Toward fully self-consistent simulation of the interaction of E-Clouds and beams with WARP-POSINST
To predict the evolution of electron clouds and their effect on the beam, the high energy physics community has relied so far on the complementary use of 'buildup' and 'single/multi-bunch instability' reduced descriptions. The former describes the evolution of electron clouds at a given location in the ring, or 'station', under the influence of prescribed beams and external fields [1], while the latter (sometimes also referred as the 'quasi-static' approximation [2]) follows the interaction between the beams and the electron clouds around the accelerator with prescribed initial distributions of electrons, assumed to be concentrated at a number of discrete 'stations' around the ring. Examples of single bunch instability codes include HEADTAIL [3], QuickPIC [4, 5], and PEHTS [6]. By contrast, a fully self-consistent approach, in which both the electron cloud and beam distributions evolve simultaneously under their mutual influence without any restriction on their relative motion, is required for modeling the interaction of high-intensity beams with electron clouds for heavy-ion beam-driven fusion and warm-dense matter science. This community has relied on the use of Particle-In-Cell (PIC) methods through the development and use of the WARP-POSINST code suite [1, 7, 8]. The development of novel numerical techniques (including adaptive mesh refinement, and a new 'drift-Lorentz' particle mover for tracking charged particles in magnetic fields using large time steps) has enabled the first application of WARP-POSINST to the fully self-consistent modeling of beams and electron clouds in high energy accelerators [9], albeit for only a few betatron oscillations. It was recently observed [10] that there exists a preferred frame of reference which minimizes the number of computer operations needed to simulate the interaction of relativistic objects. This opens the possibility of reducing the cost of fully self-consistent simulations for the interaction of ultrarelativistic beams with electron cloud by orders of magnitude. The computational cost of the fully self-consistent mode is then predicted to be comparable to that of the quasi-static mode, assuming that several stations per betatron period are needed. During the workshop, there was some debate about the number of stations per betatron period that are needed when using the quasi-static mode. The argument was made that if there is less than one station per betatron period, then artificial resonances can be triggered and the resulting emittance growth provides an upper bound. The emittance growth thus obtained will fall either above or below the operational requirements of the machine. In the latter case, one can conclude that the electron effect that has been simulated is of no concern. However, if the emittance growth that was obtained is above the threshold, then the results become inconclusive, and simulations which resolve the betatron motion are then needed. In this case, according to [10], the fully self-consistent approach becomes an option. The aim of this paper is to investigate whether this option is indeed practical.