3D Particle-in-cell Research Articles

Acceleration of ions with a nonadiabatic linearly polarized laser pulse

Acceleration of ions during interaction of a nonadiabatic laser pulse (i.e., a pulse with a sharp front) with a nanofilm is considered. If the amplitude of such a pulse is large enough, all electrons are removed from the target at the beginning of interaction and an energy of the most energetic ions follows approximately a parabolic law with time. Two main physical mechanisms limiting the maximal ions energy are identified and investigated in detail with the help of two-dimensional (2D) particle-in-cell (PIC) simulations. The first effect is a compensation of the ions charge due to the longitudinal return of the electrons to their initial position. The second effect is the compensation of the ions charge in the laser spot due to the transverse motion of the electrons from the periphery of the target. The theory for both effects is developed and a good agreement with the 2D PIC results is established. This theory allows predicting the optimal parameters for ions acceleration.

The generation of azimuthal magnetic field in laser-induced plasma bubbles

A two-dimensional (2D) analytical model for a laser-induced bubble is rebuilt by taking into account the generation of azimuthal magnetic field. It is shown that the azimuthal magnetic field surrounds the bubble transversely, whose amplitude peaks at the bubble edge and vanishes at laser axis. In a laser wakefield acceleration scheme, the longitudinal electric field accelerates the electrons injected from the rear of the bubble, while the azimuthal magnetic field makes the resulting energetic-electron beam converge. The analytical model is justified by a 2D Particle in Cell (PIC) simulation.

Particle in cell modelling of the observed modes of a dc wire discharge

Low-pressure dc wire induced plasma sources exhibit two stable modes of discharge—constricted below a threshold pressure and diffuse above. Starting from experimental measurements, we conduct two-dimensional particle in cell (PIC) modelling of a dc low-pressure (10−4–10−2 mbar), low-current (∼1 mA) wire discharge in helium. 2D PIC modelling is required to capture longitudinal non-uniformity of the diffuse mode. PIC simulations reproduce the two discharge modes. The voltage versus pressure curve obtained from simulations matches fairly well the experimental data, including the transition region. Discharge voltage dependence on pressure is analysed in consideration of electron impact ionization rates' evolution with energy. In light of the PIC findings, a model of the discharge mode transition based on the Child–Langmuir theory for ions is proposed. Confrontation with simulated data shows good agreement and validates the model for mode transition prediction. Simulations show that the diffuse mode is a space-charge-dominated regime.

Numerical modelling of a 10-cm-long multi-GeV laser wakefield accelerator driven by a self-guided petawatt pulse

The use of a short-pulse petawatt (PW) laser (τL<200 fs, wavelength ≈1 μm) enables experimental realization of a self-guided, multi-centimetre-long multi-GeV laser wakefield electron accelerator. A comprehensive set of numerical simulations showed that a 150 fs, 1.33 PW pulse is self-guided over 10 cm of a static filling gaseous plasma of density 1–3×1017 cm−3 and is stable against relativistic filamentation. A fully broken electromagnetic wake (electron density ‘bubble’) is excited over the entire interaction length. Variations of bubble size and shape associated with nonlinear evolution of the driving pulse result in self-injection of background plasma electrons. Self-injection begins immediately after the first nonlinear laser focus, where pulse de-focusing forces the bubble to grow. Injection continues without interruption while the bubble expands, and ceases when the laser becomes self-guided and bubble evolution stabilizes. Self-injected electrons are accelerated to ∼7 GeV with less than 10% energy spread and ∼1.3 nC charge. Numerical modelling of the laser pulse dynamics over the entire plasma length is carried out using a time-averaged, fully relativistic, quasi-static three-dimensional (3D) axi-symmetric particle-in-cell (PIC) code, WAKE. The process of electron self-injection is explored by means of both test-particle modelling (WAKE) and 3D PIC simulations using the recently developed CALDER-Circ code in quasi-cylindrical geometry.

A multidimensional theory for electron trapping by a plasma wake generated in the bubble regime

We present a theory for electron self-injection in nonlinear, multidimensional plasma waves excited by a short laser pulse in the bubble regime or by a short electron beam in the blowout regime. In these regimes, which are typical for electron acceleration in the last impressive experiments, the laser radiation pressure or the electron beam charge pushes out plasma electrons from some region, forming a plasma cavity or a bubble with a huge ion charge. The plasma electrons can be trapped in the bubble and accelerated by the plasma wakefields up to a very high energy. We derive the condition of the electron trapping in the bubble. The developed theory predicts the trapping cross section in terms of the bubble radius and the bubble velocity. It is found that the dynamic bubble deformations observed in the three-dimensional (3D) particle-in-cell (PIC) simulations influence the trapping process significantly. The bubble elongation reduces the gamma-factor of the bubble, thereby strongly enhancing self-injection. The obtained analytical results are in good agreement with the 3D PIC simulations.

Energy transfer and magnetic field generation via ion-beam driven instabilities in an electron-ion plasma

Whether an efficient collisionless temperature equilibration mechanism exists for a two-temperature ion-electron plasma, with Ti&amp;gt;Te, is important for understanding astrophysical phenomena such as two-temperature accretion flows and collisionless shocks in supernova remnants or gamma-ray bursts. In this paper, counter-streaming ion beam-driven two-stream, Weibel (or filamentation), and oblique instabilities are studied using two-dimensional (2D) particle-in-cell (PIC) simulations as a possible plasma instability that could operate in such astrophysical objects. The PIC simulations show interplay among these instabilities and that distinct stages with different dominant modes occur during the nonlinear evolution period. Although the 2D results show stronger electron-ion coupling than the one-dimensional (1D) instabilities, it is still too weak to rule out existing two-temperature accretion solutions. The nonrelativistic quasilinear equations for the 1D Weibel plus 1D two-stream modes are numerically solved to compare the results with the 2D PIC simulations and qualitative similarities were found. The equations also show that the magnetic fields generated by the Weibel instability decay to zero in the end.

Laser wakefield electron acceleration on Texas petawatt facility: Towards multi-GeV electron energy in a single self-guided stage

Laser wakefield acceleration experiments with the 150 fs Texas Petawatt laser will be carried out in the unique regime with the shortest pulse duration among available petawatt facilities. Simulations via the time-averaged, fully relativistic, quasi-static 3D axi-symmetric particle-in-cell (PIC) code WAKE show that combination of nonlinear plasma wave focusing, relativistic self-focusing, and nonlinear temporal compression guide a 1.33 PW pulse over 10 cm of uniform plasmas. Self-guided TPW pulse has intensity above 10 19 W/cm 2 and drives the laser wakefield in the blowout regime in the plasma density range n 0 > 2 × 10 17 cm −3. Both test-particle (WAKE) and full 3D PIC modelling (using recently developed quasi-cylindrical CALDER-Circ code) demonstrate robust electron self-injection in the first plasma wave bucket (“bubble”) during the periods of laser defocusing and bubble growth. Injection terminates as soon as the laser evolution stabilizes. As a result, quasi-monoenergetic acceleration of ∼1.3 nC electron bunch to the 2.5–7 GeV is expected in 10-cm long plasmas.

Characteristics of relativistic electron mirrors generated by an ultrashort nonadiabatic laser pulse from a nanofilm

For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we proposed [V. V. Kulagin, Phys. Rev. Lett. 99, 124801 (2007)] to use a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge (nonadiabatic laser pulse). In this paper, the REM characteristics are investigated in a regular way for a wide range of parameters. With the help of two-dimensional (2D) particle-in-cell (PIC) simulations, it is shown that, in spite of Coulomb forces, all of the electrons in the laser spot can be synchronously accelerated to ultrarelativistic velocities by the first half-cycle of the field, which has large enough amplitude. For the process of the REM generation, we also verify a self-consistent one-dimensional theory, which we developed earlier (cited above) and which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory shows a good agreement with the results of the 2D PIC simulations. Finally, the scaling of the REM dynamical parameters with the field amplitude and the nanofilm thickness is analyzed.

Detailed particle-in-cell simulations on the transport of a relativistic electron beam in plasmas

We present comprehensive two-dimensional (2D) particle-in-cell (PIC) simulations on the transport of a relativistic electron beam in a plasma in the context of fast ignition fusion. The 2D PIC simulations are performed by constructing two different simulation planes and have shown the complete stabilization and destabilization of the Weibel instability due to the beam temperature and background plasma collisions, respectively. Some three-dimensional PIC simulation results on the filamentary structures are also shown thereby further shedding light on the filamentation of the electron beam in plasmas. The linear growth rates of fastest growing mode in the beam-plasma system are compared with a theoretical model developed and are found in good agreement with each other.

Physics of colliding laser pulses in underdense plasmas

We report on recent experimental results on electron acceleration using two counter-propagating ultrashort and ultraintense laser pulses. At the collision, the two pulses drive a standing wave which is able to pre-accelerate plasma electrons which can then be trapped in the plasma wave. Optical diagnostics of the collision reveal signatures of this standing wave. Electron acceleration results in this regime are reviewed: the use of colliding pulses enables the generation of stable, tunable and high quality electron beams at the 100–200 MeV level. Detailed comparisons with 3D Particle in Cell (PIC) simulations give deeper insight on the role of the nonlinear propagation of the pump pulse on the performance of the accelerator. This deeper understanding has allowed us to optimize the beam charge of the accelerator at high energy.

High energy electron transport in dense plasma in fast ignition scenario

We investigate the high energy electron transport in dense plasma for different laser intensity by using 3D PIC (Three-Dimensional Particle-In-Cell) simulation. We have observed dependence of electron energy flux on incident laser intensity. The electron energy fluxes normalized by the incident laser flux, I/I0, become ≈ 0.2 for the normalized laser electric field of a = 3, ≈ 0.1 for a = 1 and no visible flux for a = 0.2 in dense plasma region, where a = eE/meω0c. For the case of a = 3, we investigated space and time resolved velocity distribution functions and induced longitudinal electric field. We show that the high energy electrons have beam-like velocity distribution with relativistic thermal spread near the energy flux front. We also discuss the electromagnetic instabilities associated with the high energy electron beam taking the relativistic thermal spread of the beam into account.

Three-Dimensional PIC-MC Modeling for Relativistic Electron Beam Transport Through Dense Plasma

We have developed a three dimensional (3D) PIC (particle-in-cell)-MC (Monte Carlo) code in order to simulate an electron beam transported into the dense matter based on our previous two dimensional code. The relativistic motion of fast electrons is treated by the particle-in-cell method under the influence of both a self-generated transverse magnetic field and an axial electric field, as well as collisions. The electric field generated by return current is expressed by Ohm's law and the magnetic field is calculated from Faraday's law. The slowing down of monoenergy electrons in DT plasma is calculated and discussed.

Theoretical Investigation of Controlled Generation of a Dense Attosecond Relativistic Electron Bunch from the Interaction of an Ultrashort Laser Pulse with a Nanofilm

For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we propose using a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge. With two-dimensional (2D) particle-in-cell (PIC) simulations, we show that, in spite of Coulomb forces, all of the electrons in the laser spot can be accelerated synchronously, and the REM keeps its surface charge density during evolution. We also developed a self-consistent 1D theory, which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory allows us to predict the REM parameters and shows a good agreement with the 2D PIC simulations.

Simulation of monoenergetic electron generation via laser wakefield accelerators for 5–25TW lasers

In 2004, using a 3D particle-in-cell (PIC) model [F. S. Tsung et al., Phys. Rev. Lett. 93, 185004 (2004)], it was predicted that a 16.5TW, 50fs laser propagating through nearly 0.5cm of 3×1018cm−3 preformed plasma channel would generate a monoenergetic bunch of electrons with a central energy of 240MeV after 0.5cm of propagation. In addition, electrons out to 840MeV were seen if the laser propagated through 0.8cm of the same plasma. The simulations showed that self-injection occurs after the laser intensity increases due to a combination of photon deceleration, group velocity dispersion, and self-focusing. The monoenergetic beam is produced because the injection process is clamped by beam loading and the rotation in phase space that results as the beam dephases. Nearly simultaneously [S. P. D. Mangles et al., Nature 431, 535 (2004); C. G. R. Geddes et al., ibid. 431, 538 (2004); J. Faure et al., ibid. 431, 541 (2004)] three experimental groups from around the world reported the generation of near nano-Coulomb of low emittance, monoenergetic electron beams using similar laser powers and pulse lengths as those reported in our simulations. Each of these experiments is modeled using the same 3D PIC code OSIRIS. The simulations indicate that although these experiments use a range of plasma parameters, density profiles, laser powers, and spot sizes; there are some commonalities to the mechanism for the generation of monoenergetic beams. Comments are given on how the energy and beam quality can be improved in the future.

Parametric study of two-dimensional potential structures induced by radio-frequency sheaths coupled with transverse currents in front of the Ion Cyclotron Resonance Heating antenna

For the first time, a two-dimensional (2D) fluid model and an analytical expression for the rectified potential with respect to the transverse polarization current are established and verified by a 2D PIC (particle in cell) code over the validity domain of our model. Then the model is extended to the overall ion cyclotron frequency range used in different heating and current drive scenarios. First, the models demonstrate that these transverse polarization currents add some inertia in the temporal dynamic. Due to the nonlinear behavior of the I-V sheath characteristic, the time average amplitude (dc potential) of the rectified potential structure is increased compared to the time average rf potential. Second, they induce only a slight widening of the potential structure. Such modifications are quantified using a “test map” initially characterized by a Gaussian shape. The map is assumed to remain Gaussian near its summit. The time behavior of the peak can be estimated analytically in the presence of polarization current as a function of its width r0 and amplitude ϕ0 (normalized to local temperature and to a characteristic length for transverse transport). A potential peaking criterion has been built to determine the peaking zone of the dc potential structure induced by the rf field. Computations made for typical parameters of the edge plasma in front of the antenna of the Tokamak Tore Supra show that the dc rectified potential is up to 50% higher than the previous computations neglecting polarization current effects. The weak diffused and high dc potential structures computed can explain the hot spot formation induced by convective cells associated to high energetic ion fluxes on the corners of the Ion Cyclotron Resonance Heating antenna.

Unstructured 3D PIC simulations of the flow in a retarding potential analyzer

A three-dimensional particle in cell (PIC) code is developed on unstructured tetrahedral grids. Zero-order (Nearest Grid Point) and linear (volume) particle charge weighting and force interpolation schemes are incorporated. A parametric investigation of the numerical heating in unstructured 3D PIC simulations is presented. The PIC methodology is applied to the simulation of the flow inside the segmented microchannel of a directional-Retarding Potential Analyzer. Simulations show the flow characteristics of the ions and electrons and provide estimates of the collected current by the microplate.

Investigation of ion beam neutralization processes with 2D and 3D PIC simulations

While it is common knowledge that ion beams are easily neutralized for both current and charge density using a variety of means, the precise process of neutralization remains unknown. With the increasing importance of electric propulsion, and in particular micropropulsion systems, this question is of significant importance. Additionally, it has bearing on thruster design, space instrument calibration, electrodynamic tethers, and ionospheric research. A review of the present state of knowledge on this topic is presented as well as results from ion beam simulations using 2D and 3D Particle-in-Cell (PIC) codes. We investigate both the early “filling” problem of the beam starting to move away from the spacecraft and the steady state problem where the beam encounters a wall at an infinite distance from the spacecraft.

Electron trapping and acceleration across a parabolic plasma density profile.

It is known that as a laser wakefield passes through a downward density transition in a plasma some portion of the background electrons are trapped in the laser wakefield and the trapped electrons are accelerated to relativistic high energies over a very short distance. In this study, by using a two-dimensional (2D) particle-in-cell (PIC) simulation, we suggest an experimental scheme that can manipulate electron trapping and acceleration across a parabolic plasma density channel, which is easier to produce and more feasible to apply to the laser wakefield acceleration experiments. In this study, 2D PIC simulation results for the physical characteristics of the electron bunches that are emitted from the parabolic density plasma channel are reported in great detail.

Self-compression of laser pulses in plasma.

We study self-compression of weakly relativistically intense laser pulses in subcritical plasmas using one- (1D) and three-dimensional (3D) direct particle-in-cell (PIC) simulations. The self-compression works in the density window from 1/4 critical to slightly below critical density, where the Raman instability is prohibited. An analytical model is developed to describe the self-compression. The model admits pulsing Gaussian solutions and a long-lived running soliton solution. The 1D PIC results agree well with the analytical model, and compressions by an order of magnitude are observed. In the 3D geometry, the longitudinal self-compression competes with the transverse self-focusing/filamentation. To damp the filamentation we use a periodic plasma-vacuum structure. The 3D PIC simulations suggest that a 30 fs long laser pulse is efficiently compressed to 5 fs.

3D electromagnetic PIC simulations of relativistic electron pulse injections from spacecraft

Relativistic electron beam accelerators (5 MeV, 0.1 A) can now be flown on spacecraft. Injection from low-Earth-orbit into the atmosphere makes it possible to perform active perturbation experiments in the 40–60 km altitude range. These include modification of the atmospheric electric potential structure over thunderstorm regions and the possible stimulation of high-altitude-lightning, as well as studies of relativistic electron precipitation effects on chemical reaction paths. In this paper, the initial stage of the beam injection process is simulated by a fully electromagnetic and relativistic Particle-in-Cell (PIC) code. The self-consistent implementation of electric charging of a spacecraft structure in an electromagnetic code is demonstrated, and beam propagation dynamics is explored for a range of beam to ambient plasma densities. It is shown that the combined effects of ambient plasma and beam self-fields may allow propagation in the ion-focused regime and that this regime primarily is expected for relativistic beams.