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In high chromaticity circular accelerators, rapid decoherence of the betatron motion of a particle beam can make the measurement of lattice and bunch values, such as Courant-Snyder parameters and betatron amplitude, difficult. A method for reconstructing the momentum distribution of a beam from beam position measurements is presented. Further analysis of the same beam position monitor data allows estimates to be made of the Courant-Snyder parameters and the amplitude of coherent betatron oscillation of the beam. The methods are tested through application to data taken on the linear nonscaling fixed field alternating gradient accelerator, EMMA.

Transfer maps for magnetic components are fundamental to studies of beam dynamics in accelerators. In the work presented here, transfer maps are computed in Taylor form for a particle moving through any specified magnetostatic field by applying an explicit symplectic integrator in a differential algebra code. The techniques developed are illustrated by their application to study the beam dynamics in the electron model for many applications (EMMA), the first nonscaling fixed-field alternating-gradient accelerator ever built. The EMMA lattice has 4 degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Transfer maps may be used to predict efficiently the dynamics in any lattice configuration. The transfer map is represented by a mixed variable generating function, obtained by interpolation between the maps for a set of reference configurations: use of mixed variable generating functions ensures the symplecticity of the map. An optimization routine uses the interpolation technique to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the lattice configuration required to produce the desired dynamical characteristics. These tools are benchmarked against data from the recent EMMA commissioning.

We describe a new technique for low-emittance tuning of electron and positron storage rings. This technique is based on calibration of the beam position monitors (BPMs) using excitation of the normal modes of the beam motion, and has benefits over conventional methods. It is relatively fast and straightforward to apply, it can be as easily applied to a large ring as to a small ring, and the tuning for low emittance becomes completely insensitive to BPM gain and alignment errors that can be difficult to determine accurately. We discuss the theory behind the technique, present some simulation results illustrating that it is highly effective and robust for low-emittance tuning, and describe the results of some initial experimental tests on the CesrTA storage ring.

Injection of fresh bunches into a storage ring can induce jitter in the stored bunches. For machines demanding beams of very low emittance and high stability, such as the damping rings of a future linear collider or the storage rings of a super flavor factory, this could be a potential performance limitation. We present an analysis, for the International Linear Collider (ILC) damping rings, of the transverse jitter induced on the extracted bunches from the jitter on the injected bunches, with the coupling between bunches mediated by the resistive-wall wakefield of the vacuum chamber. We find that it is important to include details of the local transverse focusing around the ring. We consider the impact of the finite thickness of the beam pipe wall, and of nonevaporable getter coating on the inside surface: in the parameter regime of the ILC damping rings, we find that the results are only slightly modified compared to an approximation to the resistive-wall wakefield based on a single-layer wall of infinite thickness. The results from our simulations indicate a tight specification on the jitter of the injected bunches.

We present an analytical and numerical study of the equations of motion for bunches coupled by transverse wakefields. We base our study on a recent lattice design for the damping rings in the baseline configuration of the International Linear Collider. Using the macroparticle model, and assuming resistive wall wakefield coupling, we present numerical results on the time evolution of the multibunch modes. Decay modes display growth after initial decay, and mode amplitudes exhibit high-frequency oscillations. These phenomena are not expected if the beta function is assumed to have a constant, averaged value. We show analytically that they can come from coupling between modes caused by variation of the beta function in a real lattice. The effect is shown to be comparable to the effect of a nonuniform fill pattern and significantly larger than that of the higher-order mode wakefield localized in the rf cavities. Turning to the case of constant beta function, we develop a more complete treatment of the equations of motion. We derive general formulas for the bunch trajectories, and show that such formulas can only be valid in the limit of small wakefield coupling.

The consequences of beam conditioning in four example cases [VISA, a soft x-ray free-electron laser (FEL), LCLS, and a “Greenfield” FEL] are examined. It is shown that in emittance limited cases, proper conditioning reduces sensitivity to the transverse emittance and, furthermore, allows for stronger focusing in the undulator. Simulations show higher saturation power, with gain lengths reduced by a factor of 2 or more. The beam dynamics in a general conditioning system are studied, with “matching conditions” derived for achieving conditioning without growth in the effective emittance. Various conditioning lattices are considered, and expressions derived for the amount of conditioning provided in each case when the matching conditions are satisfied. These results show that there is no fundamental obstacle to producing beam conditioning, and that the problem can be reduced to one of proper lattice design. Nevertheless, beam conditioning will not be easy to implement in practice.