Donohue, J. T.
(John Thomas Donohue)

MOPOS22 Off-Axis Orbits in Realistic Helical Wigglers: Fixed Points and Time Averaged Dynamical Variables
John Thomas Donohue (CENBG, Gradignan), Jean-Luc Rullier (CESTA, Le Barp)

Many years ago Fajans, Kirkpatrick and Bekefi studied off-axis orbits in a realistic helical wiggler, both experimentally and theoretically. They found that as the distance from the axis of symmetry to the guiding center increased, both the mean axial velocity and the precession frequency of the guiding center varied. . They proposed a clever semi-empirical model which yielded an excellent description of both these variations. We point out that a approximate model proposed by us several years ago can be made to predict these delicate effects correctly, provided we extend our truncated quadratic Hamiltonian to include appropriate cubic terms. We develop an argument similar to the virial theorem to compare time averaged and fixed-point values of dynamical variables. Illustrative comparisons of our model with numerical calculation are presented.

MOPOS23 Analytic Electron Trajectories in an Extremely Relativistic Helical Wiggler: an Application to the Proposed SLAC E166 Experiment.
John Thomas Donohue (CENBG, Gradignan)

The proposed experiment SLAC E166 intends to generate circularly polarized gamma rays of energy 10 MeV by passing a 15 GeV electron beam through a meter long wiggler with approximately 400 periods. Using an analytic model formulated by Rullier and me, I present calculations of electron trajectories. At this extremely high energy the trajectories are described quite well by the model, and an extremely simple picture emerges, even for trajectories that that fail to encircle the axis of the wiggler. Our calculations are successfully compared with standard numerical integration of the Lorentz force equations of motion. In addition, the calculation of the spectrum and angular distribution of the radiated photons is easily carried out.