UNM, Albuquerque, New Mexico
LBNL, Berkeley, California
SLAC, Menlo Park, California
We discuss our progress on integration of the coupled Vlasov-Maxwell equations in 4D. We emphasize Coherent Synchrotron Radiation from particle bunches moving on arbitrary curved planar orbits, with shielding from the vacuum chamber, but also include space charge forces. Our approach provides simulations with lower numerical noise than the macroparticle method, and will allow the study of emittance degradation and microbunching in bunch compressors. The 4D phase space density (PSD) is calculated in the beam frame with the method of local characteristics (PF). The excited fields are computed in the lab frame from a new double integral formula. Central issues are a fast evaluation of the fields and a deep understanding of the support of the 4D PSD. As intermediate steps, we have (1) developed a parallel self-consistent code using particles, where an important issue is the support of the charge density*; (2) studied carefully a 2D phase space Vlasov analogue; and (3) derived an improved expression of the field of a 1D charge/current distribution which accounts for the interference of different bends and other effects usually neglected**. Results for bunch compressors are presented.
* Self Consistent Particle Method to Study CSR Effects in Bunch Compressors, Bassi, et.al., this conference.** CSR from a 1-D Bunch on an Arbitrary Planar Orbit, Warnock, this conference.
LBNL, Berkeley, California
SLAC, Menlo Park, California
UNM, Albuquerque, New Mexico
SLAC, Menlo Park, California
We report on the implementation of a self consistent particle code to study CSR effects on particle bunches traveling on arbitrary planar orbits. Shielding effects are modeled with parallel perfectly conducting plates. The "vertical" charge distribution is assumed to be stationary. The macroscopic Maxwell equations are solved in the lab frame while the equations of motion are integrated in the beam frame interaction picture where the dynamics is governed by the self fields alone. We study different methods to construct a smooth charge density from particles, e.g. gridless nonparametric curve estimation and charge deposition plus filtering. We present numerical results for bunch compressors. In particular, we study different initial distributions. The transverse initial distribution is Gaussian and we study different initial longitudinal distributions: Gaussian, parabolic and nonlinear chirp. A parallel version of the code has been implemented and this will speed up parameter analysis and allow micro-bunching studies.
SLAC, Menlo Park, California
LBNL, Berkeley, California
One of the action items for the damping rings of the International Linear Collider (ILC) is to compute the broad-band impedance and, from it, the threshold to the microwave instability. For the ILC it is essential that the operating current be below threshold. Operating above threshold would mean that the longitudinal emittance of the beam would be increased. More seriously, above threshold there is the possibility of time dependent variation in beam properties (e.g. the "sawtooth" effect) that can greatly degrade collider performance. In this report, we present the status of our study including calculations of: an impedance budget, a pseudo-Green's function suitable for Haissinski equation and instability calculations, and instability calculations themselves.
SLAC, Menlo Park, California
Realistic modeling of coherent synchrotron radiation (CSR) and the space charge force in single-pass systems and rings usually requires at least a two-dimensional (2-D) description of the charge/current density of the bunch. Since that leads to costly computations, one often resorts to a 1-D model of the bunch for first explorations. This paper provides several improvements to previous 1-D theories, eliminating unnecessary approximations and physical restrictions.