Analytical studies on the evolution processes of rarefied deuterium plasma shell Z-pinch by PIC and MHD simulations

In this paper, we analytically explore the magnetic field and mass density evolutions obtained in particle-in-cell（PIC）and magnetohydrodynamics（MHD） simulations of a rarefied deuterium shell Z-pinch and compare those results, and also we study the effects of artificially increased Spitzer resistivity on the magnetic field evolution and Z-pinch dynamic process in the MHD simulation. There are significant differences between the profiles of mass density in the PIC and MHD simulations before 45 ns of the Z-pinch in this study. However, after the shock formation in the PIC simulation,the mass density profile is similar to that in the MHD simulation in the case of using multiplier 2 to modify the Spitzer resistivity. Compared with the magnetic field profiles of the PIC simulation of the shell, the magnetic field diffusion has still not been sufficiently revealed in the MHD simulation even though their convergence ratios become the same by using larger multipliers in the resistivity. The MHD simulation results suggest that the magnetic field diffusion is greatly enhanced by increasing the Spitzer resistivity used, which, however, causes the implosion characteristic to change from shock compression to weak shock, even shockless evolution, and expedites the expansion of the shell. Too large a multiplier is not suggested to be used to modify the resistivity in some Z-pinch applications, such as the Z-pinch driven inertial confinement fusion（ICF） in a dynamic hohlraum. Two-fluid or Hall MHD model, even the PIC/fluid hybrid simulation would be considered as a suitable physical model when there exist the plasma regions with very low density in the simulated domain.

The E×B drift instability in Hall thruster using 1D PIC/MCC simulation

The E×B drift instability is studied in Hall thruster using one-dimensional particle in cell(PIC)simulation method.By using the dispersion relation,it is found that unstable modes occur only in discrete bands in k space at cyclotron harmonics.The results indicate that the number of unstable modes increases by increasing the external electric field and decreases by increasing the radial magnetic field.The ion mass does not affect the instability wavelength.Furthermore,the results confirm that there is an instability with short wavelength and high frequency.Finally,it is shown that the electron and ion distribution functions deviate from the initial state and eventually the instability is saturated by ion trapping in the azimuthal direction.Also for light mass ion,the frequency and phase velocity are very high that could lead to high electron mobility in the axial direction.

PIC-MC Code to Model Fast Electron Beam Transport Through Dense Matter

A PIC （particle-in-cell）-MC （Monte Carlo） code to model electron beam transport into dense matter is developed. The background target is treated as a cold, stationary fluid and the fast electrons as particles with the relativistic motions. The process is described by a particle-in-cell method with consideration of the influence of both the self-generated electric and magnetic fields as well as collisions between the fast electrons and the target. The collisional part of the code is solved by the Monte Carlo-type method. Furthermore by assuming that the background current balances with the fast electron current, the electric field is given by the Ohm＇s law and the magnetic field is calculated from the Faraday＇s law. Both are solved in a two-dimensional cylindrical geometry. The algorithms implemented in the code are demonstrated and the numerical experiments are performed for monoenergy homogeneous fast electron beam transport in an aluminum target when the fields, collision and angular scattering are switched on and off independently.

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.

PIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen

A two-dimensional PIC/MCC model is developed to simulate the nitrogen radio frequency hollow cathode discharge（rf-HCD）.It is found that both the sheath oscillation heating and the secondary electron heating together play a role to maintain the rf-HCD under the simulated conditions.The mean energy of ions（N＋_2,N＋）in the negative glow region is greater than the thermal kinetic energy of the molecular gas（N2）,which is an important characteristic of rf-HCD.During the negative portion of the hollow electrode voltage cycle,electrons mainly follow pendulum movement and produce a large number of ionization collisions in the plasma region.During the positive voltage of the rf cycle,the axial electric field becomes stronger and its direction is pointing to the anode（substrate）,therefore the ions move toward the anode（substrate）via the axial electric field acceleration.Compared with dc-HCD,rf-HCD is more suitable for serving as a plasma jet nozzle at low pressure.

Effects of electron trapping on nonlinear electron-acoustic waves excited by an electron beam via particle-in-cell simulations

By performing one-dimensional particle-in-cell simulations,the nonlinear effects of electronacoustic(EA)waves are investigated in a multispecies plasma,whose constituents are hot electrons,cold electrons,and beam electrons with immobile neutralized positive ions.Numerical analyses have identified that EA waves with a sufficiently large amplitude tend to trap cold electrons.Because EA waves are dispersive,where the wave modes with different wavenumbers have different phase velocities,the trapping may lead to the nlixing of cold electrons.The cold electrons finally get thermalized or heated.The investigation also shows that the excited EA waves give rise to a broad range of wave frequencies,which may be helpful for understanding the broadband-electrostatic-noise spectrum in the Earth's auroral region.

Simulations of Stimulated Raman Scattering in Low-Density Plasmas

Stimulated Raman particle-in-cell （PIC） simulations scattering （SRS） in a low-density The backward stimulated Raman plasma slab is investigated by scattering （B-SRS） dominates initially and erodes the head of the pump wave, while the forward stimulated Raman scattering （F-SRS） subsequently develops and is located at the rear part of the slab. Two-stage electron acceleration may be more efficient due to the coexistence of these two instabilities. The B-SRS plasma wave with low phase velocities can accelerate the background electrons which may be further boosted to higher energies by the F-SRS plasma wave with high phase velocities. The simulations show that the peaks of the main components in both the frequency and wave number spectra occur at the positions estimated from the phase-matching conditions.

1d3v PIC/MCC simulation of dielectric barrier discharge dynamics in hydrogen sulfide

In this study,we computationally examined the dynamics of dielectric barrier discharge in hydrogen sulfide.The simulations were performed with a 1 d3 v particle-in-cell/Monte Carlo collision model in which a parallel-plate electrode geometry with dielectrics was used.Particle recombination process is represented in the model.The discharge mode was found to be initially Townsend discharge developing from the cathode to the anode,and at the peak of the current,a more stable glow discharge develops from the anode to the cathode.A higher applied voltage results in sufficient secondary electrons to trigger a second current peak,and then the current amplitude increases.As the frequency is increased,it leads to the advance of the phase and an increase in the amplitude of the current peak.A higher dielectric permittivity also makes the discharge occur earlier and more violently in the gap.

Non-Maxwellian electron distributions resulting from direct laser acceleration in near-critical plasmas

The irradiation of few-nm-thick targets by a finite-contrast high-intensity short-pulse laser results in a strong pre-expansion of these targets at the arrival time of the main pulse.The targets decompress to near and lower than critical densities with plasmas extending over few micrometers,i.e.multiple wavelengths.The interaction of the main pulse with such a highly localized but inhomogeneous target leads to the generation of a short channel and further self-focusing of the laser beam.Experiments at the Glass Hybrid OPCPA Scaled Test-bed(GHOST)laser system at University of Texas,Austin using such targets measured non-Maxwellian,peaked electron distribution with large bunch charge and high electron density in the laser propagation direction.These results are reproduced in 2D PIC simulations using the EPOCH code,identifying direct laser acceleration(DLA)[1]as the responsible mechanism.This is the first time that DLA has been observed to produce peaked spectra as opposed to broad,Maxwellian spectra observed in earlier experiments[2].This high-density electrons have potential applications as injector beams for a further wakefield acceleration stage as well as for pump-probe applications.

Radiation reaction induced spiral attractors in ultra-intense colliding laser beams

The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions.For the first time,the properties of fixed points in electron phase-space were analyzed with linear stability theory,showing that center nodes will become attractors if the classical radiation reaction is considered.Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentially near the attractors.The density growth rates are derived theoretically and further verified by particle-in-cell sim-ulations,which can be detected in experiments to explore the effects of radiation reaction qualitatively.The attractor can also facilitate realizing a series of nanometer-scaled flying electron slices via adjusting the colliding laser frequencies.

Dense pair plasma generation and its modulation dynamics in counter-propagating laser field

With two-dimensional quantum electrodynamics（QED） particle-in-cell simulations, a dense electron-positron（e^-e~＋） pair generation from laser-solid interactions is demonstrated. When the interaction of two linearly polarized laser pulses with a thin target enters into the relativistic transparency regime, a stable standing wave（SW） field can be formed by the overlap of the two counter-propagating laser pulses directly. The present study aims to clarify the effects of the S W field on the dynamics of e^-e^＋ pair plasmas. Our results indicate that under the combined effect of the SW field and radiation reaction（RR） effect, the created e^-e^＋ pairs can be trapped into the electric field nodes when the field strength is strong.The trapping effect contributes to the generation of γAV≥400 and ultra-dense pair plasmas in the two-side irradiation scheme. Despite different laser intensities, these pair plasmas have a Maxwellian spectral distribution with a peak energy of 150 MeV. Besides, the periodical modulation of the average energy, spatial, phase-space, and angular patterns of the e^-e^＋ pair plasmas can be triggered. In the angular patterns, as long as the SW field exists, pair plasmas can be pinched along the laser polarization direction. These results may offer a better understanding of the laser-solid interactions in the experiments when 10-PW laser facilities come into operation in the future.

Validity of the two-term Boltzmann approximation employed in the fluid model for high-power microwave breakdown in gas

The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.

Electrostatic Structure of the Electron Phase-space Holes Generated by the Electron Two-stream Instability with a Finite Width

Space satellite observations in an electron phase-space hole(electron hole) have shown that bipolar structures are discovered at the parallel cut of parallel electric field, while unipolar structures spring from the parallel cut of perpendicular electric field. Particle-in-cell(PIC) simulations have demonstrated that the electron bi-stream instability induces several electron holes during its nonlinear evolution. However, how the unipolar structure of the parallel cut of the perpendicular electric field formed in these electron holes is still an unsolved problem,especially in a strongly magnetized plasma(Ω_e >ω_(pe), where Ω_e is defined as electron gyrofrequency and ω_(pe) is defined as plasma frequency, respectively). In this paper, with two-dimensional(2D) electrostatic PIC simulations, the evolution of the electron two-stream instability with a finite width in strongly magnetized plasma is investigated. Initially, those conditions lead to monochromatic electrostatic waves, and these waves coalesce with each other during their nonlinear evolution. At last, a solitary electrostatic structure is formed. In such an electron hole, a bipolar structure is formed in the parallel cut. of parallel electric field, while a unipolar structure presents in the parallel cut of perpendicular electric field.

The Effect of Gas Flow Rate on Radio-Frequency Hollow Cathode Discharge Characteristics

It is known that gas flow rate is a key factor in controlling industrial plasma processing. In this paper, a 2D PIC/MCC model is developed for an rf hollow cathode discharge with an axial nitrogen gas flow. The effects of the gas flow rate on the plasma parameters are calculated and the results show that： with an increasing flow rate, the total ion（N＋2, N＋） density decreases, the mean sheath thickness becomes wider, the radial electric field in the sheath and the axial electric field show an increase, and the energies of both kinds of nitrogen ions increase;and, as the axial ion current density that is moving toward the ground electrode increases, the ion current density near the ground electrode increases. The simulation results will provide a useful reference for plasma jet technology involving rf hollow cathode discharges in N2.

Steady and oscillatory plasma properties in the near-field plume of a hollow cathode

Hollow cathodes serve as electron sources in Hall thrusters,ion thrusters and other electric propulsion systems.One of the vital problems in their application is the cathode erosion.However,the basic erosion mechanism and the source of high-energy ions cause of erosion are not fully understood.In this paper,both potential measurements and simulation analyses were performed to explain the formation of high-energy ions.A high-speed camera,a single Langmuir probe and a floating emissive probe were used to determine the steady and oscillatory plasma properties in the near-field plume of a hollow cathode.The temporal structure,electron temperature,electron density,and both static and oscillation of plasma potentials of the plume have been obtained by the diagnostics mentioned above.The experimental results show that there exists a potential hill（about 30 V） and also severe potential oscillations in the near-plume region.Moreover,a simple 2 D particle-in-cell model was used to analyze the energy transition between the potential hill and/or its oscillations and the ions.The simulation results show that the energy of ions gained from the static potential background is about 20 e V,but it could reach to 60 e V when the plasma oscillates.

Study on the influence of the discharge voltage on the ignition process of Hall thrusters

A high-speed charge-coupled device camera was used to capture images of the plume and acceleration channel of a Hall effect thruster during ignition at different discharge voltages.To better understand the influence of changes in the discharge voltage on the plasma parameters during thruster ignition,a particle-in-cell numerical model was used to calculate the distribution characteristics of the ion density and electric potential at different ignition moments under different discharge voltages.The results show that when the discharge voltage is high,the ion densities in the plume and acceleration channel are significantly higher at the initial phase of thruster ignition;with the gradual strengthening of the ignition process,the propellant avalanche ionization during thruster ignition occurs earlier and the pulse current peak increases.The main reason for these phenomena is that the change in the discharge voltage results in different energy acquisitions of the emitted electrons entering the thruster channel.

Detecting the meteoroid by measuring the electromagnetic waves excited by the collision between the hypervelocity meteoroid and spacecraft

The electromagnetic pulse excited by the collision between a hypervelocity meteoroid and a spacecraft is studied both numerically and theoretically.It is found that there are two kinds of electromagnetic pulse.The high-frequency electromagnetic pulse may be excited by the sum of all the electric dipoles.Each electron can be considered as an electric dipole.The low-frequency electromagnetic pulse is produced by the Langmuir oscillation of electrons.The energy flux density and the duration time of the excited low-frequency electromagnetic pulse by the meteoroid are also studied in the present paper.It is shown that the energy flux density increases as either the impact speed or the mass of the meteoroid increases.It is also shown that the duration time decreases as both the impact speed and the mass of the meteoroid increase.By measuring the strength and the duration time of the electromagnetic pulse excited by the collision between the hypervelocity meteoroid and spacecraft,we can estimate the speed and the mass of the hypervelocity meteoroid,which will be helpful in space flight and space exploration.

Study on plasma sheath and plasma transport properties in the azimuthator

A physical model of transport in an azimuthator channel with the sheath effect resulting from the interaction between the plasma and insulation wall is established in this paper. Particle in cell simulation is carried out by the model and results show that, besides the transport due to classical and Bohm diffusions, the sheath effect can significantly influences the transport in the channel.As a result, the ion density is larger than the electron density at the exit of azimuthator, and the non-neutral plasma jet is divergent, which is unfavorable for mass separation. Then, in order to improve performance of the azimuthator, a cathode is designed to emit electrons. Experiment results have demonstrated that the auxiliary cathode can obviously compensate the space charge in the plasma.

Physical properties of relativistic electron beam during long-range propagation in space plasma environment

It is known that ion channel can effectively limit the radial expansion of an artificial electron beam during its longrange propagation in the space plasma environment.Most prior studies discussed the focusing characteristics of the beam in the ion channel,but the establishment process and transient properties of the ion channel itself,which also plays a crucial role during the propagation of the relativistic electron beam in the plasma environment,were commonly neglected.In this study,a series of two-dimensional(2D)particle-in-cell simulations is performed and an analytical model of ion channel oscillation is constructed according to the single-particle motion.The results showed that when the beam density is higher than the density of plasma environment,ion channel can be established and always continues to oscillate periodically over the entire propagation.Multiple factors,including the beam electron density,initial beam radius,and the plasma density can affect the oscillation properties of ion channel.Axial velocity of the beam oscillates synchronously with the ion channel and this phenomenon will finally develop into a two-stream instability which can seriously affect the effective transport for relativistic electron beam.Choosing appropriate beam parameters based on various plasma environments may contribute to the improvement of the stability of ion channel.Additionally,radial expansion of the beam can be limited by ion channel and a stable long-range propagation in terrestrial atmosphere may be achieved.

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.