Vittorio Vaccaro legacy: The impedance and collective effect in modern accelerators.

Vittorio Vaccaro began his activity at CERN in 1966 as an electronic engineer in the RF group. It was the year in which construction of the ISR (Intersecting Storage Ring) accelerator started, it was the first hadron collider in the world, which went into operation in 1971. The machine was made of two intersecting rings, and to reach a high luminosity it was necessary to store a high current of protons beyond the then-known stability limits of the accumulated beams. In November 1966, Vittorio wrote the internal report "Longitudinal instability of a coasting beam above transition, due to the action of lumped discontinuities". In February 1967, together with Andrew Sessler, he presented a more general treatment in the CERN Yellow Report, "Longitudinal instabilities of azimuthally uniform beams in circular vacuum chambers of arbitrary electrical properties". In 1969, with Kurt Hubner and Alessandro Ruggiero, he extended his research to transverse instabilities in the article "Stability of the coherent transverse motion of a coasting beam for realistic distribution functions and any given coupling with its environment". In a few years, with these works, Vittorio Vaccaro laid the foundations of a solid theory for the study of instabilities in a storage ring. Using Vlasov's equation, he obtained the dispersion relationship in terms of quantity, which he defined as the "Coupling Impedance", which accounts for the electromagnetic interaction of the particle beam with the vacuum chamber and with the surrounding devices installed on the machine. Regarding these studies, Simon Van de Meer, Nobel Prize, stated: "The stream of this research, born at CERN and still lasting, gave and gives results that have been of great importance for the ISR project and for particle accelerator in general". Indeed, these works were the beginning of many studies which have taken place in the last fifty years; impedance and wake fields continue to be an important field of activity in theory, simulations, and particle beam measurements. Building a reliable impedance model for a machine is today the first step necessary to evaluate the performance limits of circular accelerators, used as colliders and synchrotron radiation sources, as well as of linear accelerators.