### Speaker

### Description

Inventing and fine-tuning laser and plasma based electron accelerators is a hot topic of contemporary physics, either considering experimental, theoretical or applied physics. One of the most prominent experiments in this field is the CERN-AWAKE experiment [1]. In this experiment, electrons are accelerated by the wakefields generated by a series of proton microbunches in a 10-meter-long rubidium plasma channel. The series of proton microbunches is generated via the self-modulation instability: first, the proton beam, obtained from the SPS experiment, enters the plasma channel, then the head of the proton beam generates plasma wakes that split the proton beam into a series of microbunches with a length of a few tens of micrometers each.

The plasma itself is generated via photoionisation of rubidium vapour with an ionising laser pulse with $780 \, \mathrm{nm}$ wavelength, $120 \, \mathrm{fs}$ pulse duration and $450 \, \mathrm{mJ}$ pulse energy [2].

The spatial extent of the plasma channel that is generated by the ionizing laser pulse can be investigated using a Schlieren imaging setup. To obtain parameters for the extent of the plasma channel, we assume the plasma density distribution to be of the form:

\begin{equation}

\mathcal{N}*{plasma} = \left{
\begin{aligned}
&\mathcal{N}_0 P*{max}, \mathrm{~if~} r\leq r_0\

&\mathcal{N}

*0 P*{max}\exp\left(-\frac{(r-r_0)^2}{t_0^2}\right) , \mathrm{~if~} r>r_0

\end{aligned}\right.

\end{equation}

with $\mathcal{N}_0$ being the vapour density, $P_{max}$ the maximum of the photoionisation probability, i.e.~ the value measured in the center of the plasma channel, $r=\sqrt{(y-y_0)^2+z^2}$ the distance from the center of the plasma channel that is located at $(y,z)=(y_0,0)$ and $r_{0}$ the radius of the plasma channel. $t_{0}$ characterises the width of the region where the photoionisation probability rises from $0$ to $P_{max}$. The output of the imaging setup can be calculated in a straightforward way with any given plasma density distribution. The reverse is not true, however, as the measured image depends on the plasma channel parameters $P_{max}, y_0, r_0, t_0$ in a complicated way. The task of inverting the problem, that is, to determine the plasma parameters from the calculated image can be attempted by using machine learning methods. Below we shortly summarize the key features of our approach and our recent results. We invite the Reader to look at our paper, currently available on arXiv, for a detailed description [3].

Using computer simulations, a sufficient amount of good quality learning data can be generated with low computational costs. Machine learning methods have the capability of determining the parameters of the plasma density distribution, shown in the Equationgiven above. We applied different deep neural network architectures to achieve the goal, and will present three models that produce the best predictions. Our results show that using a machine learning approach, the plasma parameters can be determined with high accuracy, regardless of the background noise. We also compared the predicted Schlieren signals with the reference signals and experienced that our neural networks predicted the signals themselves accurately, with only a few percents of mean amplitude error and phase error. The calculated probability distributions of these errors also confirm the high accuracy of the predictions. Furthermore, we tested how sensitive our networks are to the uncertainty of the vapour density and the probe laser beam intensity. We found if the actual vapor density or the probe laser intensity differs not more than $\sim 2.5 \, \%$ from the reference value, i.e.~the value for which our networks have been trained, the accuracy of the predictions remains acceptable. This suggests that our approach is a reliable, robust method, with possibly better performance than other, classical methods, and is suitable for the automated evaluation of experimental data.

**References**

- E. Gschwendtner, et al., AWAKE, the Advanced Proton Driven Plasma Wake?eld Acceleration experiment at CERN, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 829 (2016) 76-82. 2nd European Advanced Accelerator Concepts Workshop - EAAC 2015.
- E. Adli, A. Ahuja, O. Apsimon, R. Apsimon, A.-M. Bachmann, D. Barrientos, F. Batsch, J. Bauche, V. B. Olsen, M. Bernardini, et al., Acceleration of electrons in the plasma wakefield of a proton bunch, Nature 561 (2018) 363.
- G. Bíró, M. A. Pocsai, I. F. Barna, J. T. Moody, G. Demeter, Machine learning methods for schlieren imaging of a plasma channel in tenuous atomic vapor, 2022. URL: https://arxiv.org/abs/2205.12731 . doi:10.48550/arxiv.2205.12731.