Nonlinear Beam Dynamics Study with Matlab

The importance of nonlinear beam dynamics effects in synchrotron light sources is caused by strong demands on beam quality to obtain long lifetime, small emittance and stability. In this paper, the non-linear particle trajectory equation modifications are given, which simplify the single particle tracking simulation in storage ring using the Matlab environment [1]. The radiation damping times in electron storage rings are of the order of few ms (10 – 10 turns) and the beam short-term stability is determinant. Therefore the tracking method symplecticity condition for the electron machines is not as important as in hadron machines. Applying recently introduced modern tools for post process analyzing, such as interpolated FFT, early indicators for determination of the onset of chaotic behavior etc, the dynamic aperture, amplitude dependent tunes, phase space distortions, nonlinear resonances and other beam dynamics aspects in the ring can be evaluated. The developed code is applied for nonlinear beam dynamics study in CANDLE [2] storage ring.