arXiv subjects

Xinlu Xu

Publications and source records attributed to Xinlu Xu.

30 records · Page 2Linked to original sources

arXiv2020

Generation of terawatt, attosecond pulses from relativistic transition radiation

When a fs duration and hundreds of kA peak current electron beam traverses the vacuum and high-density plasma interface a new process, that we call relativistic transition radiation (R-TR) generates an intense $\sim100$ as pulse containing $\sim$ TW power of coherent VUV radiation accompanied by several smaller fs duration satellite pulses. This pulse inherits the radial polarization of the incident beam field and has a ring intensity distribution. This R-TR is emitted when the beam density is comparable to the plasma density and the spot size much larger than the plasma skin depth. Physically, it arises from the return current or backward relativistic motion of electrons starting just inside the plasma that Doppler up-shifts the emitted photons. The number of R-TR pulses is determined by the number of groups of plasma electrons that originate at different depths within the first plasma wake period and emit coherently before phase mixing.

physics.plasm-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↗

arXiv2020

A quasi-static particle-in-cell algorithm based on an azimuthal Fourier decomposition for highly efficient simulations of plasma-based acceleration: QPAD

The 3D quasi-static particle-in-cell (PIC) algorithm is a very efficient method for modeling short-pulse laser or relativistic charged particle beam-plasma interactions. In this algorithm, the plasma response to a non-evolving laser or particle beam is calculated using Maxwell's equations based on the quasi-static approximate equations that exclude radiation. The plasma fields are then used to advance the laser or beam forward using a large time step. The algorithm is many orders of magnitude faster than a 3D fully explicit relativistic electromagnetic PIC algorithm. It has been shown to be capable to accurately model the evolution of lasers and particle beams in a variety of scenarios. At the same time, an algorithm in which the fields, currents and Maxwell equations are decomposed into azimuthal harmonics has been shown to reduce the complexity of a 3D explicit PIC algorithm to that of a 2D algorithm when the expansion is truncated while maintaining accuracy for problems with near azimuthal symmetry. This hybrid algorithm uses a PIC description in r-z and a gridless description in $ϕ$. We describe a novel method that combines the quasi-static and hybrid PIC methods. This algorithm expands the fields, charge and current density into azimuthal harmonics. A set of the quasi-static field equations are derived for each harmonic. The complex amplitudes of the fields are then solved using the finite difference method. The beam and plasma particles are advanced in Cartesian coordinates using the total fields. Details on how this algorithm was implemented using a similar workflow to an existing quasi-static code, QuickPIC, are presented. The new code is called QPAD for QuickPIC with Azimuthal Decomposition. Benchmarks and comparisons between a fully 3D explicit PIC code, a full 3D quasi-static code, and the new quasi-static PIC code with azimuthal decomposition are also presented.

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↗

arXiv2019

Generating high quality ultra-relativistic electron beams using an evolving electron beam driver

A new method of controllable injection to generate high quality electron bunches in the nonlinear blowout regime driven by electron beams is proposed and demonstrated using particle-in-cell simulations. Injection is facilitated by decreasing the wake phase velocity through varying the spot size of the drive beam and can be tuned through the Courant-Snyder (CS) parameters. Two regimes are examined. In the first, the spot size is focused according to the vacuum CS beta function, while in the second, it is focused by the plasma ion column. The effects of the driver intensity and vacuum CS parameters on the wake velocity and injected beam parameters are examined via theory and simulations. For plasma densities of $\sim 10^{19} ~\text{cm}^{-3}$, particle-in-cell (PIC) simulations demonstrate that peak normalized brightnesses $\gtrsim 10^{20}~\text{A}/\text{m}^2/\text{rad}^2$ can be obtained with projected energy spreads of $\lesssim 1\%$ within the middle section of the injected beam, and with normalized slice emittances as low as $\sim 10 ~\text{nm}$.

physics.plasm-ph↗

arXiv2019

Phase-stable self-modulation of an electron-beam in a magnetic wiggler

Electron-beams with a sinusoidal energy modulation have the potential to emit sub-femtosecond x-ray pulses in a free-electron laser. The energy modulation can be generated by overlapping a powerful infrared laser with an electron-beam in a magnetic wiggler. Here we report on a new infrared source for this modulation, coherent radiation from the electron-beam itself. In this self-modulation process, the current spike on the tail of the electron-beam radiates coherently at the resonant wavelength of the wiggler, producing a six-period carrier-envelope-phase (CEP) stable infrared field with gigawatt power. This field creates a few MeV, phase-stable modulation in the electron-beam core. The modulated electron-beam is immediately useful for generating sub-femtosecond x-ray pulses at any machine repetition rate, and the CEP-stable infrared field may find application as an experimental pump or timing diagnostic.

physics.acc-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↗

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↗