Three-dimensional Particle In Cell Simulations Research Articles

VSHPIC: a particle-in-cell algorithm based on vector spherical harmonics expansion

The particle-in-cell (PIC) method has been widely used for studying plasma physics. However, fully three-dimensional PIC simulations always require huge computational resources. For problems with near azimuthal symmetry, recent work (Lifschitz et al 2009 J. Comput. Phys. 228 1803–14, Davidson et al 2015 J. Comput. Phys. 281 1063–77, Li et al 2021 Comput. Phys. Commun. 261 107784, Li et al 2022 J. Comput. Phys. 470 111599) has shown that expanding all the quantities defined on the grid in azimuthal harmonics and truncating the expansion can improve the code efficiency. In this paper, we describe a novel parallel algorithm for efficiently simulating three-dimensional near-spherical symmetry problems. Our approach expands all physical quantities in the θ and ϕ directions in spherical coordinates using vector spherical harmonics. The code is capable of simulating three-dimensional asymmetric scenarios by accurately tracking the evolution of distinct individual modes while preserving the charge conservation law. The fundamental dispersion relation of EM waves in the plasma has been obtained using VSHPIC simulation results. The code also shows a well strong scalability up to more than 1000 cores.

Ultra-short pulse laser acceleration of protons to 80 MeV from cryogenic hydrogen jets tailored to near-critical density

Laser plasma-based particle accelerators attract great interest in fields where conventional accelerators reach limits based on size, cost or beam parameters. Despite the fact that particle in cell simulations have predicted several advantageous ion acceleration schemes, laser accelerators have not yet reached their full potential in producing simultaneous high-radiation doses at high particle energies. The most stringent limitation is the lack of a suitable high-repetition rate target that also provides a high degree of control of the plasma conditions required to access these advanced regimes. Here, we demonstrate that the interaction of petawatt-class laser pulses with a pre-formed micrometer-sized cryogenic hydrogen jet plasma overcomes these limitations enabling tailored density scans from the solid to the underdense regime. Our proof-of-concept experiment demonstrates that the near-critical plasma density profile produces proton energies of up to 80 MeV. Based on hydrodynamic and three-dimensional particle in cell simulations, transition between different acceleration schemes are shown, suggesting enhanced proton acceleration at the relativistic transparency front for the optimal case.

Ion effects on the scaling of magnetic field amplification in plasmas with the system size

Magnetic field amplification during the nonlinear stage of the current filamentation instability excited by ultra-relativistic electron beams is investigated with a two-dimensional electromagnetic particle-in-cell (PIC) simulation code, with special attention paid to the effects of plasma ions and the system size. The effect of plasma ions is shown to be significant and enhanced magnetic field amplification and beam energy deposition are found due to plasma cavity expansion and merger. When the system size in the transverse direction (perpendicular to the beam propagation direction) is enlarged by a factor of m, the transverse magnetic field energy is found to increase by a factor of m 2 in the case of the plasma with movable ions, in contrast to m with immovable ions. The results are also confirmed by three-dimensional PIC simulations.

On the control of electron heating for optimal laser radiation pressure ion acceleration

We study the onset of electron heating in intense laser–solid interactions and its impact on the spectral quality of radiation pressure accelerated ions in both hole boring and light sail regimes. Two- and three-dimensional particle-in-cell (PIC) simulations are performed over a wide range of laser and target parameters and reveal how the pulse duration, profile, polarization and target surface stability control the electron heating, the dominant ion acceleration mechanisms and the ion spectra. We find that the onset of strong electron heating is associated with the growth of the Rayleigh–Taylor-like instability at the front surface and must be controlled to produce high-quality ion beams, even when circularly polarized lasers are employed. We define a threshold condition for the maximum duration of the laser pulse that allows mitigation of electron heating and radiation pressure acceleration of narrow energy spread ion beams. The model is validated by three-dimensional PIC simulations, and the few experimental studies that reported low energy spread radiation pressure accelerated ion beams appear to meet the derived criteria. The understanding provided by our work will be important in guiding future experimental developments, for example for the ultrashort laser pulses becoming available at state-of-the-art laser facilities, for which we predict that proton beams with $\sim$ 150–250 MeV, $\sim$ 30% energy spread, and a total laser-to-proton conversion efficiency of $\sim$ 20% can be produced.

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.

Electrostatic and electromagnetic waves driven by current free electron beam instability: Effects of positron, background composition, and ion-to-electron mass ratio

Counterstreaming electron beams drifting along the magnetic field in electron–proton plasmas may lead to the generation of electrostatic (ES) waves and structures widely observed in planetary magnetospheres. In electron–positron plasmas, streaming electron/positron beams along the background magnetic field may first result in ES waves followed by the electromagnetic (EM) waves with substantial magnetic field perturbations, as shown by Jao and Hau [Phys. Rev. E 98, 013203 (2018)]. In this study, we examine the formation of ES and EM waves driven by current free counterstreaming electron beams in electron–ion background plasmas and current free electron–positron beams in electron–proton–positron background plasmas based on one-dimensional EM particle-in-cell simulations with the drift velocity being along the background magnetic field. For the former cases, the effects of ion-to-electron mass ratios are examined, which have implications for two- and three-dimensional particle in cell simulations with reduced mass ratios. For the latter cases, the effects of positrons are examined, which have applications to astrophysical plasma environments and laboratory experiments. It is shown that the presence of positrons or light ions may shorten the occurrence times between the ES and EM waves driven by current free electron beam instability. The EM waves have relatively longer wavelengths as compared to the ES waves and the magnetic field evolution resembles parallel proton firehose instability. The effects of positrons, background compositions, and ion-to-electron mass ratios on the occurrence of ES and EM waves are consistent with the linear fluid theory.

A method to calculate the electron sheath profile of the nonaxisymmetrical magnetic insulation

The nonaxisymmetrical magnetic insulation would occur due to the disalignment of inner electrodes in long magnetically insulated transmission lines, or the nonuniform distributions of injected currents in induction cavities of magnetically insulated induction voltage adders (MIVA). The electron sheath profile is a very important parameter to characterize the nonaxisymmetrical magnetic insulation. In the past, the three-dimensional particle in cell simulation was usually used to determine the electron sheath profile, which is extremely time-consuming and inefficient. In this paper, a fast and efficient calculation method is proposed. The classical one-dimensional Creedon theory of the magnetic insulation equilibrium is generalized to a two-dimensional plane of (r, ) via introducing a parameter defined as the azimuthal mode number. Two-dimensional Creedon is developed to model the asymmetric magnetic insulation of the MIVA. Provided the azimuthal distributions of magnetic flux density on the cathode, which is in proportion to the cathode current, the two-dimensional Creedon model is numerically solved. A numerical solution method to calculate the electron sheath profile is proposed, and then the calculation error is also given. As the azimuthal distribution of magnetic flux density on the cathode meets a cosine function, the profile of the electron sheath is approximate to the Gauss function. As the nonuniform portion of cathode current increases, the electron sheath becomes more eccentric, and the calculation error is also much larger.

Development of a 14-vane, double-strapped, 5.8-GHz magnetron oscillator

Experiments on a 14-vane, double-strapped magnetron oscillator were performed to demonstrate high-power, high-efficiency coherent radiation at 5.8 GHz. The double-strapped magnetron was designed by using the Buneman-Hatree resonance condition, electromagnetic simulations and non-linear three-dimensional particle-in-cell (PIC) simulations. Experiments showed an oscillation output power of 5.3 kW at 5.79 GHz, corresponding to a DC-RF conversion efficiency of 57%. The cathode voltage was 9.2 kV, the collected anode current was 1 A, and the external magnetic field is 7.5 kG. Experimental results for the RF power, oscillation frequency, and efficiency were in good agreement with the corresponding values from non-linear three-dimensional PIC simulations.

Optimized stability of a modulated driver in a plasma wakefield accelerator

AbstractWe analyze the transverse stability for a configuration of multiple Gaussian bunches subject to the self-generated plasma wakefield. Through a semi-analytical approach we first study the equilibrium configuration for the modulated beam and then we investigate the evolution of the equilibrium configuration due to the emittance-driven expansion of the beam front that results in a rigid backward shift. The rear-directed shift brings the modulated beam out of the equilibrium, with the possibility for some of the bunch particles to be lost with a consequent deterioration of the driver. We look therefore for the proper position of the single bunches that maximize the stability without severely affecting the accelerating field behind the driver. We then compare the results with three-dimensional particle in cell simulations.

Three-dimensional particle in cell simulation of multi-mode ion thruster optics system

The optics is one of the main components of an ion thrust, which influences the performance and thruster lifetime. The operation of ion thruster can be evaluated by numerical simulation based on the current-voltage entrance condition, especially for thruster with a variety of operating modes. The plasma transport process is simulated with 3D-PIC (particle in cell) method for a two-grids optic. The performances of the NSTAR thruster under different operating modes are calculated and compared with the results of in-orbit test, verifying the correctness of the simulation mode. The influences of operation modes on the electric field distribution and the beam state are analyzed, and the requirements of multi-mode design for ion thruster are discussed. The results show that a convex sheath and concave zero equipotential surface away from the optic, low value of “saddle point”, and gentle downstream potential distribution, which help to improve ion pass rate, suppress electronic reflux and reduce Pits-and-Grooves corrosion, are the target of ion thruster mode design. Increasing beam voltage will result in a high loss caused by the divergence angle, and extend the beam current range for a good operation condition. For a large beam current mode, high beam voltage will make the beam have a better “focus” state, and reduce the Barrel corrosion. The results will provide a reference for the operation mode design for the multi-mode ion thruster.

Two-stage acceleration of protons from relativistic laser-solid interaction

A two-stage proton acceleration scheme using present-day intense lasers and a unique target design is proposed. The target system consists of a hollow cylinder with conical inner wall, which is followed by the main target with a flat front and a dishlike flared rear surface. At the center of the latter is a tapered proton layer, which is surrounded by side proton layers at an angle to it. In the first acceleration stage, protons in both layers are accelerated by target normal sheath acceleration. The center-layer protons are accelerated forward along the axis while the side protons are accelerated and focused towards them. As a result, the side-layer protons radially compress as well as axially further accelerate the front part of the center-layer protons in the second stage. Two-dimensional (2D) particle-in-cell (PIC) simulations show that a quasimonoenergetic proton bunch with the maximum energy over 250 MeV and energy spread similar to 17% can be generated when such a target is irradiated with an 80 fs laser pulse with focused intensity 3.1 x 10(20) W/cm(2). Three-dimensional (3D) PIC simulation gives the reduced maximum energy similar to 112 MeV but even smaller energy spread similar to 3% under the same laser conditions due to anisotropic electron acceleration with linearly polarized lasers.

Near-GeV Acceleration of Electrons by a Nonlinear Plasma Wave Driven by a Self-Guided Laser Pulse

The acceleration of electrons to approximately 0.8 GeV has been observed in a self-injecting laser wakefield accelerator driven at a plasma density of 5.5x10(18) cm(-3) by a 10 J, 55 fs, 800 nm laser pulse in the blowout regime. The laser pulse is found to be self-guided for 1 cm (>10zR), by measurement of a single filament containing >30% of the initial laser energy at this distance. Three-dimensional particle in cell simulations show that the intensity within the guided filament is amplified beyond its initial focused value to a normalized vector potential of a0>6, thus driving a highly nonlinear plasma wave.

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.

The Role of the Guide Field in Relativistic Pair Plasma Reconnection

We study the role of the guide field in relativistic magnetic reconnection in a Harris current sheet of pair (e±) plasmas, using linear theories and particle-in-cell (PIC) simulations. Two-dimensional PIC simulations exhibit the guide field dependence to the linear instabilities; the tearing or reconnection modes are relatively insensitive, while the relativistic drift-kink instability (RDKI), the fastest mode in a relativistic current sheet, is stabilized by the guide field. Particle acceleration in the nonlinear stage is also investigated. A three-dimensional PIC simulation demonstrates that the current sheet is unstable to the RDKI, although a small reconnection occurs in the deformed current sheet. Another three-dimensional PIC simulation with a guide field demonstrates a completely different scenario. Secondary magnetic reconnection is triggered by nonlinear coupling of oblique instabilities, which we call the relativistic drift-sausage tearing instability. Therefore, particle acceleration by relativistic guide field reconnection occurs in three-dimensional configuration. Based on the plasma theories, we discuss an important role of the guide field: to enable nonthermal particle acceleration by magnetic reconnection.

Polarization effects and anisotropy in three-dimensional relativistic self-focusing.

The relativistic self-focusing of high-intensity laser pulses in underdense plasmas is investigated with three-dimensional particle in cell simulations. The different behavior of a linearly polarized pulse in the two transverse directions is interpreted as a combination of two two-dimensional responses with different polarizations. In the polarization plane a high density sheet is formed, which separates the two regions of oppositely directed quasistatic magnetic field.