Simulations of sawtooth instability

Abstract

The equilibrium self-consistent distribution of particles in a high intensity electron synchrotron can be found using the Haissinski equation and the wake ®eld. At some threshold intensity the bunch becomes unstable. However, radiation damping causes the particles to be con®ned and the instability does not necessarily cause loss of particles.It was observed in simulations with a very simple wake ®eld and short bunches, that energy spread and bunch length oscillate in a sawtooth fashion. We ®nd that this is due to the doublepeaked nature of the stationary distribution. Over many synchrotron oscillations, particles diffuse from the head peak to the tail to the point where the tail peak becomes as large as the head. The two resulting sub-bunches then collapse together in less than one synchrotron oscillation, causing a net blow-up in emittance. Radiation damping reduces the emittance and diffusion begins again.

Longitudinal instability studies at the SURF II storage ring at NIST.

“…This, as well as the cyclical bunch length variation in Fig. 1, is very similar to the so-called "sawtooth" instability observed in the SLC damping rings [8]. In SURF II, the first harmonic is present, but does not grow.…”

High-intensity single bunch instability behavior in the new SLC damping ring vacuum chamber

“…Some of the results with the old chamber 4 and some preliminary results with the new one have been or could be interpreted with the ideas in a number of theoretical and simulation papers. [8][9][10][11][12][13] We look forward to quantitative comparisons with the data in this paper.…”

Low frequency longitudinal relaxation oscillation

“…Although our beam bursting behavior is sinusoidal rather than sawtooth, our relaxation oscillation is a kind of the sawtooth instability [1]. When the amplitude of the longitudinal relaxation oscillation is high, horizontally oscillating wide beams are observed at the diagnostic beamline, and the beam lifetime is fluctuated due to the sinusoidal modulation in the synchrotron oscillation.…”

“…According to one simulation model [1], this relaxation oscillation can be explained as following: Under the high intensity or the strong CBMI status, electrons can be randomly excited when the the synchrotron radiation is emitted. In this case, the electrons within a bunch can easily diffuse to other stable fixed point or the tail sub-bunch at the downstream through the unstable fixed point.…”