2D PIC Simulations Research Articles

3D-PIC simulation of the electron beam interaction with modulated density plasma

In this paper, the three-dimensional(3D3V) numerical model is developed for the simulation of enhanced electromagnetic emission due to the beam injection into the modulated density plasma. The proposed model is fully kinetic and based on Particle-In-Cell method. The results of numerical experiments for different beam and plasma parameters are presented. Comparison of the radiation efficiency for the flat plasma layer and circle plasma column with different plasma density modulation amplitude are obtained. Numerical experiments have been performed using computer systems with parallel architecture.

Betatron resonance electron acceleration and generation of relativistic electron beams using 200 fs Ti:sapphire laser pulses

The generation of relativistic electron beams with quasi-thermal energy distribution (maximum energy: 30 MeV) by the interaction of a Ti:sapphire laser pulse of 200 fs duration, focussed to an intensity of ∼2.1 × 1018 W cm−2, with an underdense (electron density ∼3.6 × 1019 to ∼1.1 × 1020 cm−3) He gas-jet plasma was observed. We observed two stages of self-focusing of the laser pulse in the plasma. Two groups of accelerated electrons associated with these two stages of laser channeling were also observed, and are attributed to the betatron resonance acceleration mechanism. This is supported by 2D PIC simulations performed using the EPOCH code and a detailed theoretical analysis. Further, the generation of quasi-monoenergetic (ΔE/E ∼ 10%–20%) electron beams with a peak energy of ∼17–22 MeV was also observed, even with such long laser pulses, although with a low probability of occurrence.

Trains of electron micro-bunches in plasma wake-field acceleration

Plasma-based charged particle accelerators have been intensively investigated in the past three decades due to their capability to open up new horizons in accelerator science and particle physics yielding electric field accelerating gradient more than three orders of magnitudes higher than in conventional devices. At the current stage the most advanced and reliable mechanism for accelerating electrons is based on the propagation of an intense laser pulse or a relativistic electron beam in a low density gaseous target. In this paper we concentrate on the electron beam-driven plasma wake-field acceleration and demonstrate using 3D PiC simulations that a train of electron micro-bunches with ∼10 fs period can be generated behind the driving beam propagating in a density down-ramp. We will discuss the conditions and properties of the micro-bunches generated aiming at understanding and study of multi-bunch mechanism of injection. It is show that the periodicity and duration of micro-bunches can be controlled by adjusting the plasma density gradient and driving beam charge.

Theory and simulations of radiation friction induced enhancement of laser-driven longitudinal fields

We consider the generation of a quasistatic longitudinal electric field by intense laser pulses propagating in a transparent plasma with radiation friction (RF) taken into account. For both circular and linear polarization of the driving pulse we develop a 1D analytical model of the process, which is valid in a wide range of laser and plasma parameters. We define the parameter region where RF results in an essential enhancement of the longitudinal field. The amplitude and the period of the generated longitudinal wave are estimated and optimized. Our theoretical predictions are confirmed by 1D and 2D PIC simulations. We also demonstrate numerically that RF should substantially enhance the longitudinal field generated in a plasma by a 10 PW laser such as ELI Beamlines.

Design and optimization of G-band extended interaction klystron with high output power

A ladder-type Extended Interaction Klystron (EIK) with unequal-length slots in the G-band is proposed and designed. The key parameters of resonance cavities working in the π mode are obtained based on the theoretical analysis and 3D simulation. The influence of the device fabrication tolerance on the high-frequency performance is analyzed in detail, and it is found that at least 5 μm of machining precision is required. Thus, the dynamic tuning is required to compensate for the frequency shift and increase the bandwidth. The input and output coupling hole dimensions are carefully designed to achieve high output power along with a broad bandwidth. The effect of surface roughness of the metallic material on the output power has been investigated, and it is proposed that lower surface roughness leads to higher output power. The focusing magnetic field is also optimized to 0.75 T in order to maintain the beam transportation and achieve high output power. With 16.5 kV operating voltage and 0.30 A beam current, the output power of 360 W, the efficiency of 7.27%, the gain of 38.6 dB, and the 3 dB bandwidth of 500 MHz are predicted. The output properties of the EIK show great stability with the effective suppression of oscillation and mode competition. Moreover, small-signal theory analysis and 1D code AJDISK calculations are carried out to verify the results of 3D PIC simulations. A close agreement among the three methods proves the relative validity and the reliability of the designed EIK. Thus, it is indicated that the EIK with unequal-length slots has potential for power improvement and bandwidth extension.

TNSA proton maximum energy laws for 2D and 3D PIC simulations

Numerical simulations are a prominent tool in laser-plasma experiments. Their role, as a guide in new regime explorations and as a support for understanding laboratory results, is undisputed. But as the experiments themselves are growing in costs, setup time and complexity, so are the numerical counterparts. Nowadays it is often necessary to investigate, with great accuracy, a huge set of parameters, in order to explore interesting features.In literature, it is well known that two-dimensional particle in cell (2D PIC) simulations can only give a qualitative estimation of experimental results, often through a great layer of arbitrariness. On the other hand, three-dimensional (3D) PIC simulations, for the same setup, can typically require two orders of magnitude more of computational resources, to deliver results that, while being similar to laboratory results, are still far from being a real match, due to the many uncertainties, in the parameters and in the model, included in the physical engine.Following our recent published work, we discuss here a couple of empirical laws that we proposed, that can help giving quantitative insight into 2D PIC simulations and determining when 3D simulations should be stopped, if it is not really necessary to do a detailed exploration of the numerical results at long times.

Laser wakefield acceleration with high-power, few-cycle mid-IR lasers

The study of laser wakefield electron acceleration (LWFA) using mid-IR laser drivers is a promising path for future laser driven electron accelerators, when compared to traditional near-IR laser drivers operating at 0.8–1 μm central wavelength (λlaser), as the necessary vector potential (a0) for electron injection can be achieved with smaller laser powers due to the linear dependence on λlaser. In this work, we perform 2D PIC simulations on LWFA using few-cycle, high power (5–15 TW) laser systems with λlaser ranging from 0.88 to 10 μm. Such few-cycle systems are currently under development, aiming at Gas High Harmonics Generation applications, where the favorable λlaser2 scaling extends the range of the XUV photon energies. We keep a0 and ne∕ncr (ne being the plasma density and ncr the critical density for each λlaser) as common denominators in our simulations, allowing for comparisons between drivers with different λlaser, with respect to the accelerated electron beam energy, charge and conversion efficiency. While the electron energies are mainly dominated by the plasma dynamics, the laser to electron beam energy conversion efficiency shows significant enhancement with longer wavelength laser drivers.

High order harmonics generation by relativistically circularly polarized laser-solid interaction

Coherent extreme ultra-violet (XUV) and soft X-ray light with attosecond duration enable the time-resolved study of electron dynamics in a completely new regime. High order harmonic generation (HHG) from the highly nonlinear process of relativistically intense laser interactions with solid-density plasma offers a very new way to generate such a light source. In this paper, we study the HHG by a relativistically circularly polarized femtosecond laser interacting with solid-density plasma. The experiment is carried out by using a 200 TW Ti:sapphire laser system at the Laboratory for Laser Plasmas in Shanghai Jiao Tong University, China. The laser system can deliver laser pulses at 800 nm with a pulse duration (full width at half maximum, FWHM) of 25 fs and repetition rate of 10 Hz. The circularly polarized laser beam with an energy of 460 mJ is used in the experiment and focused by an F/4 off-axis parabolic mirror at an incidence angle of 40 with respect to the glass target. The focal spot diameter is 6 m (FWHM) with 25% energy enclosed, giving a calculated peak intensity of 1.61019 W/cm2. We detect high order harmonics by a flat-field spectrometer. The experimental results show that high order harmonic radiation can also be efficiently generated by a circularly polarized laser at a lager incidence angle, which provides a straightforward way to obtain a circularly polarized XUV light source. Different plasma density scale lengths are obtained by introducing a prepulse with different delays. We study the dependence of HHG efficiency on plasma density scale length by the circularly polarized laser, and find an optimal density scale length to exist. The influence of laser polarization and plasma density scale length on HHG are studied by two-dimensional (2D) PIC simulations. The good agreement is found between the 2D PIC simulations and experimental results. We plan to measure the polarization characteristics of high order harmonic produced by the interaction of circularly polarized lasers with solid target in the future. It is expected to obtain a compact coherent circularly polarized XUV light source, which can be used to study the ultra-fast dynamic process of magnetic materials.

Analytical and numerical studies of positive ion beam expansion for surface treatment applications

The aim of this work is to study the expansion in vacuum, of a positive ion beam with the use of one dimensional (1D) analytic model and a two dimensional Particle-In-Cell (2D-PIC) simulation. The ion beam is extracted and accelerated from preformed plasma by an extraction system composed of two polarized parallel perforated grids. The results obtained with both approaches reveal the presence of a potential barrier downstream the extraction system which tends to reflect the ion flux. The dependence of the critical distance for which all extracted ions are reflected, is investigated as a function of the extracted ion beam current density. In particular, it is shown that the 1D model recovers the well-known Child-Langmuir law and that the 2D simulation presents a significant discrepancy with respect to the 1D prediction. Indeed, for a given value of current density, the transverse effects lead to a greater critical distance.

Extension of temperature anisotropy Weibel instability to non-Maxwellian plasmas by 2D PIC simulation

AbstractThe Weibel instability driven by temperature anisotropy is investigated in a two-dimensional (2D) particle-in-cell simulation in non-extensive statistics in the relativistic regime. In order to begin the simulation, we introduced a new 2D anisotropic distribution function in the context of non-extensive statistics. The heavy ions considered to be immobile and form the neutralizing background. The numerical results show that non-extensive parameterqplays an important role on the magnetic field saturation time, the time of reduction temperature anisotropy, evolution time to the quasi-stationary state, and the peak energy density of magnetic field. We observe that the instability saturation time increases by increasing the non-extensive parameterq. It is shown that structures with superthermal electrons (q< 1) could generate strong magnetic fields during plasma thermalization. The simulation results agree with the previous simulations for an anisotropic Maxwellian plasma (q= 1).

Plasma effects on relativistic pair beams from TeV blazars: PIC simulations and analytical predictions

Pair beams produced by very high-energy radiation from TeV blazars emit gamma rays in the GeV band by inverse-Compton scattering of soft photons. The observed GeV-band signal is smaller than that expected from the full electromagnetic cascade. This means that the pair beams must be affected by other physical processes reducing their energy flux. One possible loss mechanism involves beam-plasma instabilities that we consider in the present work. For realistic parameters the pair beams can not be simulated by modern computers. Instead, we use a simple analytical model to find a range of the beam parameters that (i) provides a physical picture similar to that of realistic pair beams and (ii) at the same time can be handled by available computational resources. Afterwards, we performed corresponding 2D PIC simulations. We confirm that the beams experience only small changes in the relevant parameter regime, and other processes such as deflection in magnetic field must be at play.

Massive parallel 3D PIC simulation of negative ion extraction

The 3D PIC-MCC code ONIX is dedicated to modeling Negative hydrogen/deuterium Ion (NI) extraction and co-extraction of electrons from radio-frequency driven, low pressure plasma sources. It provides valuable insight on the complex phenomena involved in the extraction process. In previous calculations, a mesh size larger than the Debye length was used, implying numerical electron heating. Important steps have been achieved in terms of computation performance and parallelization efficiency allowing successful massive parallel calculations (4096 cores), imperative to resolve the Debye length. In addition, the numerical algorithms have been improved in terms of grid treatment, i.e., the electric field near the complex geometry boundaries (plasma grid) is calculated more accurately. The revised model preserves the full 3D treatment, but can take advantage of a highly refined mesh. ONIX was used to investigate the role of the mesh size, the re-injection scheme for lost particles (extracted or wall absorbed), and the electron thermalization process on the calculated extracted current and plasma characteristics. It is demonstrated that all numerical schemes give the same NI current distribution for extracted ions. Concerning the electrons, the pair-injection technique is found well-adapted to simulate the sheath in front of the plasma grid.

Double-cusp simulation during northward IMF using 3D PIC global code

The cusp has important effects on the transportation of particles and their energy from the solar wind to the magnetosphere, and ionosphere, and high-altitude atmosphere. The cusp can be considered to be a part of the magnetospheric boundary layer with weaker magnetic fields. It has been studied since 1971 by different satellite observations. Despite many years of investigation, some problems, such as the boundaries, shapes, and method of construction, remain to be solved. The double cusp was first reported by Wing using the observation of the DMSP satellite. He also compared the results of observations with the results of a 2D MHD simulation. In this study, by performing simulations and analyzing the results, we report the observation of a V-shaped double-cusp structure under the northward Interplanetary Magnetic Field (IMF). In our simulation, the double cusp was seen only for electrons, although a weak double cusp was observed for ions as well. We showed that this double cusp occurred because of electron precipitation from different sources of solar wind and magnetosphere with different magnetic field strengths. In previous studies of the double cusp, there were debates on its spatial structure or on its temporal behavior due to the cusp movement caused by the sharp solar wind effects on the magnetosphere shape. Here we report the spatial detection of the double cusp similar to the one observed by the DMSP satellite, but for the northward IMF case. Also, we investigate the asymmetry along the dawn-dusk side of the magnetosphere using our 3D PIC simulation code.

Rise time of proton cut-off energy in 2D and 3D PIC simulations

The Target Normal Sheath Acceleration regime for proton acceleration by laser pulses is experimentally consolidated and fairly well understood. However, uncertainties remain in the analysis of particle-in-cell simulation results. The energy spectrum is exponential with a cut-off, but the maximum energy depends on the simulation time, following different laws in two and three dimensional (2D, 3D) PIC simulations so that the determination of an asymptotic value has some arbitrariness. We propose two empirical laws for the rise time of the cut-off energy in 2D and 3D PIC simulations, suggested by a model in which the proton acceleration is due to a surface charge distribution on the target rear side. The kinetic energy of the protons that we obtain follows two distinct laws, which appear to be nicely satisfied by PIC simulations, for a model target given by a uniform foil plus a contaminant layer that is hydrogen-rich. The laws depend on two parameters: the scaling time, at which the energy starts to rise, and the asymptotic cut-off energy. The values of the cut-off energy, obtained by fitting 2D and 3D simulations for the same target and laser pulse configuration, are comparable. This suggests that parametric scans can be performed with 2D simulations since 3D ones are computationally very expensive, delegating their role only to a correspondence check. In this paper, the simulations are carried out with the PIC code ALaDyn by changing the target thickness L and the incidence angle α, with a fixed a0 = 3. A monotonic dependence, on L for normal incidence and on α for fixed L, is found, as in the experimental results for high temporal contrast pulses.

Proton acceleration from magnetized overdense plasmas

Proton acceleration by an ultraintense short pulse circularly polarized laser from an overdense three dimensional (3D) particle-in-cell (PIC) 3D-PIC simulations. The axial magnetic field modifies the dielectric constant of the plasma, which causes a difference in the behaviour of ponderomotive force in case of left and right circularly polarized laser pulse. When the laser is right circularly polarized, the ponderomotive force gets enhanced due to cyclotron effects generating high energetic electrons, which, on reaching the target rear side accelerates the protons via target normal sheath acceleration process. On the other hand, in case of left circular polarization, the effects get reversed causing a suppression of the ponderomotive force at a short distance and lead towards a rise in the radiation pressure, which results in the effective formation of laser piston. Thus, the axial magnetic field enhances the effect of radiation pressure in case of left circularly polarized laser resulting in the generation of high energetic protons at the target front side. The transverse motion of protons get reduced as they gyrate around the axial magnetic field which increases the beam collimation to some extent. The optimum thickness of the overdense plasma target is found to be increased in the presence of an axial magnetic field.

Design analysis and simulation study of an efficiency enhanced L-band MILO

In this article, an experimental L-band compact magnetically insulated transmission line oscillator (MILO) has been simulated using the 3D PIC simulation code “Particle Studio,” and an improvement in the device efficiency has been obtained. The detailed interaction and operating mechanism describing the role of sub-assemblies have been explained. The performance of the device was found to be the function of the distance between the end-surface of the cathode and the beam-dump disk. During simulation, a high power microwave of the TM01 mode is generated with the peak RF-power of 6 GW and the power conversion efficiency of 19.2%, at the operating voltage of ∼600 kV and at the current of 52 kA. For better impedance matching or maximum power transfer, four stubs have been placed at the λg/4 distance from the extractor cavity, which results in the stable RF power output. In this work, an improved L-band MILO along with a new type beam-dump disk is selected for performance improvement with typical design parameters and beam parameters. The total peak power of improved MILO is 7 GW, and the maximum power conversion efficiency is 22.4%. This improvement is achieved due to the formation of the virtual cathode at the load side, which helps in modulating the energy of electrons owing to maximum reflection of electrons from the mesh or foil.

Surface modulation and back reflection from foil targets irradiated by a Petawatt femtosecond laser pulse at oblique incidence.

A significant level of back reflected laser energy was measured during the interaction of ultra-short, high contrast PW laser pulses with solid targets at 30° incidence. 2D PIC simulations carried out for the experimental conditions show that at the laser-target interface a dynamic regular structure is generated during the interaction, which acts as a grating (quasi-grating) and reflects back a significant amount of incident laser energy. With increasing laser intensity above 1018 W/cm2 the back reflected fraction increases due to the growth of the surface modulation to larger amplitudes. Above 1020 W/cm2 this increase results in the partial destruction of the quasi-grating structure and, hence, in the saturation of the back reflection efficiency. The PIC simulation results are in good agreement with the experimental findings, and, additionally, demonstrate that in presence of a small amount of pre-plasma this regular structure will be smeared out and the back reflection reduced.

Simulation of laser-driven plasma beat-wave propagation in collisional weakly relativistic plasmas

The process of interaction of lasers beating in a plasma has been explored by virtue of particle-in-cell (PIC) simulations in the presence of electron-ion collisions. A plasma beat wave is resonantly excited by ponderomotive force by two relatively long laser pulses of different frequencies. The amplitude of the plasma wave become maximum, when the difference in the frequencies is equal to the plasma frequency. We propose to demonstrate the energy transfer between the laser beat wave and the plasma wave in the presence of electron-ion collision in nearly relativistic regime with 2D-PIC simulations. The relativistic effect and electron-ion collision both affect the energy transfer between the interacting waves. The finding of simulation results shows that there is a considerable decay in the plasma wave and the field energy over time in the presence of electron-ion collisions.

Explosion of relativistic electron vortices in laser plasmas

The interaction of high intensity laser radiation with an underdense plasma may lead to the formation of electron vortices. Though being quasistationary on the electron timescales, these structures tend to expand on a proton timescale due to Coulomb repulsion of ions. Using a simple analytical model of a stationary vortex as an initial condition, 2D PIC simulations are performed. A number of effects are observed such as vortex boundary field intensification, multistream instabilities at the vortex boundary, and bending of the vortex boundary with the subsequent transformation into smaller electron vortices.

Electromagnetic analysis of the HPM oscillator—Reltron

In this paper, electromagnetic analysis of the reltron, which is a compact, simple, and efficient high power microwave source has been presented. The beam wave interaction process of the reltron oscillator has been analyzed to understand the device physics. The split cavity oscillator and relativistic klystron principles have been extended to demonstrate the electric field responsible for beam bunching and the electron beam modulation process in the reltron. The analytical formulation to obtain the RF energy growth and efficiency of the device has also been presented. To validate the analytical results and to evaluate the overall performance of the device, beam present simulation of reltron has been performed using commercial 3D PIC simulation code “CST Particle Studio.” With the parameters of a previously reported experimental reltron device, the present analytical calculation provided ∼240 MW RF output power with ∼38% efficiency while the PIC simulation provided RF output power of ∼225 MW with ∼36% efficiency at 2.75 GHz frequency. The obtained analytical and simulation results have also been found to be in agreement of ∼6% with this experimental work.