Propagation of numerical noise in particle-in-cell tracking

Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well known that PIC algorithms occupy intrinsic limitations as they introduce numerical noise. Although not significant for short-term tracking, this becomes important in simulations for circular machines over millions of turns as it may induce artificial diffusion of the beam. In this work, we present a modeling of numerical noise induced by PIC algorithms, and discuss its influence on particle dynamics. The combined effect of particle tracking and noise created by PIC algorithms leads to correlated or decorrelated numerical noise. For decorrelated numerical noise we derive a scaling law for the simulation parameters, allowing an estimate of artificial emittance growth. Lastly, the effect of correlated numerical noise is discussed, and a mitigation strategy is proposed.Comment: 14 pages, 12 figure

Fix-lines and stability domain in the vicinity of the coupled third order resonance

The single particle stability in a circular accelerator is of concern especially for operational regimes involving beam storage of hours. In the proximity to a resonance this stability domain shrinks, and the phase space fragments into a jungle of exotic objects like for instance "fix-lines". The concept of fix-points is easily understandable in a 2D phase space. It becomes quite challenging when the effect of resonances is considered in the 4D phase space, which leads then to the concept of fix-lines. In this paper we investigate the fix-lines in the proximity of a coupled third order resonance and find the relation of these objects with the stability of motion.Comment: 35 pages, 29 figure

Linear beam optics in solenoidal channels

In this paper we study beam transport through a straight solenoidal channel using the single-particle and linear optics approach. We derive the single-particle invariants and show their use in an extended Courant-Snyder theory (1958) for a solenoidal coupled system. Matching between solenoidal channels and between solenoidal and quadrupolar channels is discussed. We give envelope solutions and illustrate them with some numerical examples. (15 refs)

Single Particle Description of Ionization Cooling

In this note we derive thestochastic equations which describe the single particle dynamics in an uniform cooling channel. Formulae and graphics for design optimizations are discussed

Incoherent effects of electron cloud in proton storage rings

Electron clouds in the beam pipe of high-energy proton or positron storage rings can give rise to significant incoherent emittance growth, at densities far below the coherent-instability threshold. We identify two responsible echanisms, namely: (1) a beam particle periodically crosses a resonance and (2) a beam particle periodically crosses a region of the bunch where its motion is linearly unstable. Formation of halo or beam-core blow up, respectively, are the result. Key ingredients for both processes are synchrotron motion and electron-induced tune shift. The mechanisms considered provide a possible explanation for reduced beam lifetime and emittance growth observed at several operating accelerators. Similar phenomena are likely to occur in other two- stream systems

Resonance Trapping, Halo Formation and Incoherent Emittance Growth due to Electron Cloud

The pinched electron cloud introduces a tune shift along the bunch, which, together with synchrotron motion, leads to a periodic crossing of resonances. The resonances are excited by the longitudinal distribution of the electron cloud around the storage ring. We benchmark the PIC code HEADTAIL against a simplified weak-strong tracking code based on an analytical field model, obtaining an excellent agreement. The simplified code is then used for exploring the long term evolution of the beam emittance, and for studying more realistic lattice models. Results are presented for the CERN SPS and the LHC

Transverse self-consistent modeling of a 3D bunch in SIS100 with micromap

We present the upgrade of the MICROMAP beam dynamics simulation library to include a 2 1/2 D space charge modeling of a 3D bunch using local slices in z. We discuss the parallelization technique, the performances, several tests and comparison with existing well-established analytical/numerical results in order to validate the code. An application to the SIS 100 synchrotron of the FAIR project at GSI is outlined