Highly nonlinear ellipsoid bubble regime of the laser wake-field acceleration with high-intensity laser pulse is considered with analytical and numerical calculations. The important property of this regime is the production of the mono-energetic high-quality electron beam. We introduce a new twofold ellipsoid structure of the bubble (egg shape) by referring to some published two-dimensional (2D) and 3D simulations. In this paper, a new analytical formalism is introduced, in which dimensions of the front part of the ellipsoid bubble are related to the laser pulse and plasma parameters. These relationships are in agreement with 2D particle-in-cell code results in recent work (Benedetti et al., 2013).

Runaway electrons preionized diffuse discharge (REP DD) could generate volume non-thermal plasmas at atmospheric pressure, thus is widely used for surface modification. In this paper, two pulsed generators are used to produce REP DD for modifying copper (Cu) foil in atmospheric air. One generator produces repetitive pulses with a peak voltage of 40 kV and a rise time of 150 ns. The other generator produces single pulse with a peak voltage of 280 kV and a rise time of 0.5 ns. After the treatment, the modification results for including the macro topography, chemical composition and microhardness in different depths of the Cu surface are analyzed. In order to estimate the modification results in different areas of the Cu foil, several points from the center to the edge of the Cu sample are selected. It could be observed that the maximal modification effect usually appears in the area where the density of the diffuse discharge plasma is highest. The experimental results show REP DD treatment could significantly decrease the water contact angle and increase surface energy of the Cu foil. Meanwhile, it could decrease the carbon concentration and increase oxygen concentration in the near-surface layer of the Cu sample, and enhance the microhardness in different depths of the Cu foil.

Three-dimensional (3D) density distribution of inhomogeneous dense deuterium tritium plasmas in laser fusion is revealed by the energy loss of fast protons going through the plasmas. The fast protons generated in the laser–plasma interaction can be used for the simulation of a plasma density diagnostics. The large linear and ill-posed equation set of the densities of all grids is obtained and then solved by the Tikhonov regularization method after dividing a 3D area into grids and knowing the initial and final energies of the protons. 3D density reconstructions with six proton sources are done without and with random noises added to the final energy. The revealed density is a little smaller than the simulated one in most simulated zones and the error is as much as those of 2D reconstructions with four proton sources. The picture element N is chosen as 2744 with consideration of smoothness and calculation memory of the computers. With fast calculation speed and low error, the Tikhonov regularization method is more suitable for 3D density reconstructions with large calculation amount than simultaneous iterative reconstruction method. Also the analytical expressions between the errors and the noises are established. Furthermore, the density reconstruction method in this paper is particularly suitable for plasmas with small density gradient. The errors without noises and with 2% noises added to the final proton energies are 3 and 20%, respectively, for the homogeneous plasma.

Recent advances in the production of high repetition, high power, and short laser pulse have enabled the generation of high-energy proton beam, required for technology and other medical applications. Here we demonstrate the effective laser driven proton acceleration from near-critical density hydrogen plasma by employing the short and intense laser pulse through three-dimensional (3D) particle-in-cell (PIC) simulation. The generation of strong magnetic field is demonstrated by numerical results and scaled with the plasma density and the electric field of laser. 3D PIC simulation results show the ring shaped proton density distribution where the protons are accelerated along the laser axis with fairly low divergence accompanied by off-axis beam of ring-like shape.

This paper presents a scheme for excitation of an electron-plasma wave (EPW) by beating two q-Gaussian laser beams in an underdense plasma where ponderomotive nonlinearity is operative. Starting from nonlinear Schrödinger-type wave equation in Wentzel–Kramers–Brillouin (WKB) approximation, the coupled differential equations governing the evolution of spot size of laser beams with distance of propagation have been derived. The ponderomotive nonlinearity depends not only on the intensity of first laser beam, but also on that of second laser beam. Therefore, the dynamics of one laser beam affects that of other and hence, cross-focusing of the two laser beams takes place. Due to nonuniform intensity distribution along the wavefronts of the laser beams, the background electron concentration is modified. The amplitude of EPW, which depends on the background electron concentration, is thus nonlinearly coupled with the laser beams. The effects of ponderomotive nonlinearity and cross-focusing of the laser beams on excitation of EPW have been incorporated. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on cross-focusing of the two laser beams and further its effect on EPW excitation.

We use an Eulerian Vlasov code to study the efficient ion acceleration in dense targets by the ponderomotive force of a high-intensity circularly polarized laser beam, normally incident on a dense plasma. The code solves the one-dimensional relativistic Vlasov–Maxwell equations for both electrons and ions. We follow in details the mechanism of formation and evolution of a double-layer structure, where electrons are pushed steadily in the forward direction by the ponderomotive force of the laser beam, trapping an ion population, while an induced space charge electric field pulls ions behind them, forming a double-layer structure supported by the strong ponderomotive pressure of the intense laser beam. We consider the case of a high-density deuterium plasma with n/ncr = 100, where ncr is the critical density. Three cases are studied, by varying the width of the dense target and the intensity of the laser beam (with the normalized vector potential or quiver momentum a0 = 50 and a0 = 100), to follow the physical processes involved in the ion acceleration and the final formation of a neutral plasma jet ejected from the back of the target. We follow the transition from a situation where the laser pulse radiation pressure is acting on the double layer in the target, to a situation where below a given thickness a fraction of the laser energy is transmitted through the target. The absence of noise in the Eulerian Vlasov code allows us to follow accurately the evolution of the phase-space structures of the distribution functions.

An exploding wire system has been experimentally studied by the observation of its plasma dynamics and the electrical energy delivered by the supporting circuit to the metallic wire. Plasma radial expansion has been obtained from visible light streak images, meanwhile electrical energy transfer dynamics was derived from the analysis of voltage and current traces of the exploding wire circuit. In these measurements, a significant portion of the electrical energy has been transferred to the exploding wire circuit during the plasma expansion, and lower limits for the resistivity during the plasma expansion confirm the existence of a central liquid or solid metallic core in addition to the expanding plasma.

In this paper, a three-dimensional (3D) model as a new module of LAP3D code is presented to study the crossed-beam energy transfer (CBET) process. This model is not limited by the paraxial approximation and can be used to deal with a large crossing angle case. Besides, this model is also appropriate for the multi-ion species conditions and even multi-beams problems, which will be very helpful in relevant experiment analysis and the target design. In our 3D simulations, we take the overlapped beams with a 60° crossing angle as an example, and observe obvious energy transfer process, which indicates CBET process might occur between the incident laser beams with a large crossing angle when the matching condition is satisfied. This large crossing angle CBET process also can change the spatial shape of the beam spot, and may have some potential important influence on other laser–plasma interaction instabilities and the energy symmetry in hohlraum.

Second-harmonic generation by an obliquely incident s-polarized laser from an underdense plasma in the presence of a magnetic field has been investigated analytically. An expression for the relativistic factor γ has been obtained in the presence of magnetic field. The efficiency of second-harmonic radiation η has been obtained as a function of angle of incidence θ, normalized electric field amplitude of laser beam a0, normalized electron density ${\rm \omega} _{\rm p}^2 /{{\rm \omega} ^2}$, and magnetic field b. It is observed that γ increases with b. In turn, the conversion efficiency decreases with an increase in b. It is seen that the conversion efficiency is affected by the magnetic field due to the modified relativistic factor. In the absence of magnetic field, η increases with a0 and θ. However, in the presence of magnetic field, the conversion efficiency starts decreasing as the magnetic field is increased.

In this paper, a heuristic algorithm based on particle-in-cell (PIC) simulation is introduced to investigate the harmonic generation during the ionization and formation of plasma by a non-relativistic laser field when it propagates through hydrogen atoms. The harmonic generation is considered for the radiative recombination of an ionized electron with its nearest ion. The ionization algorithm is improved by considering the Stark effect and nonzero velocity for ionized electrons. Energy conservation is evaluated during the recombination process. In our code, for the first time, Maxwell's equations are integrated for harmonic fields in a separate mesh using the artificial recombination current as a source term. The simulation results are then used to illustrate the intensity spectrum of generated fields. It is shown that the initial momentum of ionized electrons affects the harmonic spectrum because the energy of radiated photons varies with the electron energy.

Using two-dimensional particle-in-cell simulations, the properties of a proton beam generated from a thin erbium hydride target irradiated by a 25 fs laser pulse of intensity ranging from 1020 to 1021 W/cm2 are investigated and compared with the features of a proton beam produced from a hydrocarbon (CH) target. It is shown that in case of using the hydride target the mean proton energy and the number of high-energy (>10 MeV) protons as well as the peak proton pulse intensity can be higher by a factor ~10 than the ones obtained from the CH target.

A two-dimensional particle-in-cell simulation is carried out to study the focusing effects of the long proton beam propagating in background plasmas. It is found that the smooth beam, with the long length and the small density gradient profile, is focused to high density. The sharp beam, with long length and the large density gradient profile, is modulated into many high density and periodic short beam pulses due to the wakefield induced by the beam. In addition, increasing the plasma density and adopting the non-uniform plasmas are the effective ways to reduce the wakefield.

The stopping power of warm dense matter (WDM) is estimated by means of the individual contributions of free electrons and bound electrons existing in this special kind of matter, located between classical and degenerate plasmas. For free electrons, the dielectric formalism, well described in our studies, is used to estimate the free electron stopping power. For bound electrons, the mean excitation energy of ions is used. Excitation energies are obtained through atomic calculations of the whole atom or, shell by shell in order to estimate their stopping power. Influence of temperature and density is analyzed in case of an impinging projectile. This influence becomes important for low projectile velocities and is negligible for high ones. Using free and bound electron analysis, the stopping power of an extended WDM is inferred from a dynamical calculation of energy transferred from the projectile to the plasma, where the stopping range is calculated. Finally, this theoretical framework is used to study a typical plasma density profile of a WDM heated by lasers.

We apply an Eulerian Vlasov code to study the amplification of an ultra-short seed pulse via stimulated Raman and Brillouin backscattering of energy from a long pump pulse, assumed at constant amplitude, in a plasma embedded in an external magnetic field. Detailed analysis of the spectra developed during the amplification process are presented, together with the evolution showing the pump depletion, accompanied by the counter-propagating seed-pulse amplification, compression and increased steepness of the waveform. In addition to the problem of the amplification of ultra-short seed pulses, there is an obvious academic interest in the study of problems of amplification of electromagnetic waves observed in many situations in laboratory plasmas and in the magnetosphere and other geophysical situations, such as in the environments of planets, where important variations in the presence and strength of magnetic fields are observed. The numerical code solves a one-dimensional relativistic Vlasov–Maxwell set of equations for a plasma in a magnetic field for both electrons and ions. We also apply the code to the problem of wakefield acceleration. The absence of noise in the Eulerian Vlasov code allows one to follow the evolution of the system with an accurate representation of the phase-space structures of the distribution functions.

We present a scheme of electron beam radiography to dynamically diagnose the high energy density (HED) matter in three orthogonal directions simultaneously based on electron Linear Accelerator. The dynamic target information such as, its profile and density could be obtained through imaging the scattered electron beam passing through the target. Using an electron bunch train with flexible time structure, a very high temporal evolution could be achieved. In this proposed scheme, it is possible to obtain 1010 frames/second in one experimental event, and the temporal resolution can go up to 1 ps, spatial resolution to 1 µm. Successful demonstration of this concept will have a major impact for both future inertial confinement fusion science and HED physics research.

Development of a detonation wave due to α heating following short pulse laser irradiation in pre-compressed deuterium–tritium (DT) plasma is considered. The laser parameters required for development of a detonation wave are calculated. We find that a laser irradiance and energy of IL = 1.75 × 1023 W/cm2 and 12.8 kJ accordingly during 1.0 ps in a pre-compressed target at 900 g/cm3 creates an α heating fusion detonation wave. In this case, the nuclear fusion ignition conditions for the pre-compressed DT plasma are achieved along the detonation wave orbit.

The paper presents the results of calculation and optimization of a structure of a radial insulating magnetic field in an acceleration gap of a high-power ion diode. A diode configuration with an induction plasma source and an anode configuration with azimuthally symmetrical slots and a pair of cathode coils of a magnetic diode system have been studied. When the size of the slots is ≤5 mm and codirectional magnetic fields of a diode and shock induction coil, the perturbation of the B-field does not exceed ≤20% and is located in the region near the anode. In this condition, the topology of the magnetic field В = f(1/r) is maintained in the acceleration gap. It was shown that the required radial distribution of the B-field can be optimized by varying the anode profile in the region opposite to two cathode coils of the diode magnetic system.

This paper aims at a test of a plasma focus (PF) device as a metallic plasma jet generator. The experiment was carried out at the DPF-1000U device in which the inner electrode face was conically shaped. Deuterium (D2) with the initial pressure of 0.9 Torr was used as a filling gas. In the experiment, a metallic plasma was ensured due to erosion of the inner electrode during a PF discharge. To create the metallic plasma jet, the eroded copper (Cu) plasma, swept by the deuterium plasma sheath, was accelerated axially and compressed to very small radius (about 1–2 mm). The Cu plasma jet achieved a velocity of 3 × 107 cm/s. To study processes of the plasma jet creation and propagation a 16-frame laser interferometer and a four-frame X-ray pinhole camera were used. Recorded images prove a successful adaptation of the PF device to the metallic plasma jet generator.

Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.

The paper presents the results of the analysis of the influence of curvature of the electrons trajectory in the anode–cathode gap of an ion diode on the diode impedance and evaluation of applicability of the one-dimensional (1D) Child–Langmuir (CL) ratio for calculation of the electron current. Investigations of an ion diode with a graphite anode in self-magnetic insulation mode were carried out. Experiments were performed on the TEMP-4M ion accelerator set in a double pulse mode, with the first negative pulse (150–200 kV, 400–600 ns) followed by the second positive pulse (250–300 kV, 150 ns). The result of this study is that we have determined the boundary conditions for the applicability of 1D CL ratio for calculation of the electron current in the ion diode. It was found that the deviation of the diode current–voltage characteristics from CL ratio will be observed only with a significant change in the acceleration voltage during electron drift or when the electron drift time exceeds the transit time of ions.