Parsec: Parallel Self-consistent 3d Electron-cloud Simulation in Arbitrary External Fields∗

We present PARSEC, a 3D parallel self-consistent particle tracking program which allows electron-cloud calculations in arbitrary external fields. The program is based on an general particle tracking framework called GenTrackE [5]. The Lorentz force equation is integrated with time as the independent variable. A 3D parallel Multigrid solver computes the electric field for the drive beam in the beam frame, while the space-charge field of the electrons is computed in the lab frame. The resulting total field, obtained by superposition, acts on both the beam particles and the cloud electrons. Primary and secondary emission takes place at each time step of the calculation. This sort of computation is only possible by the use of massive parallelization of the particle dynamics and the Poisson solver in combination with modern numerical algorithms such as the Multigrid solver with Gauss-Seidel smoothing. INTRODUCTION AND MOTIVATION The electron-cloud effect (ECE) has been investigated in various storage rings for several years now [1]. The ECE arises from the strong coupling of a two-species plasma with the surrounding vacuum chamber. Several analytical models and simulation programs and have been developed to study this effect [2]. Owing to the complexity of the problem, these simulation codes typically make one or more simplifying assumptions, such as: (i) the electrons are dynamical but the beam is a prescribed function of space and time; (ii) the beam is dynamical but the electron cloud is a prescribed function of space and time; (iii) both the beam and the electrons are dynamical, but the electronwall interaction, particularly the secondary emission process, is either absent or much simplified; (iv) the geometry of the beam and/or vacuum chamber is much simplified (eg. round beams and/or cylindrical chambers); (v) the simulation “looks” at only one specific region of the machine, typically a field-free region or one magnet of a specific kind; (vi) the forces on the particles, both from, and on, the electrons and the beam, are purely transverse. Computer codes involving these approximations, when applied in the proper context, have shed valuable information on one or more aspects of the ECE. There are problems, however, in which any of these approximations may render the reliability of code inadequate for a quantitative understanding of the dynamics. One such example concerns problems involving very long, intense, ∗Work supported by the US DOE under contract DE-AC0376SF00098. † [email protected] bunches with significant variation in the longitudinal profile, which require a self-consistent, fully 3D simulation, including a full description of the storage ring lattice (or at least, a section of the lattice at least as long as the bunch). Another example might be the simulation of damping rings for future linear colliders, which make significant use of wigglers. In this article we report on progress towards the goal of a fully self-consistent and realistic simulation of the ECE which, in its final stage, will not invoke any of the above-mentioned simplifications. THE OVERALL SIMULATION MODEL Self-consistent Formulation Let the particle coordinates of particle k be xk = (q1, q2, q3)k, and the normalized velocity be βk = (vx/c, vy/c, vz/c)k where c is the speed of light (all quantities in MKS units unless explicit stated otherwise). We consider = 1, 2, · · · magnetic elements which makes up what is called the lattice L. Defining I = {1, 2, · · · } and J = {1, 2, · · · } the index sets for the beam particles and electrons, respectively as unique identifiers, we are able to distinguish beam particle (i ∈ I) and electron coordinates (j ∈ J) in an natural way (see Figure 1 as an illustration). For each particle k ∈ I ∪ J we solve formally ...... ...... Lab Frame