Holger Schmitz

Contemporary particle-in-cell approach to laser-plasma modelling

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

Kinetic Vlasov simulations of collisionless magnetic reconnection

A fully kinetic Vlasov simulation of the Geospace Environment Modeling Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions fk (k=i,e) are discretized on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm’s law are compared by calculating each of the terms from the moments of the fk. The important role of the off-diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X line is found to be dominated by the nongyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic...

Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields

The standard approach for integrating the multidimensional Vlasov equation using grid based, conservative schemes is based on a time splitting approach. Here, we show that although the truncation error is of second order, time splitting can introduce systematic heating of the plasma. We introduce a backsubstitution method, which not only avoids this deficiency but also is computationally less expensive. The general approach is demonstrated in conjunction with Boris’ scheme for evaluating the characteristics.

Cascaded nonlinear absorption of femtosecond laser pulses in dielectrics

We investigated the energy deposition process leading to the waveguide inscription in transparent dielectrics both experimentally and theoretically. Parameters of multiphoton absorption process and inscription thresholds were measured in a range of materials including YAG, ZnSe, RbPb2Cl5 crystals, and in fused silica and BK7 glasses.

Theory of the collisional presheath in a magnetic field parallel to the wall

In the limit of a small Debye length (λD→0) the plasma boundary layer in front of a negative absorbing wall is split up into a collision‐free planar space charge sheath and a quasineutral presheath, where the ions are accelerated to fulfill the Bohm criterion. Apart from ion inertia, the mechanism of the presheath depends on an additional effect controlling the ion field acceleration. The present paper considers a stationary presheath dominated by the deflection of the ion orbits in a magnetic field parallel to the wall. The ion transport is provided by charge exchange collisions with cold neutrals. The potential profiles and ion distributions resulting from the self‐consistent kinetic analysis are compared with expectations based on a previous hydrodynamic model. The transition from ‘‘closed’’ to ‘‘open’’ ion orbits results in typical deviations near the sheath edge. The kinetic Bohm criterion is found to be fulfilled marginally.

Darwin-Vlasov simulations of magnetised plasmas

We present a new Vlasov code for collisionless plasmas in the nonrelativistic regime. A Darwin approximation is used for suppressing electromagnetic vacuum modes. The spatial integration is based on an extension of the flux-conservative scheme, introduced by Filbet et al. [F. Filbet, E. Sonnendrucker, P. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. Phys. 172 (2001) 166]. Performance and accuracy is demonstrated by comparing it to a standard finite differences scheme for two test cases, including a Harris sheet magnetic reconnection scenario. This comparison suggests that the presented scheme is a promising alternative to finite difference schemes.

Particle simulation of a magnetized plasma contacting the wall

One-dimensional particle simulations are performed to study the influence of a strong magnetic field on the plasma boundary layer in front of a completely absorbing wall. The magnetic field lines are parallel to the wall, and the ion transport is provided by charge exchange collisions with cold neutrals. The Debye length is small compared with the ion gyroradius and the electrons are Boltzmann distributed. A modified Particle-in-Cell Monte-Carlo-Collision (PIC-MCC) code is developed to avoid the problem of different time scales of electrons and ions. The self-consistent steady-state simulation is performed for a system with one spatial coordinate and two velocity components (1d, 2v). The results are compared with corresponding results of a self-consistent stationary solution of the ion Boltzmann equation. Although the potential and density profiles are essentially confirmed, the ion velocity distribution functions disagree with analytic solutions in certain singular regions unless certain pertubations in ...

Collisional particle-in-cell modelling of the generation and control of relativistic electron beams produced by ultra-intense laser pulses

We present two-dimensional fully kinetic collisional particle-in-cell (PIC) simulations of the interaction of an ultra-intense laser with a solid density target. We find that the angular spread of the electrons is mostly due to the curved geometry of the electron acceleration region. Electron scattering off the magnetic fields caused by Weibel-like instabilities plays a smaller role. The angular spread can be counteracted by structuring the target into regions of different resistivity and we present a novel elliptical geometry of the high-Z core which can keep the electrons collimated for larger distances behind the target compared with cylindrical geometry.

Femtosecond laser microfabrication of subwavelength structures in photonics

This paper describes experimental and numerical results of the plasma-assisted microfabrication of subwavelength structures by means of point-by point femtosecond laser inscription. It is shown that the spatio-temporal evolution of light and plasma patterns critically depend on input power. Subwavelength inscription corresponds to the supercritical propagation regimes when pulse power is several times self-focusing threshold. Experimental and numerical profiles show quantitative agreement.

Full-vectorial modeling of femtosecond pulses for laser inscription of photonic structures

During the last decade, microfabrication of photonic devices by means of intense femtosecond (fs) laser pulses has emerged as a novel technology. A common requirement for the production of these devices is that the refractive index modification pitch size should be smaller than the inscribing wavelength. This can be achieved by making use of the nonlinear propagation of intense fs laser pulses. Nonlinear propagation of intense fs laser pulses is an extremely complicated phenomenon featuring complex multiscale spatiotemporal dynamics of the laser pulses. We have utilized a principal approach based on finite difference time domain (FDTD) modeling of the full set of Maxwells equations coupled to the conventional Drude model for generated plasma. Nonlinear effects are included, such as self-phase modulation and multiphoton absorption. Such an approach resolves most problems related to the inscription of subwavelength structures, when the paraxial approximation is not applicable to correctly describe the creation of and scattering on the structures. In a representative simulation of the inscription process, the signature of degenerate four wave mixing has been found.