The operational characteristics of the duoplasmatron ion source are investigated in order to obtain the maximum achievable extraction current of the $He^+$ ion beam with the small divergence. Under the variations of the gas pressure, the arc current, the magnet current and the extraction voltage of the ion source, the change of the extracted $He^+$ ion beam current is observed. An oxide filament, the mixture of BaO and SrO coated on Ni meshes, is used as the hot cathode, and its average lifetime is about 100 hours. The extraction current is linearly proportional to the arc current. As the magnet current of the ion source is increased, the extraction current increases, but the beam divergence becomes larger. The maximum extraction current is obtained at the source pressure of 0.084 Torr. The extraction current is proportional to the extraction voltage raised to the power of 3/2 as estimated from theory. At the extraction voltage of 5.72 kV, the maximum extraction current of 50 $\mu$A is obtained under the optimized extraction condition.