This paper proposes a method to generate virtual intensity field in space. The sound field of a zone enclosing the listener position is controlled to have maximum acoustic intensity to the desired direction. In order to control acoustic intensity of a zone, space-averaged active intensity is introduced. The ratio of space-averaged active intensity and control effort is defined as a cost function and expressed as a function of source control signals. It is shown that the cost function represents radiation efficiency of multiple sources. The control signals maximizing the cost function is found through eigenvalue analysis. The proposed method is verified by numerical simulations performed in free field condition, and the results provide a relation between wavelength and the size of controllable intensity field.