We discuss the physics case for and the concept of a medium-scale axion helioscope with sensitivities in the axion-photon coupling a few times better than CERN Axion Solar Telescope (CAST). Search for an axion-like particle with these couplings is motivated by several persistent astrophysical anomalies. We present early conceptual design, existing infrastructure, projected sensitivity and timeline of such a helioscope (Troitsk Axion Solar Telescope Experiment, TASTE) to be constructed in the Institute for Nuclear Research, Troitsk, Russia. The proposed instrument may be also used for the search of dark-matter halo axions.
