We present a charge-conserving electromagnetic particle-in-cell (EM-PIC) algorithm on unstructured grids based on a finite element (FE) time-domain methodology with explicit field update, i.e., requiring no linear solver. The proposed explicit EM-PIC algorithm attains charge conservation from first principles by representing fields, currents, and charges by differential forms of various degrees, following the methodology put forth in reference [25]. The need for a linear solver is obviated by constructing a sparse approximate inverse (SPAI) for the FE system matrix, which also preserves the locality (sparsity) of the algorithm. We analyze in detail the residual error caused by SPAI on the motions of charged particles and beam trajectories and show that this error is several orders of magnitude smaller than the inherent error caused by the spatial and temporal discretizations.

Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

Under the support of the U.S. DOE SciDAC program, SLAC has been developing a suite of 3D parallel finite- element codes aimed at high-accuracy, high-fidelity electromagnetic and beam physics simulations for the design and optimization of next-generation particle accelerators. Running on the latest supercomputers, these codes have made great strides in advancing the state of the art in applied math and computer science at the petascale that enable the integrated modeling of electromagnetics, self-consistent Particle-In-Cell (PIC) particle dynamics as well as thermal, mechanical, and multi-physics effects. This paper will present 3D results of trapped mode calculations in an ILC cryomodule and the modeling of the ILC Sheet Beam klystron, shape determination of superconducting RF (SCRF) cavities and multipacting studies of SCRF HOM couplers, as well as PIC simulation results of the LCLS RF gun.

/pdf/towards-simulation-of-electromagnetics-and-beam-physics-at-2gby26ihxo.pdf

Towards simulation of electromagnetics and beam physics at the petascale

Improved computational methods are essential to the diverse and rapidly developing field of advanced accelerator concepts. We present an overview of some computational algorithms for laser‐plasma concepts and high‐brightness photocathode electron sources. In particular, we discuss algorithms for reduced laser‐plasma models that can be orders of magnitude faster than their higher‐fidelity counterparts, as well as important on‐going efforts to include relevant additional physics that has been previously neglected. As an example of the former, we present 2D laser wakefield accelerator simulations in an optimal Lorentz frame, demonstrating >10 GeV energy gain of externally injected electrons over a 2 m interaction length, showing good agreement with predictions from scaled simulations and theory, with a speedup factor of ∼2,000 as compared to standard particle‐in‐cell.

/pdf/new-developments-in-the-simulation-of-advanced-accelerator-7liolfudww.pdf

New developments in the simulation of advanced accelerator concepts

Over the past year, we have worked out a baseline design for PEP-X, as an ultra-low emittance storage ring that could reside in the existing 2.2-km PEPII tunnel. The design features a hybrid lattice with double bend achromat (DBA) cells in two arcs and theoretical minimum emittance (TME) cells in the remaining four arcs. Damping wigglers are used to reduce the horizontal emittance to 86 pm-rad at zero current for a 4.5 GeV electron beam. At a design current of 1.5 A, the horizontal emittance increases, due to intrabeam scattering, to 164 pm-rad when the vertical emittance is maintained at a diffraction limited 8 pm-rad. The baseline design will produce photon beams achieving a brightness of 10{sup 22} (ph/s/mm{sup 2}/mrad{sup 2}/0.1% BW) at 10 keV in a 3.5-m conventional planar undulator. Our study shows that an optimized lattice has adequate dynamic aperture, while accommodating a conventional off-axis injection system. In this report, we present the results of study, including the lattice properties, nonlinear dynamics, intra-beam scattering and Touschek lifetime, RF system, and collective instabilities. Finally, we discuss the possibility of partial lasing at soft X-ray wavelengths using a long undulator in a straight section.

A Design Report of the Baseline for PEP-X: an Ultra-Low Emittance Storage Ring

A hollow-core photonic band-gap (PBG) lattice in a dielectric fiber has been proposed as a high-gradient low-cost particle accelerator operating in the optical regime where the accelerating mode confined to a defect in the PBG fiber can be excited by high-power lasers [X. Lin, Phys. Rev. ST Accel. Beams 4, 051301 (2001)]. Developing efficient methods of coupling laser power into these structures requires a thorough examination of the propagating mode and its near and far-field radiation. In this paper, we develop a simulation method using the parallel finite-element electromagnetic suite ACE3P to calculate the radiation of the propagating accelerator mode into free space at the end of the fiber. The far-field radiation will be calculated and the mechanism of coupling power from an experimental laser setup will be discussed.

https://link.aps.org/pdf/10.1103/PhysRevSTAB.13.121301

Transmission and radiation of an accelerating mode in a photonic band-gap fiber

Over the past years, SLAC's Advanced Computations Department (ACD), under SciDAC sponsorship, has developed a suite of 3D (2D) parallel higher-order finite element (FE) codes, T3P (T2P) and Pic3P (Pic2P), aimed at accurate, large-scale simulation of wakefields and particle-field interactions in radio-frequency (RF) cavities of complex shape. The codes are built on the FE infrastructure that supports SLAC's frequency domain codes, Omega3P and S3P, to utilize conformal tetrahedral (triangular)meshes, higher-order basis functions and quadratic geometry approximation. For time integration, they adopt an unconditionally stable implicit scheme. Pic3P (Pic2P) extends T3P (T2P) to treat charged-particle dynamics self-consistently using the PIC (particle-in-cell) approach, the first such implementation on a conformal, unstructured grid using Whitney basis functions. Examples from applications to the International Linear Collider (ILC), Positron Electron Project-II (PEP-II), Linac Coherent Light Source (LCLS) and other accelerators will be presented to compare the accuracy and computational efficiency of these codes versus their counterparts using structured grids.

/pdf/parallel-higher-order-finite-element-method-for-accurate-3fpke6eepx.pdf

Parallel higher-order finite element method for accurate field computations in wakefield and pic simulations

Over the past years,SLAC's Advanced Computations Department (ACD) has developed the parallel finite element (FE) particle-in-cell code Pic3P (Pic2P) for simulations of beam-cavity interactions dominated by space- charge effects. As opposed to standard space-charge dominated beam transport codes, which are based on the electrostatic approximation,Pic3P (Pic2P) includes space-charge, retardation and boundary effects as it self-consistently solves the complete set of Maxwell-Lorentz equations using higher-order FE methods on conformal meshes. Use of efficient, large-scale parallel processing allows for the modeling of photoinjectors with unprecedented accuracy, aiding the design and operation of the next-generation of accelerator facilities. Applications to the Linac Coherent Light Source (LCLS) RF gun are presented.

/pdf/parallel-finite-element-particle-in-cell-code-for-2sdh643gf9.pdf

Parallel finite element particle-in-cell code for simulations of space-charge dominated beam-cavity interactions

SLAC’s Advanced Computations Department (ACD) has developed the first parallel Finite Element 3D Particle‐In‐Cell (PIC) code, Pic3P, for simulations of RF guns and other spacecharge dominated beam‐cavity interactions. Pic3P solves the complete set of Maxwell‐Lorentz equations and thus includes space charge, retardation and wakefield effects from first principles. Pic3P uses higher‐order Finite Element methods on unstructured conformal meshes. A novel scheme for causal adaptive refinement and dynamic load balancing enable unprecedented simulation accuracy, aiding the design and operation of the next generation of accelerator facilities. Application to the Linac Coherent Light Source (LCLS) RF gun is presented.

/pdf/high-fidelity-rf-gun-simulations-with-the-parallel-3d-finite-1xo754cwtg.pdf

High‐Fidelity RF Gun Simulations with the Parallel 3D Finite Element Particle‐In‐Cell Code Pic3P

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Papers

Parallel higher-order finite element method for accurate field computations in wakefield and pic simulations

Parallel finite element particle-in-cell code for simulations of space-charge dominated beam-cavity interactions

High‐Fidelity RF Gun Simulations with the Parallel 3D Finite Element Particle‐In‐Cell Code Pic3P