The formation of tall red rays in the ionosphere has been a longstanding unresolved problem of auroral physics. These rays are pencil-like structures which can extend from 150 km at their base to as high as 600 km. At these heights it is very difficult to deposit sufficient power in order to account for the luminosity of tall rays. This work examines ohmic heating by collisional processes in strong field-aligned current sheets to account for visible tall rays. The mechanism is demonstrated by two-dimensional simulation in a fully self-consistent treatment of the ionosphere and coupling to the magnetosphere. We find that a filamentary current density of about 600 ¿Am-2 over about ten seconds can pump sufficient energy into the ambient oxygen atoms to produce visible auroral red rays. The ohmic heating leads to an electron temperature in excess of 10,000 K in the upper F-region.