The pilot stated that he was orbiting at 50 knots about 100 feet above the 11,800-foot msl (mean sea level) mountain peak. As he flew the helicopter out of the leeward side of the peak, he encountered a downdraft. He maneuvered the helicopter towards a wide open valley that descended about 5,000 feet below. The downdraft pushed the helicopter into the face of the mountain despite the pilot's application of full collective, and descending flight into the valley. The helicopter impacted the mountain slope, caught fire, and tumbled. The pilot and his two passengers egressed the burning helicopter with minor injuries. The pilot hiked to the peak, and called for rescue using a cell phone. The calculated density altitude for the conditions at 11,800 feet msl, altimeter 29.78 inHg, and temperature of 47 degrees F, is 13,918 feet. The published maximum operating density altitude for the R-44 II is 14,000 feet. The pilot stated that the helicopter had no mechanical failures or malfunctions during the flight.