One-dimensional Particle-in-cell Simulations Research Articles

Influence of different particle injection methods on plasma sheath with strong production of negative ion in one-dimensional PIC simulation

Particle injection is necessary to maintain the plasma source term in particle-in-cell (PIC) simulation. There are two commonly used particle injection methods, namely, a) constant flux injection, in which a fixed number of ion-electron pairs are injected each time step, and b) pair re-injection, in which the number of ion-electron pairs injected is according to the number of positive ions removed. Different injection methods may bring big difference to the simulation results. Therefore, the appropriate particle injection method must be selected according to the object and purpose of simulation to obtain the correct result. In this paper, a 1D3V (one dimension in space and three dimensions in velocity space) PIC model is used to analyze the evolution of plasma in the formation of space charge limited (SCL) sheath and reverse sheath with the condition of surface production, and the differences of the two particle injection methods are compared. It is found that the simulation result with pair re-injection does not match experiment result.

Resolving multi-dimensional plasma phenomena in Hall thrusters using the reduced-order particle-in-cell scheme

Plasma in Hall thrusters exhibits a complex behavior, characterized by the interplay between various dominant processes in each of the thruster’s coordinates. The emergence of high-power Hall thrusters in the recent years and the design modifications intended to extend the lifetime of these devices have further amplified the three-dimensional nature of the plasma behavior. In this regard, the novel reduced-order particle-in-cell (PIC) scheme provides the possibility to resolve the multi-dimensional interactions in a Hall thruster at a computational cost up to two orders of magnitude lower than current multi-dimensional PIC simulations. To demonstrate this point, we present in this article the results from a series of pseudo-two-dimensional simulations we performed in three configurations: axial-azimuthal, azimuthal-radial, and axial-radial. We show that, in each configuration, the pseudo-2D PIC scheme provides a significantly improved picture of the involved physics compared to a one-dimensional PIC simulation and captures self-consistently the coupling between the plasma processes in different directions, notably similar to the observations from full-2D kinetic simulations.

Comparison of 1D and 2D particle-in-cell simulations for DC magnetron sputtering discharges

One-dimensional and two-dimensional particle-in-cell (PIC)/Monte Carlo collision simulations are performed for a balanced direct current magnetron sputtering (DCMS) discharge. The plasma parameters obtained by both simulations above the target racetrack share similar features and magnitudes under similar discharge intensities, i.e., similar local discharge current densities. The commonly observed high-energy tail of electron energy distribution in DCMS discharges is reproduced in both simulations. The accuracy and applicability of using one-dimensional simulations to qualitatively investigate the characteristics of balanced DCMS discharge are confirmed. In terms of capturing the key physical mechanisms in DCMS, one-dimensional PIC simulation is an efficient method, which could largely alleviate the computational expense and preserve the physical fidelity of modeling results.

Optimizing laser–plasma interactions for ion acceleration using particle-in-cell simulations and evolutionary algorithms

The development of ultra-intense laser-based sources of high energy ions is an important goal, with a variety of potential applications. One of the barriers to achieving this goal is the need to maximize the conversion efficiency from laser energy to ion energy. We apply a new approach to this problem, in which we use an evolutionary algorithm to optimize conversion efficiency by exploring variations of the target density profile with thousands of one-dimensional particle-in-cell (PIC) simulations. We then compare this ‘optimal’ target identified by the one-dimensional PIC simulations to more conventional choices, such as with an exponential scale length pre-plasma, with fully three-dimensional PIC simulations. The optimal target outperforms the conventional targets in terms of maximum ion energy by 20% and show a noticeable enhancement of conversion efficiency to >2 MeV ions. This target geometry enhances laser coupling to the electrons, while still allowing the laser to strongly reflect from an effectively thin target. These results underscore the potential for this statistics-driven approach to guide research into optimizing laser–plasma simulations and experiments.

Penetration of a radio frequency electromagnetic field into a magnetized plasma: one-dimensional PIC simulation studies

Penetration of a radio frequency (rf) electromagnetic field into a magnetized plasma is discussed by performing one-dimensional particle-in-cell (PIC) simulations. We consider two models: an electrostatic (ES) model using an external rf voltage and an electromagnetic (EM) model using an external rf current. The background magnetic field is perpendicular to the one-dimensional system. In the ES model, the external rf voltage across the plasma produces the rf electric field into the plasma. When ω rf =Ω e /2, where ω rf and Ω e are the externally applied field and electron gyrofrequencies, respectively, the ion-rich sheath is formed due to the electron wall loss caused by the electron polarization drift. When ω rf =ω LH /2, where ω LH is the lower hybrid frequency, the electron-rich sheath is formed due to the ion wall loss caused by its larger gyroradius than the electron. In the EM model, an induced electromagnetic field via the external rf current forms a standing wave in the plasma region bounded by the external antennas. When the diameter of the plasma is equal to the wave length, the spatial/temporal profiles of the rf standing waves are well explained by a cold collisionless plasma linear theory except for the existence of the sheath. When the rf magnetic field is increased to 10 % of the background magnetic field, the waveforms become irregular and complex because of the boundary effects.

Residual Bernstein-Greene-Kruskal-like waves after one-dimensional electron wave breaking in a cold plasma

A one-dimensional particle in cell simulation of large amplitude plasma oscillations is carried out to explore the physics beyond wave breaking in a cold homogeneous unmagnetized plasma. It is shown that after wave breaking, all energy of the plasma oscillation does not end up as random kinetic energy of particles, but some fraction, which is decided by Coffey's wave breaking limit in warm plasma, always remains with two oppositely propagating coherent Bernstein-Greene-Kruskal like modes with supporting trapped particle distributions. The randomized energy distribution of untrapped particles is found to be characteristically non-Maxwellian with a preponderance of energetic particles.

Generation of ultraintense proton beams by multi-ps circularly polarized laser pulses for fast ignition-related applications

A scheme of generation of ultraintense proton beams relevant for proton fast ignition (PFI) which employs multi-ps, circularly polarized laser pulse irradiating a thick (≥ 10 μm) H-rich target is proposed and examined using one-dimensional particle-in cell-simulations. It is shown that a 5-ps laser pulse of intensity ∼ (2–5) × 1020W/cm2 irradiating the target of the areal proton density ∼ 2 × 1020cm−2 can produce – with a high energetic efficiency – a proton beam (plasma block) of parameters (intensity, energy fluence, pulse duration, proton energy spectrum) close to those required for PFI. At a fixed total laser energy, the proton beam parameters can be controlled and fitted to the PFI requirements by changing the laser intensity (energy fluence) and/or the target thickness as well as by using a shaped (curved) target inserted into a guiding cone.

Moving electron density gratings induced in the beat-wave field of two counterpropagating laser pulses

The production and physical characteristics of moving electron density gratings (MEDGs) are investigated by analytical model and particle-in-cell (PIC) simulations. When the frequency difference of two counterpropagating pump pulses is equal to the electron plasma frequency, large amplitude electron plasma wave is resonantly excited in the plasma. As a result, electrons are excited to form a moving, gratinglike structure in the interfering region of pump pulses, while the ions keep at rest. The spatial period and velocity of the MEDG are obtained by solving the electron density modulation equation, which agrees well with one-dimensional PIC simulation results. When a short signal laser pulse is scattered on the MEDG, the frequency of the backscattering wave shifts due to the stimulated Raman scattering.

Generation of plasma intrinsic oscillation at the front surface of a target irradiated by a circularly polarized laser pulse

In laser-target interaction, the effects of laser intensity on plasma oscillation at the front surface of targets have been investigated by one-dimensional particle in cell simulations. The periodical oscillations of the ion density and electrostatic field at the front surface of the targets are reported for the first time, which is considered as an intrinsic property of the target excited by the laser. The oscillation period depends only on initial plasma density and is irrelevant with laser intensity. Flattop structures with curves in ion phase space are found with a more intense laser pulse due to the larger amplitude variation of the electrostatic field. A simple but valid model is proposed to interpret the curves.

Theoretical analysis and simulations of strong terahertz radiation from the interaction of ultrashort laser pulses with gases

Terahertz (THz) radiation from the interaction of ultrashort laser pulses with gases is studied both by theoretical analysis and particle-in-cell (PIC) simulations. A one-dimensional THz generation model based on the transient ionization electric current mechanism is given, which explains the results of one-dimensional PIC simulations. At the same time the relation between the final THz field and the initial transient ionization current is shown. One- and two-dimensional simulations show that for the THz generation the contribution of the electric current due to ionization is much larger than the one driven by the usual ponderomotive force. Ionization current generated by different laser pulses and gases is also studied numerically. Based on the numerical results we explain the scaling laws for THz emission observed in the recent experiments performed by Xie et al. [Phys. Rev. Lett. 96, 075005 (2006)]. We also study the effective parameter region for the carrier envelop phase measurement by the use of THz generation.

Analysis of the excited argon atoms in the GEC RF reference cell by means of one-dimensional PIC simulations

We examine the question of whether the excited states in argon contribute significantly to ionization in a capacitively coupled plasma through metastable pooling and step-ionization processes. We look at this issue by means of a one-dimensional particle-in-cell (PIC) code, with collisions treated by a Monte Carlo collision package. In the range explored, 50–1000 mTorr, the main source of ionization, in the absence of secondary emission, is direct ionization from the ground state with a contribution from excited states that is negligible at lower pressures, but increases in importance at higher pressures. When secondary electrons are included, their interaction with ground state neutrals dominates the ionization. At higher pressures the metastable profiles can reveal useful information on the non-uniform mean electron energy across the discharge, even though these states do not necessarily play a significant role in ionization.

Interacting eigenmodes of a plasma diode with a density gradient

The formation of narrow high frequency electric field spikes in plasma density gradients is investigated using one-dimensional particle in cell simulations. It is found that the shape of the plasma density gradient is very important for the spike formation. A coupling to the ion motion, is not necessary for the formation of hf spikes. However, the hf spike influences the ion motion, and ion waves are seen in the simulations. Dispersion relations are calculated using realistic, non-Maxwellian, distribution functions. The spike can be seen as a coupled system of two eigenmodes of a plasma diode fed by a beam-plasma interaction. Based on a simplified fluid description of such eigenmodes, explanations for the localization of the spike, spatially and in frequency, are given. The amplitude of the oscillating density is comparable with the dc level close to the cathode. This sets a limit of a wave amplitude in the whole system.

The effects of a small transverse magnetic field upon a capacitively coupled RF discharge

A capacitively-coupled RF argon discharge at a pressure of 10 mTorr with a plate separation of 7.5 cm has been studied both experimentally and using a one-dimensional particle in cell simulation with Monte Carlo collisions. A magnetic field of 0 to 60 G is applied in the direction parallel to the capacitor plates. In the simulation it was found that as the magnetic field was increased such that the electron cyclotron orbit radius of the hot electrons became smaller than of the order of the discharge length, the electron heating in the bulk of the discharge increased. The dominant electron heating mechanism was observed to change from a stochastic sheath to a bulk ohmic electron heating mode, with a variation of field from a to 10 G. This was accompanied by a drop in the plasma density at small magnetic fields, which was also observed experimentally. At higher magnetic fields the plasma density was found to increase, A detailed discussion of the simulation results is presented drawing comparisons with the experimental results, with which there is good agreement, and a simple magnetohydrodynamic model for the bulk heating. >