Synchro-beam interaction

Combined Phenomena of Beam-Beam and Beam Electron Cloudeffects in Circular E+ E- Colliders

“…We propose a calculation algorithm. The algorithm has been used in weak-strong simulation [8]. We treat the col- Figure 8 shows the luminosity variation for new and old methods.…”

A Symplectic Beam-Beam Interaction with Energy Change

“…We have derived the synchro-beam mapping using direct differentiation of U. Note that there is an alternative way to obtain (Ix ,fy , g) based on a calculation of the electric field 10. Although, of course, the resulting mapping is the same, the calculation shows us that our interpretation of the mapping was right.…”

“…In this case, the system is described by (10) and the Hamiltonian for the beam-beam kick can be written as (11) where N * is the number of particles of the strong slice and Q == (Q 1, Q2, ...) represents a set of parameters characterizing the transverse distribution function of the strong slice (12) since the longitudinal extension is ignored, the whole bunch is represented by a single slice. It is well known that U is essentially the electric scalar potential of the strong slice:…”

Applications of parallel computational methods to charged-particle beam dynamics

“…The longitudinal domain decomposition makes use of Hirata slicing [5]. For field calculation, we make use of a convex interpolation method proposed by Ohmi [11] to avoid field discontinuities close to slice boundaries (at the cost of having to do two field calculations for each timestop).…”

“…The code models the beam-beam interactions as a synchro-betatron mapping [5], the beam-beam kick itself is calculated from the Bassetti-Erskine [6] formula, using the Chiarella-Matta-Reichel approximation [7] for the evaluation of the complex error function. In a hadron machine, it is important to avoid all sources of numerical noise; the Chiarella algorithm is implemented as a templated C þ þ function with accuracy selectable at compile time.…”