We present a particle-in-cell simulation of the relativistic Kelvin-Helmholtz Instability (KHI) that for the first time delivers angularly resolved radiation spectra of the particle dynamics during the formation of the KHI. This enables studying the formation of the KHI with unprecedented spatial, angular and spectral resolution. Our results are of great importance for understanding astrophysical jet formation and comparable plasma phenomena by relating the particle motion observed in the KHI to its radiation signature.

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