Accurate electron beam phase-space theory for ionization-injection schemes driven by laser pulses

After the introduction of the ionization-injection scheme in laser wake field acceleration and of related high-quality electron beam generation methods,such as two-color and resonant multi-pulse ionization injection(Re MPI),the theory of thermal emittance has been used to predict the beam normalized emittance obtainable with those schemes.We recast and extend such a theory,including both higher order terms in the polynomial laser field expansion and non-polynomial corrections due to the onset of saturation effects on a single cycle.Also,a very accurate model for predicting the cycle-averaged distribution of the extracted electrons,including saturation and multi-process events,is proposed and tested.We show that our theory is very accurate for the selected processes of Kr^(8+→10+) and Ar^(8+→10+),resulting in a maximum error below 1%,even in a deep-saturation regime.The accurate prediction of the beam phase-space can be implemented,for example,in laser-envelope or hybrid particle-in-cell(PIC)/fiuid codes,to correctly mimic the cycle-averaged momentum distribution without the need for resolving the intra-cycle dynamics.We introduce further spatial averaging,obtaining expressions for the whole-beam emittance fitting with simulations in a saturated regime,too.Finally,a PIC simulation for a laser wakefield acceleration injector in the Re MPI configuration is discussed.

AnAll-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes

We propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations.By all regime,we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M,i.e.such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1.The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M.This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy.A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism.A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed.Then a simple and efficient semi implicit scheme is also proposed.The resulting scheme is stable under a CFL condition driven by the(slow)material waves and not by the(fast)acoustic waves and so verifies the all regime property.Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.

A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows

We present a new numerical method to approximate the solutions of an Euler-Poisson model,which is inherent to astrophysical flows where gravity plays an important role.We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations,paying particular attention to the gravity source term involved in the latter equations.In order to approximate this source term,its discretization is introduced into the approximate Riemann solver used for the Euler equations.A relaxation scheme is involved and its robustness is established.The method has been implemented in the software HERACLES[29]and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.