A. Corstanje et al., "The shape of the radio wavefront of extensive air showers as measured with LOFAR," Astroparticle Physics, V61, pp22-31, February 2015.
abstract:
Extensive air showers, induced by high energy cosmic rays impinging on
the Earth's atmosphere, produce radio emission that is measured with
the LOFAR radio telescope. As the emission comes from a finite
distance of a few kilometers, the incident wavefront is non-planar. A
spherical, conical or hyperbolic shape of the wavefront has been
proposed, but measurements of individual air showers have been
inconclusive so far. For a selected high-quality sample of 161
measured extensive air showers, we have reconstructed the wavefront by
measuring pulse arrival times to sub-nanosecond precision in 200 to
350 individual antennas. For each measured air shower, we have fitted
a conical, spherical, and hyperboloid shape to the arrival times. The
fit quality and a likelihood analysis show that a hyperboloid is the
best parameterization. Using a non-planar wavefront shape gives an
improved angular resolution, when reconstructing the shower arrival
direction. Furthermore, a dependence of the wavefront shape on the
shower geometry can be seen. This suggests that it will be possible to
use a wavefront shape analysis to get an additional handle on the
atmospheric depth of the shower maximum, which is sensitive to the
mass of the primary particle.
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