase contrast imaging (X-PCi) is a very promising method of dramatically enhancing the contrast of X-ray images of microscopic weakly absorbing objects and soft tissue, which may lead to significant advancement in medical imaging with high-resolution and low-dose. The interest in X-PCi is giving rise to a demand for effective simulation methods. Monte Carlo codes have been proved a valua...

The proposed next generation accelerator and synchrotron light facilities will require active feedback systems to control multi-bunch instabilities. These feedback systems must operate in machines with thousands of circula,ting bunches and with short (2-4 ns) interbunch intervals. The functional requirements for transverse (betatron) and longitudinal (synchrotron) feedback systems are presenti....

We propose to use an electron lens for slow extraction of proton bunches from the Fermilab Main Injector. Negatively charged electron beam colliding with protons causes positive tune shift proportional to the electron current. If the resulting tune satisfies resonance condition, protons move to larger betatron amplitudes as in conventional slow extraction systems. Time variation of the electron...

Here, and in a sequel, we invoke the invariant spin field to provide an in–depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarisation at and near so–called snake resonances in proton storag...

The asymptotic form of the beam break-up instability is computed up to quadrature for an arbitrary wakefield, in the presence of a linear variation in betatron tune from head to tail along the beam. For illustration, the result is applied to a broadband impedance (resistive wall) and a narrow-band impedance (single resonator), and benchmarked against simulation, for parameters of interest in in...

Non-paraxial propagation of ultrashort, high power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the non-adiabatic limit, the coupling of forward Hainan scattering (FRS) and the self-modulation instability (SMI) is...

Emittance growth due to the non-linear beam-beam interaction is a major concern at all hadron colliders. The tunes (i.e. the rotation numbers of the transverse betatron oscillations) are always chosen to avoid low order resonances and the overlap of high order resonances does not create chaotic regions large enough to lead to significant amplitude growth. The dynamics are qualitatively differen...

We have developed a time domain transverse feedback system with the high bandwidth needed to control transverse instabilities when the CESR ee collider is filled with trains of closely spaced bunches. This system is based on parallel digital processors and a stripline driver. It is capable of acting on arbitrary patterns of bunches having a minimum spacing of 14 ns. Several simplifying features...