The helicon wave plasma (HWP) sources have well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies on mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge (PHD) code. The mode transitions also known as density jumps of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude SHWs are responsible for the mode transitions, similar to those of a resonant cavity for laser generation. This paper intends to give a complete and quantitative standing helicon wave (SHW) resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.