Jinr: International Scientific Centre Bringing Nations Together

Transverse feedback system with digital filter

“…It is known [7] that in radiotechnical sense the circuit is stable if all the singular points of K(t) lie inside the circle ]z] < 1. If this condition is fulfilled, the singular points Lk in (4) are found from the equation [8]:…”

“…This leads to modification of stability region, ]Zk] 5 1, especially when ]K] 2 1. The maximum damping rate is achieved by the fast feedback system at optimum positions of PU and DK (1 sinRe$pK] = 1) connected via feedback without filter [3] and its value is…”

“…It means that Re+pK will differ from its optimum value. The particle motion is stable, if [3] ] sin (Re$pK)] > ) sinh (2zImQ)].…”

“…These systems have been used widely and provide an amplitude decrease of 25% per revolution [l]. In order to suppress fast resistive wall instability in UNK-1 (Serpukhov, Russia) [2] a more effective system is studied and developed [3]. It consists of two PU and two DK per plane connected by a feedback circuit with a digital filter and delay.…”

“…It consists of two PU and two DK per plane connected by a feedback circuit with a digital filter and delay. The digital filters are used in a classical TFS [4] and designed for a fast TFS [5] to remove the revolution frequency harmonics. Feedbacks with digital filters have essential advantages for new large accelerators such as UNK, LHC, SSC where the revolution period is 70 + 29Op.s and the digital procedures for signal transformations can be realized with signal processors.…”