# Generation of gamma-rays and hard X-rays by intense ultra-short laser pulses interacting with foils: normal and oblique incidence

During the last 30 years an outstanding progress in ultrashort-pulse laser technology has been achieved. This allowed one to obtain ultra-high values of electromagnetic fields (so electrons and even ions become relativistic is such fields) in the laboratory. The maximum attainable laser intensity nowadays is of the order of 10^{22} W/cm^{2}. That results in near-QED regimes of laser-matter interaction.

Interaction of ultrashort laser pulses with different targets is expected to be a very promising mechanism of electron and ion acceleration, and generation of high-energy quanta (hard X-rays and gamma-rays). This topic is heavily studied nowadays: for example, use of intense laser pulses for generating bright gamma-ray flashes has been showed in the papers of Nakamura et. al. [1] and Nerush et. al. [2] At the described laser intensities the electrons in the target are quickly accelerated up to ultra-relativistic velocities and begin to emit gamma-rays and hard X-rays very efficiently. The maximum achieved conversion efficiency of the laser pulse energy into the energy of hard photons is tens of percent. However, the properties of the gamma-ray flash are usually much worse than what is obtained with help of traditional sources (i.e. radioactive sources or based on Compton backscattering) and there is still space for optimization of the laser-matter interaction scheme. For example, the effect of use of oblique-incident laser pulses is not much investigated.

To our knowledge, there is lack of understanding of what happens during laser-foil interaction and how gamma-quanta are generated. There are several theoretical models but most of them can’t help to know the Lorentz factor of the electrons and they can be barely used for estimating the gamma-ray radiation pattern. In the current work we try to explain the interaction process by using a theoretical model of thin surface electron layer which almost reflects the falling laser pulse. In the framework of this model, the layer is moving under both electric and magnetic laser fields, the change separation fields from the ions and the radiation reaction force (which should be also taken into consideration at our laser field intensities). The electron layer dynamics can be described with self-consistent equations (more detail one can find in our paper [3]). After solving the equations of electron layer dynamics we can govern the trajectory of the layer and the electrons Lorentz factor (this is the most important feature of the model being used). This model can be also applied to the case of oblique incidence by performing a Lorentz transform into the appropriate reference frame (see [4] for more detail). We show that the model can be still applicable for the case of oblique incidence for some angles. The modeling of the plasma surface showed good correspondence with the numerical simulation results.

We also show that in the case of oblique incidence the gamma-ray generation efficiency increases. In order to optimize the interaction parameters (the incidence angle, the target density) we have carried out a series of particle-in-cell (PIC) 3D numerical simulations. This allowed us to determine the optimal parameters that lead to the best efficiency – the optimal incidence angle is 30° and the target density is about 2 times lower than the dimensionless laser field amplitude *a _{0}* (see Fig. 1). In our numerical experiments

*a0*was of the order of 100. If to define gain

*G*as the product of gamma-ray generation efficiency and the radiation pattern directivity (i.e. the ratio between the maximum value in the radiation pattern and the average value), we can see that high G region also lies near the angle of 30° (see Fig. 2), but the optimal plasma density becomes lower.

In the fig. 2 we can also see that at high angles (approximately 66° and higher) the gain increases. In this region the generation efficiency is not very high but gamma-rays have very narrow radiation pattern which may be useful for different applications. We also discuss theoretical reasons for qualitative change in the shape of the radiation pattern.

Figure 1. Gamma-ray generation efficiency as a function of plasma density and angle of incidence.

Figure 2. Gain *G* as a function of plasma density and angle of incidence.

References:

- Nakamura T., Koga J.K., Esirkepov T.Zh., Kando M., Korn G., Bulanov S.V.
*Phys. Rev. Lett.*,**108**, 195001 (2012). - Nerush E.N., Kostyukov I.Yu., Ji L., Pukhov A.
*Phys. Plasmas*,**21**, 013109 (2014). - Serebryakov D.A., Nerush E.N., Kostyukov I.Yu.
*Phys. Plasmas*,**22**, 123119 (2015). - Serebryakov D.A., Nerush E.N.
*Quantum Electronics*,**46**(4) 299-304 (2016).