English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the effect of a passive harmonic cavity, introduced to cause bunchlengthening, in an electron storage ring. We derive a formula for the inducedvoltage from such a cavity with high $Q$, excited by a a sequence of bunches,allowing for arbitrary gaps in the sequence and arbitrary currents. Except fora minor term that can be determined iteratively, the voltage is given in termsof a single mode of the Fourier transforms of the bunch forms, namely the modeat the resonant frequency of the cavity. Supposing that the only wake field isfrom the harmonic cavity, we derive a system of coupled Ha\"issinski equationswhich determine the bunch positions and profiles in the equilibrium state. Thenumber of unknowns in the system is only twice the number of bunches, and itcan be solved quickly by a Newton iteration, starting with a guess determinedby path-following from a solution at weak current. We explore the effect of thefill pattern on the bunch lengthening, and also the dependence on the shuntimpedance and detuning of the cavity away from the third harmonic of the mainaccelerating cavity. We consider two measures to reduce the effects of gaps: 1)distribution of the gaps around the ring to the greatest extent allowed, and 2)"guard bunches" with higher charges adjacent to the gaps, compensating for thecharge missing in gaps. Results for parameters of the forthcoming ALS-U lightsource are presented.

Equilibrium of an Arbitrary Bunch Train in Presence of a Passive Harmonic Cavity: Solution through Coupled Ha\" issinski Equations