Star Interpolation Tool

The radio-band emission from air shower can be simulated using the CORSIKA extension, CoREAS. This tool calculates the emission from each particle as would be seen by an observer at pre-defined locations. Since the observers must be specified beforehand, CoREAS showers cannot be resampled, unlike for typical CORSIKA showers. Instead a tool has been developed which makes use of a regularly spaced set of observers. It is then possible to feed in a set of target locations at which the waveforms are interpolated based on the known location from the actual CoREAS simulation.

Here a brief description is given about how the interpolation tool is implemented, but more about this and particularlly about how well it performs can be seen here. You can also read more in the “radcube paper”.

Star Pattern

The tool works by producing simulations where the observer locations are on a “star shaped” layout. This star shape must be on a layout where in the magnetic (or VxB) coordinate system (see Coordinate Systems) has N spokes with observer locations located on a set of radii along the spokes. The radii of the observers must be the same for each spoke. That is, the star shape pattern, in the magnetic coordinate system should have N-fold rotational symmetry.

When using the tool, no extrapolation is done so the length of each spoke is the maximum radius out to which an electric field will be interpolated. It is important that one of the legs is aligned with the VxB direction.

Interpolation Method

The interpolation is performed using bilinear interpolation in polar coordinates. The four closest neighbors with radii and zenith angles \(r_i, \theta_i\), and which surround a target location are used to produce an electric field. The interpolation is done in the frequency domain, specifically on the Discrete Fourier Tansform (see Fourier Transforms and Derived Dataclasses/Functions).

Further, the interpolation is done in 3 steps. The logrithm of the Fourier amplitudes are interpolated. The corresponding phase, \(\phi\) is interpolated, but instead of directly interpolating this value, instead \(\exp(i \phi)\) is interpolated after which the phase is extracted using the complex-polar angle. Finally the star times of the waveforms are interpolated. This is done by first shifting the start time by its deviation from a plane wave moving at the speed of light, or \(t' = t - z/c\) where z is the distance along the shower axis from the core.

Using the tool

This tool uses the CoREAS reading tools that are part of this project (see Reading in Data). An AntennaTimeSeriesMap is given to the Star Interpolator tool along with an instance of the corresponding I3AntennaGeoMap.

The interpolated waveforms can then be directly asked for by calling GetEFieldMapAtTarget and supplying an instance of a I3AntennaGeoMap containing the target locations. The tool returns an AntennaTimeSeriesMap.

There is also a dedicated module to use this tool which is located at $I3_SRC/radcube/python/modules/SimulateFromStar.py.