A high rate algae pond (HRAP) reactor for the cultivation of microalgae or mixotrophic microalgae-bacterial cultures comprising: - a flow channel, through which a sheet of water with a water level ranging between 0.2 and 0.6 m passes, in the shape of a rounded rectangle with four sections: two straight parallel segments, separated by an intermediate partition and joined at their ends with 180° semicircular curves, each one of them provided with an entry and an exit depending on the direction in which the water sheet runs; and - at least a first agitation system for said water sheet, located between the exit of one of the curves and the end of the contiguous straight segment of the channel, wherein at least the first curve, contiguous to the agitation system, is 2 to 4 times narrower than the main straight segments of the channel and has an average curvature radius 1 to 2 times larger than the width of the curve, the entry of said curve being joined to the contiguous straight segment by means of a first transition region consisting of a narrowing from the straight segment to the entry of the curve in the shape of an isosceles trapezoid, with flat walls, presenting a depth increase in the same proportion as the narrowing of its width with respect to the straight segment, and a length such that the ratio between the length and the width of the straight segment of the channel is comprised between 1 and 3; the reactor being characterized in that: - the agitation system is a flow accelerator that comprises a flow acceleration device with an axial flow propeller, producing an axial flow at rotational speed equal to or lower than 100 rpm, which is housed inside a closed tubular walled conduit with two open ends for the passage of the entire water sheet through its interior, the highest point of which is at a height below the lower level of water at the inlet of the agitation system, and with a distance between the inner diameter of the conduit and the end of the propellers comprised between 2 and 20 mm; said agitation system being located between two transition sections, the first one joining the rectangular section of the curve with the circular section of the conduit at one end, and the second one joining the circular section of the conduit with the section of a second transition region of the channel at the other end, with the same configuration as the first, that is also joined to the contiguous straight segment; the cross sectional area of all the sections of the reactor being constant, and the flow speed being also constant between 0.2 and 0.4 m/s. - a flow channel, through which a sheet of water with a water level ranging between 0.2 and 0.6 m passes, in the shape of a rounded rectangle with four sections: two straight parallel segments, separated by an intermediate partition and joined at their ends with 180° semicircular curves, each one of them provided with an entry and an exit depending on the direction in which the water sheet runs; and - at least a first agitation system for said water sheet, located between the exit of one of the curves and the end of the contiguous straight segment of the channel, - the agitation system is a flow accelerator that comprises a flow acceleration device with an axial flow propeller, producing an axial flow at rotational speed equal to or lower than 100 rpm, which is housed inside a closed tubular walled conduit with two open ends for the passage of the entire water sheet through its interior, the highest point of which is at a height below the lower level of water at the inlet of the agitation system, and with a distance between the inner diameter of the conduit and the end of the propellers comprised between 2 and 20 mm; said agitation system being located between two transition sections, the first one joining the rectangular section of the curve with the circular section of the conduit at one end, and the second one joining the circular section of the conduit with the section of a second transition region of the channel at the other end, with the same configuration as the first, that is also joined to the contiguous straight segment;