PARTICLE TRACKING AND BUNCH POPULATION IN TRAFIC-4 2.0

Coherent Synchrotron Radiation (CSR) plays an important role in the design of accelerator components with high peak currents and small bending radii, such as magnetic bunch compressors, wigglers, and compact storage rings. The code TraFiC4 has been developed to design such elements[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] ; it simulates CSR effects from first principles. We present a re-write of the tracking and user interface components of TraFiC4 . Extensions and corrections include: expanded input language; generalized bunch populations (rectangular, Gaussian, user-specified function); new element types; truly three-dimensional dynamics (i. e., the restriction to a single plane of motion has been abandoned), vastly expanded documentation; documented C++ class interface; and improved dynamic load-balancing for parallel computers. FULLY THREE-DIMENSIONAL TREATMENT Generalized Local Coordinates TraFiC4 now handles fully three-dimensional problems; there is no limitation to one plane of movement. This makes it necessary to choose a more general system of local coordinates: while TraFiC4 does all of its tracking in laboratory coordinates, as it needs to store the history of all particles to calculated the retarded fields, accelerator physics is usually done in a co-moving frame. As a local system, we choose the Frenet coordinate system associated with an orbit particle’s trajectory r0(s), where s is the arc length. The co-moving frame is spanned by r′ 0(s), r ′′ 0 (s), and r ′ 0(s) × r′′ 0 (s); the associated normalized vectors are t(s), n(s), and b(s). Given another particle trajectory r(s(t)), parametrized by the lab time t, we find that particle’s local coordinates x, y, l by r(s(t)) = x n(s(t) + l) + y b(s(t) + l). Note that this decomposition is not unique, as there might be several l for which t(s0(t) + l) · ( r(s(t)) − r(s0(t) + l)) = 0. TraFiC4 starts looking around l = 0, however. Note that this generalized prescription leads to some unfamiliar effects, such as x and y coordinate flipping their sign when the curvature does or switching roles when a sideways bend turns into an upward bend. Also note that the prescription is not unique on drifts, as r′′ = 0. We use the parallel-transported n from the last ∗Work supported by Department of Energy contract DE–AC03– 76SF00515. curved section in these cases; by convention, we start our beamline with t(0) ‖ xLab and n(0) ‖ yLab.