Abstract
The resources needed for particle-in-cell simulations of laser wakefield acceleration can be greatly reduced in many cases of interest using an envelope model. However, the inclusion of tunneling ionization in this time-averaged treatment of laser-plasma acceleration is not straightforward, since the statistical features of the electron beams obtained through ionization should ideally be reproduced without resolving the high-frequency laser oscillations. In this context, an extension of an already known envelope ionization procedure is proposed, valid also for laser pulses with higher intensities, which consists in adding the initial longitudinal drift to the newly created electrons within the laser pulse ionizing the medium. The accuracy of the proposed procedure is shown with both linear and circular polarization in a simple benchmark where a nitrogen slab is ionized by a laser pulse and in a more complex benchmark of laser plasma acceleration with ionization injection in the nonlinear regime. With this addition to the envelope ionization algorithm, the main phase space properties of the bunches injected in a plasma wakefield with ionization by a laser (charge, average energy, energy spread, rms sizes, and normalized emittance) can be estimated with accuracy comparable to a nonenvelope simulation with significantly reduced resources, even in cylindrical geometry. Through this extended algorithm, preliminary studies of ionization injection in laser wakefield acceleration can be easily carried out even on a laptop.
Highlights
In the last few decades, the limits in accelerating gradients of conventional electron accelerators based on metallic cavities prompted considerable efforts in the development of alternative electron acceleration techniques
The acceleration of electrons in the wake of an intense laser pulse propagating in an underdense plasma (Laser Wakefield Acceleration, or LWFA [1,2,3,4]) has been proven promising, generating smaller electron accelerators with high accelerating gradients [5,6,7], GeV level final energies [8, 9] and femtoseconds duration accelerated beams [10]
In the context of an existing ionization algorithm for LWFA simulations with an envelope model, an extension of this algorithm was presented, showing a good agreement with standard laser LWFA simulations for a0 > 1. This feature proves useful for simulations involving high Z dopant gases like nitrogen where the last ionization levels are accessed with lasers driving highly nonlinear wakefields
Summary
In the last few decades, the limits in accelerating gradients of conventional electron accelerators based on metallic cavities prompted considerable efforts in the development of alternative electron acceleration techniques. Modeling tunneling ionization in envelope simulations as in standard laser simulations, using the ADK DC ionization rate and the zero-momentum initialization for the new electrons, does not yield accurate results, since the high frequency laser oscillations and the electron motion is not well resolved. The residual momentum of the electrons stripped from the atoms/ions after the passage of the laser pulse strongly depends on the extraction field phase, which is normally poorly resolved in an envelope simulation To circumvent this problem, in the cylindrical envelope code INF&RNO a reconstruction of the high frequency laser oscillations near the laser pulse is performed at each timestep, calculating the full ionization rate and describing the ionization-quiver dynamics of the new electrons [40]. In Appendix B the derivation of the initial momentum values assigned to the electrons created with the proposed ionization procedure is described
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