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The high-current fast electron beams generated in high-intensity laser-solid interactions require the onset of a balancing return current in order to propagate in the target material. Such a system of counter-streaming electron currents is unstable to a variety of instabilities such as the current filamentation instability and the two-stream instability. An experimental study aimed at investigating the role of instabilities in a system of symmetrical counter-propagating fast electron beams is presented here for the first time. The fast electron beams are generated by double-sided laser-irradiation of a layered target foil at laser intensities above 1019W/cm². High-resolution X-ray spectroscopy of the emission from the central Ti layer shows that locally enhanced energy deposition is indeed achieved in the case of counter-propagating fast electron beams. [ABSTRACT FROM AUTHOR]