  The self-consistent nonlinear dynamics of a relativistic charged particle
beam interacting with its complete self-fields is a fundamental problem
underpinning many of the accelerator design issues in high brightness beam
applications, as well as the development of advanced accelerators.
Particularly, synchrotron radiation induced effects in a magnetic dispersive
beamline element can lead to collective beam instabilities and emittance
growth. A novel beam dynamic code is developed based on a Lagrangian method for
the calculation of the particles' radiation near-fields using wavefront/wavelet
meshes via the Green's function of the Maxwell equations. These fields are then
interpolated onto a moving mesh for dynamic update of the beam. This method
allows radiation co-propagation and self-consistent interaction with the beam
in the simulation at greatly reduced numerical errors. Multiple levels of
parallelisms are inherent in this method and implemented in our code CoSyR to
enable at-scale simulations of nonlinear beam dynamics on modern computing
platforms using MPI, multi-threading, and GPUs. CoSyR has been used to evaluate
the transverse and longitudinal coherent radiation effects on the beam and to
investigate beam optics designs proposed for mitigation of beam brightness
degradation in a magnetic bunch compressor. In this paper, the design of CoSyR,
as well as the benchmark with other coherent synchrotron radiation models, are
described and discussed.
