arXiv subjects

Frank S. Tsung

Publications and source records attributed to Frank S. Tsung.

At least 19 recordsLinked to original sources

arXiv2026

Generalized multi-dimensional conservation laws for stimulated Raman and Brillouin scattering in a density gradient

Generalized local and multi-dimensional conservation laws of action, energy, momentum, and angular momentum are derived for stimulated Raman (SRS) and Brillouin backscattering (SBS) in a density gradient within the paraxial ray approximation. A Lagrangian density is found that reproduces the well known envelope equations for SRS and SBS in density gradients in the absence of damping. Using Noether's theorem, the symmetries of the Lagrangian density are used to obtain local conservation laws for quantities that can easily be identified as the action, energy, and momentum. These multi-dimensional conservation laws reduce to the well known one dimensional Manley-Rowe relations, and frequency and wavenumber matching conditions. Additional symmetries of the action lead to conversation laws for new quantities that are identified as orbital angular momentum and contributions to the energy and momentum of the wave from frequency and wavenumber shifts.

physics.plasm-ph↗

arXiv2024

A fully plasma based electron injector for a linear collider or XFEL

We demonstrate through high-fidelity particle-in-cell simulations a simple approach for efficiently generating 20+ GeV electron beams with the necessary charge, energy spread, and emittance for use as the injector for an electron arm of a future linear collider or a next generation XFEL. The self-focusing of an unmatched, relatively low quality, drive beam results in self-injection by elongating the wakefield excited in the nonlinear blowout regime. Over pump depletion distances, the drive beam dynamics and self-loading from the injected beam leads to extremely high quality and high energy output beams. For plasma densities of $10^{18} \ \text{cm}^{-3}$, PIC simulation results indicate that self-injected beams with $0.52 \ \text{nC}$ of charge can be accelerated to $\sim 20$ GeV energies with projected energy spreads, $\lesssim 1\%$ within the beam core, slice normalized emittances as low as $110 \ \text{nm}$, a peak normalized brightness $\gtrsim 10^{19} \ \text{A}/\text{m}^2/\text{rad}^2$, and energy transfer efficiencies $\gtrsim 54\%$.

physics.acc-ph↗

arXiv2023

Accurate simulation of direct laser acceleration in a laser wakefield accelerator

In a laser wakefield accelerator (LWFA), an intense laser pulse excites a plasma wave that traps and accelerates electrons to relativistic energies. When the pulse overlaps the accelerated electrons, it can enhance the energy gain through direct laser acceleration (DLA) by resonantly driving the betatron oscillations of the electrons in the plasma wave. The particle-in-cell (PIC) algorithm, although often the tool of choice to study DLA, contains inherent errors due to numerical dispersion and the time staggering of the electric and magnetic fields. Further, conventional PIC implementations cannot reliably disentangle the fields of the plasma wave and laser pulse, which obscures interpretation of the dominant acceleration mechanism. Here, a customized field solver that reduces errors from both numerical dispersion and time staggering is used in conjunction with a field decomposition into azimuthal modes to perform PIC simulations of DLA in an LWFA. Comparisons with traditional PIC methods, model equations, and experimental data show improved accuracy with the customized solver and convergence with an order-of-magnitude fewer cells. The azimuthal-mode decomposition reveals that the most energetic electrons receive comparable energy from DLA and LWFA.

physics.plasm-ph↗

arXiv2023

Ultra-compact attosecond X-ray free-electron lasers utilizing unique beams from plasma-based acceleration and an optical undulator

Accelerator-based X-ray free-electron lasers (XFELs) are the latest addition to the revolutionary tools of discovery for the 21st century. The two major components of an XFEL are an accelerator-produced electron beam and a magnetic undulator which tend to be kilometer-scale long and expensive. Here, we present an ultra-compact scheme to produce 10s of attosecond X-ray pulses with several GW peak power utilizing a novel aspect of the FEL instability using a highly chirped, pre-bunched and ultra-bright electron beam from a plasma-based accelerator interacting with an optical undulator. The self-selection of electrons from the combination of a highly chirped and pre-bunched beam leads to the stable generation of attosecond X-ray pulses. Furthermore, two-color attosecond pulses with sub-femtosecond separation can be produced by adjusting the energy distribution of the electron beam so that multiple FEL resonances occur at different locations within the beam. Such a tunable coherent attosecond X-ray sources may open up a new area of attosecond science enabled by X-ray attosecond pump/probe techniques.

physics.plasm-ph↗

arXiv2022

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High-fidelity modeling of plasma-based acceleration (PBA) requires the use of 3D fully nonlinear and kinetic descriptions based on the particle-in-cell (PIC) method. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the beam-plasma interaction. In a QSA-PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA-PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA-PIC algorithm that combines another speedup technique known as azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can significantly reduce the algorithmic complexity. Modeling the laser-plasma interaction in a full 3D PIC algorithm is very computationally expensive due to the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible with the QSA PIC algorithms based on the azimuthal mode expansion. This algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described.

physics.plasm-ph↗

arXiv2022

Ultra-Bright Electron Bunch Injection in a Plasma Wakefield Driven by a Superluminal Flying Focus Electron Beam

We propose a new method for self-injection of high-quality electron bunches in the plasma wakefield structure in the blowout regime utilizing a "flying focus" produced by a drive beam with an energy chirp. In a flying focus the speed of the density centroid of the drive bunch can be superluminal or subluminal by utilizing the chromatic dependence of the focusing optics. We first derive the focal velocity and the characteristic length of the focal spot in terms of the focal length and an energy chirp. We then demonstrate using multidimensional particle-in-cell simulations that a wake driven by a superluminally propagating flying focus of an electron beam can generate GeV-level electron bunches with ultralow normalized slice emittance ($\sim$30 nm rad), high current ($\sim$ 17 kA), low slice energy-spread ($\sim$0.1%) and therefore high normalized brightness ($>10^{19}$ A/rad$^2$/m$^2$) in a plasma of density $\sim10^{19}$ cm$^{-3}$. The injection process is highly controllable and tunable by changing the focal velocity and shaping the drive beam current. Near-term experiments at FACET II where the capabilities to generate tens of kA, <10 fs drivers are planned, could potentially produce beams with brightness near $10^{20}$ A/rad$^2$/m$^2$.

physics.plasm-ph↗

arXiv2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power lasers that can be focused to intensities exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In strong fields, the motion of charged particles and their spin is affected by radiation reaction. Standard PIC codes usually use Boris or its variants to advance the particles, which requires very small time steps in the strong-field regime to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a 9D particle phase space (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime are desired. We present a new 9D phase space particle pusher based on analytical solutions to the position, momentum and spin advance from the Lorentz force, together with the semi-classical form of RR in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step for each particle from the simulation time step. Due to the analytical integration, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. We present single-particle simulations and full PIC simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 9D phase space for given laser fields. A discussion on the numerical efficiency of the proposed pusher is also provided.

physics.comp-ph↗

arXiv2021

A multi-sheath model for highly nonlinear plasma wakefields

An improved description for nonlinear plasma wakefields with phase velocities near the speed of light is presented and compared against fully kinetic particle-in-cell simulations. These wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term $S \equiv -\frac{1}{en_p}(ρ-J_z/c)$ where $ρ$ and $J_z$ are the charge and axial current densities. Previously, the sheath source term was described phenomenologically with a positive-definite function, resulting in a positive definite wake potential. In reality, the wake potential is negative at the rear of the ion column which is important for self-injection and accurate beam loading models. To account for this, we introduce a multi-sheath model in which the source term, $S$, of the plasma wake can be negative in regions outside the ion bubble. Using this model, we obtain a new expression for the wake potential and a modified differential equation for the bubble radius. Numerical results obtained from these equations are validated against particle-in-cell simulations for unloaded and loaded wakes. The new model provides accurate predictions of the shape and duration of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying loaded wakefield. We present beam loading results for laser wakefields and discuss how the model can be improved for laser drivers in future work. Finally, we discuss differences between the predictions of the multi- and single-sheath models for beam loading.

physics.plasm-ph↗

arXiv2020

Generation and acceleration of high brightness electrons beams bunched at X-ray wavelengths using plasma-based acceleration

We show using particle-in-cell (PIC) simulations and theoretical analysis that a high-quality electron beam whose density is modulated at angstrom scales can be generated directly using density downramp injection in a periodically modulated density in nonlinear plasma wave wakefields. The density modulation turns on and off the injection of electrons at the period of the modulation. Due to the unique longitudinal mapping between the electrons' initial positions and their final trapped positions inside the wake, this results in an electron beam with density modulation at a wavelength orders of magnitude shorter than the plasma density modulation. The ponderomotive force of two counter propagating lasers of the same frequency can generate a density modulation at half the laser wavelength. Assuming a laser wavelength of $0.8\micro\meter$, fully self-consistent OSIRIS PIC simulations show that this scheme can generate high quality beams modulated at wavelengths between 10s and 100 angstroms. Such beams could produce fully coherent, stable, hundreds of GW X-rays by going through a resonant undulator.

physics.acc-ph↗

arXiv2020

A new field solver for modeling of relativistic particle-laser interactions using the particle-in-cell algorithm

A customized finite-difference field solver for the particle-in-cell (PIC) algorithm that provides higher fidelity for wave-particle interactions in intense electromagnetic waves is presented. In many problems of interest, particles with relativistic energies interact with intense electromagnetic fields that have phase velocities near the speed of light. Numerical errors can arise due to (1) dispersion errors in the phase velocity of the wave, (2) the staggering in time between the electric and magnetic fields and between particle velocity and position and (3) errors in the time derivative in the momentum advance. Errors of the first two kinds are analyzed in detail. It is shown that by using field solvers with different $\mathbf{k}$-space operators in Faraday's and Ampere's law, the dispersion errors and magnetic field time-staggering errors in the particle pusher can be simultaneously removed for electromagnetic waves moving primarily in a specific direction. The new algorithm was implemented into OSIRIS by using customized higher-order finite-difference operators. Schemes using the proposed solver in combination with different particle pushers are compared through PIC simulation. It is shown that the use of the new algorithm, together with an analytic particle pusher (assuming constant fields over a time step), can lead to accurate modeling of the motion of a single electron in an intense laser field with normalized vector potentials, $eA/mc^2$, exceeding $10^4$ for typical cell sizes and time steps.

physics.comp-ph↗

arXiv2019

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes

The particle-in-cell (PIC) method is widely used to model the self-consistent interaction between discrete particles and electromagnetic fields. It has been successfully applied to problems across plasma physics including plasma based acceleration, inertial confinement fusion, magnetically confined fusion, space physics, astrophysics, high energy density plasmas. In many cases the physics involves how relativistic particles are generated and interact with plasmas. However, when relativistic particles stream across the grid both in vacuum and in plasma there are many numerical issues that may arise which can lead to incorrect physics. We present a detailed analysis of how discretized Maxwell solvers used in PIC codes can lead to numerical errors to the fields that surround particles that move at relativistic speeds across the grid. Expressions for the axial electric field as integrals in k space are presented. Two types of errors to these expressions are identified. The first arises from errors to the numerator of the integrand and leads to unphysical fields that are antisymmetric about the particle. The second arises from errors to the denominator of the integrand and lead to Cerenkov like radiation in "vacuum". These fields are not anti-symmetric, extend behind the particle, and cause the particle to accelerate or decelerate depending on the solver and parameters. The unphysical fields are studied in detail for two representative solvers - the Yee solver and the FFT based solver. A solution for eliminating these unphysical fields by modifying the k operator in the axial direction is also presented. Using a customized finite difference solver, this solution was successfully implemented into OSIRIS. Results from the customized solver are also presented. This solution will be useful for a beam of particles that all move in one direction with a small angular divergence.

physics.plasm-ph↗

arXiv2016

Controlling the Numerical Cerenkov Instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift ($\hat 1$ direction). We show that this eliminates the main NCI modes with moderate $\vert k_1 \vert$, while keeps additional main NCI modes well outside the range of physical interest with higher $\vert k_1 \vert$. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along $\hat 1$ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasmas, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

physics.comp-ph↗

arXiv2015

Lorentz boosted frame simulation of Laser wakefield acceleration in quasi-3D geometry

When modeling laser wakefield acceleration (LWFA) using the particle-in-cell (PIC) algorithm in a Lorentz boosted frame, the plasma is drifting relativistically at $β_b c$ towards the laser, which can lead to a computational speedup of $\sim γ_b^2=(1-β_b^2)^{-1}$. Meanwhile, when LWFA is modeled in the quasi-3D geometry in which the electromagnetic fields and current are decomposed into a limited number of azimuthal harmonics, speedups are achieved by modeling three dimensional problems with the computation load on the order of two dimensional $r-z$ simulations. Here, we describe how to combine the speed ups from the Lorentz boosted frame and quasi-3D algorithms. The key to the combination is the use of a hybrid Yee-FFT solver in the quasi-3D geometry that can be used to effectively eliminate the Numerical Cerenkov Instability (NCI) that inevitably arises in a Lorentz boosted frame due to the unphysical coupling of Langmuir modes and EM modes of the relativistically drifting plasma in these simulations. In addition, based on the space-time distribution of the LWFA data in the lab and boosted frame, we propose to use a moving window to follow the drifting plasma to further reduce the computational load. We describe the details of how the NCI is eliminated for the quasi-3D geometry, the setups for simulations which combine the Lorentz boosted frame and quasi-3D geometry, the use of a moving window, and compare the results from these simulations against their corresponding lab frame cases. Good agreement is obtained, particularly when there is no self-trapping, which demonstrates it is possible to combine the Lorentz boosted frame and the quasi-3D algorithms when modeling LWFA to achieve unprecedented speedups.

physics.plasm-ph↗

arXiv2015

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit

A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to correctly account for the EM calculation in hybrid Yee-FFT solver. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.

physics.comp-ph↗

arXiv2015

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes

When using an electromagnetic particle-in-cell (EM-PIC) code to simulate a relativistically drifting plasma, a violent numerical instability known as the numerical Cerenkov instability (NCI) occurs. The NCI is due to the unphysical coupling of electromagnetic waves on a grid to wave-particle resonances, including aliased resonances, i.e., $ω+ 2πμ/Δt=(k_1+ 2πν_1/Δx_1)v_0$, where $μ$ and $ν_1$ refer to the time and space aliases and the plasma is drifting relativistically at velocity $v_0$ in the $\hat{1}$-direction. Recent studies have shown that an EM-PIC code which uses a spectral field solver and a low pass filter can eliminate the fastest growing modes of the NCI. Based on these studies a new spectral PIC code for studying laser wakefield acceleration (LWFA) in the Lorentz boosted frame was developed. However, we show that for parameters of relevance for LWFA simulations in the boosted frame, a relativistically drifting plasma is susceptible to a host of additional unstable modes with lower growth rates, and that these modes appear when the fastest growing unstable modes are filtered out. We show that these modes are most easily identified as the coupling between modes which are purely transverse (EM) and purely longitudinal (Langmuir) in the rest frame of the plasma for specific time and space aliases. We rewrite the dispersion relation of the drifting plasma for a general field solver and obtain analytic expressions for the location and growth rate for each unstable mode, i.e, for each time and space aliased resonances. We show for the spectral solver that when the fastest growing mode is eliminated a new mode at the fundamental resonance ($μ=ν_1=0$) can be seen. (Please check the whole abstract in the paper).

physics.plasm-ph↗

arXiv2013

Modeling of Laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver

Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in which the plasma drifts towards the laser with $v_b$ can speedup the simulation by factors of $γ^2_b=(1-v^2_b/c^2)^{-1}$. In these simulations the relativistic drifting plasma inevitably induces a high frequency numerical instability that contaminates the interested physics. Various approaches have been proposed to mitigate this instability. One approach is to solve Maxwell equations in Fourier space (a spectral solver) as this has been shown to suppress the fastest growing modes of this instability in simple test problems using a simple low pass, ring (in two dimensions), or shell (in three dimensions) filter in Fourier space. We describe the development of a fully parallelized, multi-dimensional, particle-in-cell code that uses a spectral solver to solve Maxwell's equations and that includes the ability to launch a laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it is based on the components of the UCLA PIC framework (UPIC). We show that by using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary $γ_b$ can be conducted without the presence of the numerical instability. We also compare the results of a few LWFA cases for several values of $γ_b$, including lab frame simulations using OSIRIS, a EM-PIC code with a finite difference time domain (FDTD) Maxwell solver. These comparisons include cases in both linear, and nonlinear regimes. We also investigate some issues associated with numerical dispersion in lab and boosted frame simulations and between FDTD and spectral solvers.

physics.comp-ph↗

arXiv2013

Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators

A new generation of laser wakefield accelerators, supported by the extreme accelerating fields generated in the interaction of PW-Class lasers and underdense targets, promises the production of high quality electron beams in short distances for multiple applications. Achieving this goal will rely heavily on numerical modeling for further understanding of the underlying physics and identification of optimal regimes, but large scale modeling of these scenarios is computationally heavy and requires efficient use of state-of-the-art Petascale supercomputing systems. We discuss the main difficulties involved in running these simulations and the new developments implemented in the OSIRIS framework to address these issues, ranging from multi-dimensional dynamic load balancing and hybrid distributed / shared memory parallelism to the vectorization of the PIC algorithm. We present the results of the OASCR Joule Metric program on the issue of large scale modeling of LWFA, demonstrating speedups of over 1 order of magnitude on the same hardware. Finally, scalability to over $\sim 10^6$ cores, and sustained performance over $\sim 2$ PFlops is demonstrated, opening the way for large scale modeling of laser wakefield accelerator scenarios.

physics.plasm-ph↗

arXiv2012

Numerical instability due to relativistic plasma drift in EM-PIC simulations

The numerical instability observed in the Electromagnetic-Particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity and find an instability attributed to the coupling between the beam modes of the drifting plasma and the electromagnetic modes in the system. The characteristic pattern of the instability in Fourier space for various simulation setups and Maxwell Equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of instability growth rate and makes the parameter scan for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results and good agreement is found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of $|\vec{k}|$ essentially eliminates the instability while not modifying modes of physical interest. The use of spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.

physics.plasm-ph↗