Dimensional PIC Simulations Research Articles

Rise time of proton cut-off energy in 2D and 3D PIC simulations

The Target Normal Sheath Acceleration regime for proton acceleration by laser pulses is experimentally consolidated and fairly well understood. However, uncertainties remain in the analysis of particle-in-cell simulation results. The energy spectrum is exponential with a cut-off, but the maximum energy depends on the simulation time, following different laws in two and three dimensional (2D, 3D) PIC simulations so that the determination of an asymptotic value has some arbitrariness. We propose two empirical laws for the rise time of the cut-off energy in 2D and 3D PIC simulations, suggested by a model in which the proton acceleration is due to a surface charge distribution on the target rear side. The kinetic energy of the protons that we obtain follows two distinct laws, which appear to be nicely satisfied by PIC simulations, for a model target given by a uniform foil plus a contaminant layer that is hydrogen-rich. The laws depend on two parameters: the scaling time, at which the energy starts to rise, and the asymptotic cut-off energy. The values of the cut-off energy, obtained by fitting 2D and 3D simulations for the same target and laser pulse configuration, are comparable. This suggests that parametric scans can be performed with 2D simulations since 3D ones are computationally very expensive, delegating their role only to a correspondence check. In this paper, the simulations are carried out with the PIC code ALaDyn by changing the target thickness L and the incidence angle α, with a fixed a0 = 3. A monotonic dependence, on L for normal incidence and on α for fixed L, is found, as in the experimental results for high temporal contrast pulses.

One dimensional PIC simulation of relativistic Buneman instability

Spatio-temporal evolution of the relativistic Buneman instability has been investigated in one dimension using an in-house developed particle-in-cell simulation code. Starting from the excitation of the instability, its evolution has been followed numerically till its quenching and beyond. The simulation results have been quantitatively compared with the fluid theory and are found to be in conformity with the well known fact that the maximum growth rate (γmax) reduces due to relativistic effects and varies with γe0 and m/M as γmax∼32γe0(m2M)1/3, where γe0 is the Lorentz factor associated with the initial electron drift velocity (v0) and (m/M) is the electron to ion mass ratio. Further it is observed that in contrast to the non-relativistic results [A. Hirose, Plasma Phys. 20, 481 (1978)] at the saturation point, the ratio of electrostatic field energy density (∑k|Ek|2/8π) to initial drift kinetic energy density (W0) scales with γe0 as ∼1/γe02. This novel result on the scaling of energy densities has been found to be in quantitative agreement with the scalings derived using fluid theory.

Strong ionisation in carbon nanowires

Surfaces covered with nanostructures, such as nanowire arrays, are shown to facilitate a significantly higher absorption of laser energy as compared to flat surfaces. Due to the efficient coupling of the laser energy, highly energetic electrons are produced, which in turn can emit intense ultrafast X-ray pulses. Full three dimensional PIC simulations are used to analyse the behaviour of arrays of carbon nanowires in diameter, irradiated by a laser pulse of duration at FWHM and a vector potential of . We analyse the ionisation dynamics of the nanowires. The difference of the ionisation strength and structure between linearly and circularly polarised laser beam is investigated. The nanowires are found to be fully ionised after about 30 laser cycles. Circularly polarised light reveals a slightly stronger ionisation effect.

Rapid current transition in a crossed-field diode

The transmitted current in a crossed-field gap has been characterized analytically by a number of authors. Using a one dimensional PIC simulation, we explore the behavior of the crossed-field diode at B=BHull. For mono-energetic (cold) emission, a rapid reduction of transmitted current is observed when the injected current exceeds the critical current by just 1%. The addition of a small electron temperature normal to the cathode eliminates the transition, even for kT/V∼10−5 (V=10 kV, gap = 1 cm, B=337 G, J=1.69 A/cm2), while an isotropic velocity distribution accelerates the transition.