Dong-Yeop Na

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

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.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

In many problems involving particle accelerators and relativistic plasmas, the accurate modeling of relativistic particle motion is essential for accurate physical predictions. Here, we extend a charge-conserving finite element time-domain (FETD) particle-in-cell (PIC) algorithm for the time-dependent Maxwell-Vlasov equations on irregular (unstructured) meshes to the relativistic regime by implementing and comparing three particle pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Abstract We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian ρz-plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a ( TE ϕ , TM ϕ ) field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.

Discretization of Maxwell-vlasov equations based on discrete exterior calculus

We discuss the discretization of Maxwell-Vlasov equations based on a discrete exterior calculus framework, which provides a natural factorization of the discrete field equations into topological (metric-free) and metric-dependent parts. This enables a gain in geometrical flexibility when dealing with general grids and also the ab initio, exact preservation of conservation laws through discrete analogues. In particular, we describe a particle-in-cell (PIC) implementation of time-dependent discrete Maxwell-Vlasov equations, whereby the electromagnetic field are discretized using Whitney forms and coupled to particle dynamics by means of a gather-scatter scheme that yields exact charge-conservation on general grids. Numerical examples of PIC simulations such as vacuum diode and backward-wave oscillator are used to illustrate the approach.

Irregular-grid-based particle-in-cell simulations of resonant electron discharges with probabilistic secondary electron emission model

Resonant electron discharges (mutlipactor effects) in vacuum electronic devices are investigated through irregular-grids-based particle-in-cell (PIC) simulations. The Furman probabilistic model for the secondary electron emission (SEE) is embodied in a PIC algorithm that yields a self-consistent time update of fields and particles with charge-conserving and symplectic properties obtained from first principles. We study multipactor effects on different kinds of metal boundaries such as Cu and stainless steel and the saturation process due to a balanced competition between external RF potentials and space charges.

Finite-element time-domain solver for axisymmetric devices based on discrete exterior calculus and transformation optics

We present a new finite-element time-domain (FETD) solver for analysis of axisymmetric devices based on discrete exterior calculus (DEC) and transformation optics (TO) concepts. The proposed FETD solver decomposes the fields into TEϕ and TMϕ modes, which are expanded by using appropriate set of (vector or scalar) basis functions. Utilizing DEC, trigono-metric orthogonality, and a leap-frog time-integrator, we obtain energy-conserving fully discrete Maxwells equations. We explore TO principles to map the original problem from a cylindrical system to an equivalent problem on a Cartesian mesh embedded on an effective (artificial) inhomogeneous medium with radial variation. The new FETD solver is illustrated for the efficient solution of a backward-wave oscillator (BWO) encompassing a slow-wave waveguide with sinusoidal corrugations.

An efficient algorithm for simulation of plasma beam high-power microwave sources

We discuss a new electromagnetic particle-in-cell algorithm for the simulation of Maxwell-Vlasov equations on unstructured grids. The use of discrete exterior calculus and differential forms of various degrees enables numerical charge conservation from first principles, down to the numerical precision floor. In addition, energy conservation is obtained via a symplectic field update. The algorithm is illustrated for the modeling of high-power microwave devices based on Cerenkov radiation driven by relativistic plasma beams.

Charge-conserving relativistic PIC algorithm on unstructured grids

We discuss the extension of an exact charge-conserving particle-in-cell (PIC) algorithm based on unstructured grids to the relativistic regime. The present PIC algorithm is based on the representation of grid-based variables such as fields, currents, and (nodal) charges as discrete differential forms of various degrees. In gather and scatter steps, Whitney functions are used as spatial interpolators from grid-based variables to kinetic variables. In the push step, Boris method is adopted to efficiently incorporate relativistic effects into the particle updates. Computational example of a plasma ball expansion and synchrotron charge acceleration are used to illustrate the proposed algorithm in the relativistic regime.

Unstructured-grid and conservative electromagnetic particle-in-cell: Application to micromachined slow-wave structures

We present an accurate and efficient electromagnetic particle-in-cell (EMPIC) algorithm on unstructured grids for the analysis and design of axisymmetric slow-wave structures. The use of unstructured grids allows for more fidelity in the modeling of micromachined geometries. The use of a reduced-dimensionality algorithm decreases the computational costs significantly and enables its integration as a forward engine into a design loop. Special gather and scatter steps are employed to yield exact charge conservation on unstructured grids. We provide numerical examples involving travelling-wave tube amplifiers designed to harness bunching effects arisen from Cherenkov radiation.

Full-wave FETD-based PIC algorithm with local explicit update

We present a full-wave, finite-element time-domain (FETD)-based electromagnetic particle-in-cell (PIC) algorithm for unstructured grids with explicit field update. Charge conservation is attained from first principles by utilizing scatter and gather steps based on the representation of fields, currents, and charges by differential forms of various degrees. A sparse approximation inverse (SPAI) is employed for the mass (Hodge) matrix so that a linear solver is obviated during time-stepping and the field update becomes explicit. Since sparsity is preserved, the field update remains local. We investigate the effect of the approximate inverse on particle motion by comparing the proposed SPAI-based PIC algorithm versus a conventional (implicit) PIC algorithm based on LU decomposition.