SMIET: Fast and accurate synthesis of radio pulses from extensive air shower using simulated templates

Interpreting the data from radio detectors for extensive air showers typically relies on Monte-Carlo based simulation codes, which, despite their accuracy are computationally expensive and present bottlenecks for analyses. To address this issue we have developed a novel forward model called template synthesis, which synthesises the radio emission from cosmic ray air showers in a matter of seconds. This hybrid approach uses a microscopically simulated, sliced shower (the origin) as an input. It rescales the emission from each slice individually to synthesise the emission from a shower with different properties (the target). In this process it employs semi-analytical relations dependent on the shower age within the slice. We describe the connection between an antenna and a slice using the viewing angle and normalise the emission from every slice with respect to the air shower geometry using a set of scaling relations. In order to be able to change the arrival direction during synthesis, we adjust the phases based on the expected geometrical delays.

We benchmark the method by comparing synthesised traces to CoREAS simulations over a wide frequency range of [30, 500] $\text{MHz}$. We compare the signal amplitudes as well as the fluences. The synthesis quality is primarily influenced by the difference in $X_{\text{max}}$ between the origin and target shower, $\Delta X_{\text{max}}$. When $\Delta X_{\text{max}}\le 100\text{g}/{\text{cm}}^2$ , the scatter on the maximum amplitudes of the geomagnetic traces is at most 4%. For the traces from the charge-excess component this scatter is smaller than 6%. We also observe a bias with $\Delta X_{\text{max}}$ up to 5% for both components, which appears to depend on the antenna position. Since the bias is symmetrical around $\Delta X_{\text{max}}=0\text{g}/{\text{cm}}^2$, we can use an interpolation approach to correct for it. While it improves the accuracy of the synthesis, it requires multiple origin showers, increasing the complexity of the approach.

We have implemented the template synthesis algorithm in an open-source Python package called SMIET, which includes all the necessary parameters to apply the method. Users only need to provide adequate origin showers. The package provides an implementation of the algorithm in NumPy, but also offers an alternative implementation in the JAX framework which makes the code fully differentiable. This package has been successfully tested with air showers with zenith angles up to 50° and can be used with any atmosphere, observation level and magnetic field. We demonstrate that the synthesis quality remains comparable to our main benchmarks across various scenarios and discuss potential use cases, including its use in machine-learning-based reconstructions. The quality does depend strongly on the difference in zenith angle between the origin and target shower, from which we conclude that further improvements to the phase treatment are necessary.