ANL, Argonne
We are developing highly scalable solvers for space charge dominated beams based on both Particle-In-Cell (PIC) and direct Vlasov models. For the PIC model, particles are distributed evenly on different processors and space charge effect has been counted by solving Poisson's equation on a finite mesh. Several Poisson solvers have been developed using Fourier, Spectral Element (SEM) and Wavelet methods. Domain decomposition (DD) has been used to parallelize these solvers and all these solvers have been implemented into the PTRACK code. PTRACK is now widely used for large scale beam dynamics simulations in linear accelerators. For the Vlasov model, Semi-Lagrangian method and time splitting scheme have been employed to solve Vlasov equation directly in 1P1V and 2P2V phase spaces. 1D and 2D Poisson solvers have been developed with SEM. Similarly, DD has been used for parallelization of Poisson and Vlasov solvers. New efforts on developing Vlasov and Poisson solvers on unstructured mesh will also be reported.
Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock
Precise and fast 3D space-charge calculations for bunches of charged particles are still of growing importance in recent accelerator designs. A widespread approach is the particle-mesh method computing the potential of a bunch in the rest frame by means of Poisson's equation. Whereas an adaptive discretization of a bunch is often required for efficient space charge calculations in practice, such a technique is not implemented in many computer codes. For instance, the FFT Poisson solver that is often applied allows only an equidistant mesh. An adaptive discretization following the particle density is implemented in the GPT tracking code (General Particle Tracer, Pulsar Physics). The disadvantage of this approach is that jumps in the distribution of particles are not taken into account. In this paper we present a new approach to an adaptive discretization which is based on the multigrid technique. The goal is that the error estimator needed for the adaptive distribution of mesh lines can be calculated directly from the multigrid procedure. The algorithm will be investigated for several particle distributions and compared to that adaptive discretization method implemented in GPT.
TU Darmstadt, Darmstadt
TEMF, TU Darmstadt, Darmstadt
The problem of self-consistent simulations of short relativistic particle bunches in long accelerator structures exhibits a pronounced multi-scale character. The adequate resolution of the THz space charge fields excited by short ultra-relativistic bunches requires mesh spacings in the micrometer range. On the other hand, the discretization of complete accelerator sections using such fine meshes results in a vast number of degrees of freedom. Due to the spatial concentration of the particles and the excited space charge fields, the application of time-adaptive mesh refinement is an emerging idea. We reported on the implementation of time-adaptive mesh refinement for the Finite Integration Technique (FIT)*. Based on this work, we implemented an hp-adaptive discontinuous Galerkin (DG) code. The twofold refinement mechanisms of the hp-adaptive DG method offer maximum modeling freedom. We present details of the h- and p-adaptations for the DG method on Cartesian grids. Special emphasis is put on the stability and efficiency of the adaptation techniques.
GSI, Darmstadt
The head-tail instability represents a potential intensity limitation for bunched beams in the synchrotrons of the FAIR project. Parametrical studies with numerical simulations over very long time scales are necessary in order to understand the effect of direct space charge, nonlinear synchrotron oscillations and image charges, which are all important in FAIR synchrotrons. Existing analytic approaches either neglect space charge or describe simplified models, which require a numerical or experimental validation. For our simulation studies we use two different computer codes, HEADTAIL and PATRIC. In this work we verify models for wake-field kicks and space-charge effect using the analytic solution for head-tail mode frequencies and growth rates from the barrier airbag model.
PSI, Villigen
CIAE, Beijing
LANL, Los Alamos, New Mexico
OPAL (Object Oriented Parallel Accelerator Library) is a tool for charged-particle optic calculations in accelerator structures and beam lines including 3D space charge, short range wake-fields and 1D coherent synchrotron radiation. Built from first principles as a parallel application, OPAL admits simulations of any scale, from the laptop to the largest High Performance Computing (HPC) clusters available today. Simulations, in particular HPC simulations, form the third pillar of science, complementing theory and experiment. In this paper we present a fast FFT based direct solver and an iterative solver, namely a solver based on an algebraic multigrid preconditioned conjugate gradient method able to handle efficiently exact boundary conditions on complex geometry's. We present with timings up to several thousands of cores. The application of OPAL to the PSI-XFEL project as well as to the ongoing high power cyclotron upgrade will demonstrate OPAL's versatile capabilities. Plans for future developments towards a 3D finite element time domain Maxwell solver for large structures and simulation capabilities for 3D synchrotron radiation will be discussed.
SLAC, Menlo Park, California
SLAC's Advanced Computations Department (ACD) has developed the parallel Finite Element 3D electromagnetic code suite ACE3P for modeling of complex accelerator structures. The Particle-In-Cell module Pic3P was designed for simulations of beam-cavity interactions dominated by space charge effects. Pic3P solves the complete set of Maxwell-Lorentz equations self-consistently and includes space-charge, retardation and boundary effects from first principles. In addition to using conformal, unstructured meshes in combination with higher-order Finite Element methods, Pic3P also uses causal moving window techniques and dynamic load balancing for highly efficient use of computational resources. Operating on workstations and on leadership-class supercomputing facilities, Pic3P allows large-scale modeling of photoinjectors with unprecedented accuracy, aiding the design and operation of next-generation accelerator facilities. Applications include the LCLS RF gun and the BNL polarized SRF gun.
LLNL, Livermore, California
PPPL, Princeton, New Jersey
LBNL, Berkeley, California
The near-term mission of the Heavy Ion Fusion Science Virtual National Laboratory (a collaboration of LBNL, LLNL, and PPPL) is to study "warm dense matter" at ~1 eV heated by ion beams; a longer-term topic is ion-driven target physics for inertial fusion energy. Beam bunch compression factors exceeding 50x have been achieved on the Neutralized Drift Compression Experiment (NDCX) at LBNL, enabling rapid target heating; however, to meet our goals an improved platform, NDCX-II, is required. Using refurbished induction cells from the decommissioned Advanced Test Accelerator at LLNL, NDCX-II will compress a ~500 ns pulse of Li+ ions to ~1 ns while accelerating it to 3-4 MeV (a spatial compression of 100-150x) over ~15 m. Non-relativistic ions exhibit complex dynamics; the beam manipulations in NDCX-II are actually enabled by strong longitudinal space charge forces. We are using analysis, an interactive 1D PIC code (ASP) with optimizing capabilities and a centroid-offset model, and both (r,z) and 3D Warp-code simulations, to develop the NDCX-II accelerator. Both Warp and LSP are used for plasma neutralization studies. This talk describes the methods used and the resulting physics design.
TEMF, TU Darmstadt, Darmstadt
The Vlasov equation describes the evolution of a particle density under the effects of electromagnetic fields. It is derived from the fact that the volume occupied by a given number of particles in the 6D phase space remains constant when only long-range interaction as for example Coulomb forces are relevant and other particle collisions can be neglected. Because this is the case for typical charged particle beams in accelerators, the Vlasov equation can be used to describe their evolution within the whole beam line. This equation is a partial differential equation in 6D and thus it is very expensive to solve it via classical methods. A more efficient approach consists in representing the particle distribution function by a discrete set of characteristic moments. For each moment a time evolution equation can be stated. These ordinary differential equations can then be evaluated efficiently by means of time integration methods if all considered forces and a proper initial condition are known. The beam dynamics simulation tool V-Code implemented at TEMF utilizes this approach. In this paper the numerical model, main features and designated use cases of the V-Code will be presented.
TUB, Beijing
CIAE, Beijing
A high intensity compact cyclotron, CYCIAE-100, is selected as the driving accelerator for Beijing Radioactive Ion-beam Facility (BRIF). At present the physics design of this machine has been accomplished. This paper gives a brief review of the general designs of this machine. For further intensity upgrade of this compact machine in the future, it is crucial to carry out in-depth study on the self fields effects including the contributions of single bunch space charge and the interaction of many radially neighboring bunches. In order to include the neighboring bunch effects fully self-consistently in compact cyclotrons, a new physical model is established for the first time and implemented in the parallel PIC code OPAL-CYCL. After that, the impact of the single bunch space charge and neighboring bunches on the beam dynamics in CYCIAE-100 for different intensity levels are studied by the simulations using the new model.
STFC/RAL/ISIS, Chilton, Didcot, Oxon
The ISIS Facility at the Rutherford Appleton Laboratory in the UK produces intense neutron and muon beams for condensed matter research. It is based on a 50 Hz proton synchrotron which accelerates ~3·1013 protons per pulse (ppp) from 70 to 800 MeV, corresponding to beam powers of ~0.2 MW. Studies are under way for major upgrades in the Megawatt regime. Underpinning this programme of operations and upgrades is a study of the high intensity effects that impose limitations on beam power. The behaviour of the beam in the 50 Hz rapid cycling synchrotron (RCS) is largely characterised by high space charge levels and the effects of fast ramping acceleration. High intensity effects are of particular importance as they drive beam loss, but are not fully understood with only limited analytical models available. This paper reviews several methods by which these effects are explored numerically on ISIS, and compares them where possible with experimental or analytical results. In particular we outline development of a new space charge code Set, which is designed to address key issues on ISIS and similar RCS machines.
IHEP Beijing, Beijing
The China Spallation Neutron Source (CSNS) is now in the design stage. Many simulations have been done for the RCS/CSNS, including the space charge induced emittance growth and beam loss, the combined effects of space charge and magnet errors, the dependence of space charge effects on the lattice structures, etc.
NSCL, East Lansing, Michigan
The cyclotron gas stopper is a newly proposed device to stop energetic ions in a high pressure helium gas and to transport them in a singly charged state with a gas jet to a vacuum region. Ions are injected into the region with vertical magnetic field, where they first meet a degrader and then move in helium gas. Due to multiple scattering, radioactive ions lose their energy, and the process is accompanied by ionization of helium. Externally applied voltage remove electrons and single-charged helium ions from the box. Under a certain incoming particle rate, the amount of ionized charge becomes large and cannot be removed completely. As a result, a neutralized plasma is accumulated in the center of the box and new incoming particles cannot be ejected from the field-shielded area. The present study focuses on a detailed understanding of space charge effects in the central ion extraction region. Particle-in-cell simulations of electron-helium plasma are based on self-consistent particle tracking in a field obtained from solution of Poisson’s equation for particle interacting via Coulomb forces. The paper analyzes the process and estimates the maximum possible incoming particle rate.
Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock
Demanding applications such as heavy ion fusion, high energy colliders and free electron lasers require the study of beam phenomena like space-charge induced instabilities, emittance growth and halo formation. Numerical simulations for instance with GPT (General Particle Tracer, Pulsar Physics) calculate the mutual Coulomb interactions of the tracked particles *. The direct summation of the forces is rather costly and scales with O(N2). In this paper we investigate a new approach for the efficient calculation of particle-particle interactions: the fast summation by Nonequispaced Fast Fourier Transform (NFFT) **, whereas the NFFT is a generalization of the well known Fast Fourier Transformation (FFT). We describe the algorithm and discuss the performance and accuracy of this method for several particle distributions.
SLAC, Menlo Park, California
An x-ray Free-Electron Laser (FEL) calls for a high brightness electron beam. Generically, such a beam needs to be accelerated to high energy on the GeV level and compressed down to tens of microns, if not a few microns. The very bright electron beam required for the FEL has to be stable and the high quality of the electron beam has to be preserved during the acceleration and bunch compression. With a newly developed model independent global optimizer [*], here we report study for the control and error diagnostics of such a generic machine: magnetic elements, and RF cavities, and the electron beam parameters: the peak current, centroid energy, and trajectory. Collective effects, such as coherent synchrotron radiation, space charge, and various wakefields are incorporated in a parametric approach. Applicability and verification are detailed for the LINAC Coherent Light Source, an x-ray FEL project being commissioned at SLAC.
Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock
A single bunch instability caused by an electron cloud has been studied using analytical and semi-analytical methods with the wake field. The wake field in these cases was computed in the classical sense as excited electromagnetic field that transversally distorts those parts of the bunch trailing certain transversal offset in the leading part of the same bunch. The transversal wake force in this case is only depending on the longitudinal distance between the leading part of the bunch producing the wake force and the trailing parts of the bunch feeling the wake force. However during the passage of the bunch through the electron cloud the density of the electron cloud near the beam axis changes rapidly which does not allow the single variable approximation for the wake field. In this paper pursuing the idea of K. Ohmi we compute numerically the wake forces as two variable function of the position of the leading part of the bunch and the position of the bunch parts trailing the leading offset in the bunch.
IAP, Frankfurt am Main
For the development of high energy and high duty cycle RFQs accurate particle dynamic simulation tools are important for optimizing designs, especially in high current applications. To describe the external fields in RFQs, the Poisson equation has to be solved taking the boundary conditions into account. In PteqHI this is now done by using a finite difference method on a grid. This method will be described and simulation results will be compared to different RFQ particle dynamic codes.
RIKEN Nishina Center, Wako
PSI, Villigen
CIAE, Beijing
Since 1997 RIKEN Nishina center has been constructing a next-generation exotic beam facility, RI beam factory (RIBF), based on a powerful heavy ion driver accelerator . Its accelerator complex was successfully commissioned at the end of 2006 and started supplying heavy ion beams in 2007. The four ring cyclotrons (RRC, fRC, IRC and SRC) connected in series accelerate the energy of the heavy ion beams up to 400 MeV/u for the lighter ions such as argon and 345 MeV/u for heavier ions such as uranium. Intensity upgrade plans are under way, including the construction of a new 28 GHz superconducting ECR ion source. The new ECR will take all the succeeding accelerators and beam transport lines to a space charge dominant regime, which should be carefully reconsidered to avoid emittance growth due to space charge forces. Beam dynamics in the low energy cyclotron, RRC was studied by OPAL-cycl a flavor of the OPAL. The simulation results clearly show vortex motions in the isochronous field, resulting in round beam formation in the first 10 turns after the injection point. The possible increase of beam loss at beam extraction will be also discussed in this paper.
STFC/RAL/ISIS, Chilton, Didcot, Oxon
ISIS is the spallation neutron source at the Rutherford Appleton Laboratory in the UK. Presently, it runs at beam powers of ~0.2 MW, with upgrades in place to supply increased powers for the new Second Target Station. Studies are also under way for major upgrades in the megawatt regime. Underpinning this programme of operations and upgrades is a study of the high intensity effects that impose the limitations on beam power. Spallation is driven by a 50 Hz rapid cycling synchrotron, characterized by high space charge and fast ramping acceleration. High intensity effects are of particular importance as they drive beam loss, but are poorly understood analytically. This paper reviews development of the space charge charge code Set.
ORNL, Oak Ridge, Tennessee
A development of a Python driving shell for the ORBIT simulation code is presented. The original ORBIT code uses the Super Code shell to organize accelerator related simulations. It is outdated, unsupported, and it is an obstacle for the future code development. A necessity of the replacement of the old shell language and consequences are discussed. A set of modules that are currently in the core of the pyORBIT code and extensions are presented. They include particle containers, parsers for MAD and SAD lattice files, a Python wrapper for MPI libraries, space charge calculators, TEAPOT trackers, and a laser stripping extension module.
Fermilab, Batavia
The Recycler is a fixed 8 GeV kinetic energy storage ring using permanent gradient magnets. A phase trombone straight section is used to control the tunes. For ProjectX , the H-particle extracted from the Linac will be striped and painted in the Recycler Ring and then the protons will be extracted into the Main injector. A long drifting space is needed to accommodate the injection chicane with stripping foils. In this paper, the existing FODO lattice in rr10 straight section being converted into doublet will be described. Due to this change, the phase trombone straight section has to be modified to bring the tunes to the nominal working point. On the other hand, a toy lattice of recycler ring is designed to simulate the end-shim effects of each permanent gradient magnet to add the flexibility to handle the tune shift to the lattice during the operation of 1.6·1014 with KV distribution of the proton beam to give ~0.05 of space charge tune shift . The comparison or the combinations of the two modification ways for the Recycler ring lattice will be presented also in this paper.