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Shock waves in collisionless plasmas rely on kinetic processes to convert the primary incident bulk flow energy into thermal energy. That conversion is initiated within a thin transition layer but may continue well into the downstream region. At the Earth's bow shock, the region downstream of shock locations where the interplanetary magnetic field is nearly parallel to the shock normal is highly turbulent. We study the distribution of thin current events in this magnetosheath. Quantification of the energy dissipation rate made by the Magnetospheric Multiscale spacecraft shows that these isolated intense currents are distributed uniformly throughout the magnetosheath and convert a significant fraction (5%–11%) of the energy flux incident at the bow shock. Plain Language Summary: Shock waves form when a supersonic flow encounters an immovable object. Thus, ahead of the magnetic bubble formed by the Earth's extended magnetic field, the flow of charged particles emanating from the Sun known as the solar wind is shocked, slowed, and deflected around the Earth. In dense fluids, the conversion of the incident bulk flow energy into heat is accomplished by collisions between particles or molecules. However, the solar wind is so rarefied that such collisions are negligible, and the energy conversion involves more than one kinetic process that couples the different particles to the electromagnetic fields. Under some orientations of the interplanetary magnetic field carried by the wind, the shocked medium is highly turbulent. Within that turbulence are isolated thin regions carrying large electric currents. We have studied those currents, and found that they are converting energy from one form to another at a rate that is a significant fraction of the incident energy flux. Thus, these currents contribute significantly to the overall shock energetics. Key Points: Intense current events are distributed uniformly downstream of a quasi‐parallel bow shockThe events are associated primarily with a conversion of field energy into particle energyThe energy processed by these events is a non‐negligible fraction of the energy incident at the bow shock [ABSTRACT FROM AUTHOR]