# On the electromagnetic-electron rings

Note: This is a press-release of the paper by P. Valenta et al., Phys. Plasmas 28, 122104 (2021) which I co-authored.

A team of researchers from ELI Beamlines (Czech Rep.) use analytical modeling and 3D computer simulations to investigate the evolution of radial profile of high-power laser pulse in a low-density plasma, which is relevant to the laser-driven acceleration of charged particles, developing hard electromagnetic radiation, and other applications. According to their recent publication in Physics of Plasmas, they reveal the mechanisms of coupled electromagnetic and electron rings formation during the interaction and describe how these structures can be controlled.

### What is our work about

This research has been initiated after an experimental observation of stable and tunable ring-shaped beams of high-energy electrons by the ELI Beamlines electron acceleration group. The measurements of ring-shaped electron beams are quite common actually, several processes that may result in such structures were already identified and presented in literature (see, e.g., Refs. 35, 54–60 in the manuscript), none of them, however, seemed to correspond to the particular parameters used in our experiments. Our preliminary goal was thus to find out and describe the underlying physical mechanisms which could lead to the formation of ring-shaped electron beams in laser plasmas.

In general, this work investigates the propagation of high-power short-pulse laser in a low-density plasma, which is a topic relevant to a number of scientific challenges, such as laser-driven acceleration of charged particles, development of sources of hard electromagnetic radiation, and nuclear fusion within the framework of the fast ignition concept. For most of these applications, it is essential that the laser pulse propagates over extended distances and transmits its energy into the plasma in controlled way without incurring excessive losses. In this context, much of the attention has been focused on the evolution of the radial profile of the laser beam in a fully ionized plasma; it turned out that the process of self-focusing for high-power laser pulses may lead to the formation of the multifilament and, in particular, ring-shaped transverse structures (see, e.g., Refs. 17–25 in the manuscript). We show that these electromagnetic rings can become a source of high-energy ring-shaped electron beams.

### What are our central findings

The first part of the paper presents an analytical model based on geometric optics approximation which qualitatively illustrates the origin and the initial stage of the electromagnetic ring formation. We define the plasma density distribution within the Langmuir wave as well as the Hamiltonian for the photon interaction with the Langmuir wave; the trajectories of photons are then obtained by solving the Hamilton equations. The second part of the paper presents a three-dimensional particle-in-cell simulation, the results of which demonstrate the formation of the electromagnetic as well as electron ring. We discuss the mechanism of formation of the electromagnetic ring and the processes of electron injection into the accelerating phase of the secondary wakefield generated by the electromagnetic ring. Finally, the third part of the paper contains the results of a systematic multi-parametric simulation study for various plasma densities, laser intensities, and laser spot sizes revealing the relationships among the properties of the electromagnetic rings and the parameters of laser and plasma.

The main results of the paper can be summarized as follows: We identify and describe a novel physical mechanism which leads to the formation of ring-shaped electromagnetic-electron structures, where the electromagnetic rings arise from the laser pulse defocusing induced by the excitation of Langmuir waves in underdense plasma, and the ring-shaped electron beams are formed and accelerated subsequently by the secondary toroidal wakefields generated by the electromagnetic rings. We further reveal that the electromagnetic rings are relatively robust nonlinear objects, whose properties can be controlled by tuning the parameters of laser and plasma. Within the studied parameter range, we find that up to 70 % of the total initial driver pulse energy can be carried off by the electromagnetic rings having the opening angles 50 - 105 mrad.

Note: Our paper has been promoted by the editors of Physics of Plasmas journal by selecting the article as “Featured” and additionally reported by Scilight [1], which showcases the most interesting research across the physical sciences published in AIP Publishing journals. Furthermore, one of the figures from the paper was selected as the cover image of the journal’s December issue (see Figure 2).

### Why is our work important

The understanding of the physical processes that lead to the generation of the electromagnetic and electron ring structures is important due to the following reasons: (i) the electromagnetic rings may carry off a significant fraction of energy from the driver, and thus limit the overall efficiency of applications based on the laser-plasma interaction; (ii) the electron beams accelerated in the wake of the electromagnetic rings may cause a damage to surrounding equipment (e.g., capillaries used for the laser pulse guiding) and become a source of unwanted electromagnetic radiation; and (iii) the knowledge of the origin of the electromagnetic and electron rings could serve as a diagnostics for determining the regimes of laser-plasma interaction.

Tip: The simulation data are visualized using ELI Virtual Beamline – a complex interactive 3D web application that allows to explore the data with a virtual reality headset. The application can be accessed here. Note that the size of the data used for visualization is approx. 10 GB, so it takes some time to load them and also requires corresponding amount of free RAM on your machine. If you are unable to meet these requirements, you may still see the visualization in the video below.

Tip: Following the principles of reproducible science, the raw data used for our research has been uploaded to Zenodo and the data analysis can be found on GitHub.

### How to cite

P. Valenta, G. M. Grittani, C. M. Lazzarini, O. Klimo, and S. V. Bulanov, “On the electromagnetic-electron rings originating from the interaction of high-power short-pulse laser and underdense plasma”, Physics of Plasmas 28, 122104 (2021).

@article{doi:10.1063/5.0065167,
title = {On the electromagnetic-electron rings originating from the interaction of high-power short-pulse laser and underdense plasma},
author = {Valenta, P. and Grittani, G. M. and Lazzarini, C. M. and Klimo, O. and Bulanov, S. V.},
journal = {Physics of Plasmas},
volume = {28},
issue = {12},
pages = {122104},
numpages = {10},
year = {2021},
month = {Dec},
publisher = {American Institute of Physics},
doi = {10.1063/5.0065167},
url = {https://doi.org/10.1063/5.0065167}
}


### References

[1] C. Patrick, “Marrying ring-shaped structures from laser plasma interactions to their formation mechanism”, Scilight 50, 501102 (2021).

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