New analytical formalism is invented in the description of ion acceleration in the interaction of intense high-contrast short laser pulse with ultrathin target. The electrostatic shock wave acceleration is our fundamental point of view, but different criteria are obtained for description of various acceleration phenomenon. Acceleration condition for an ion with a definite charge to mass ratio ðz=mÞ and initial velocity b0 is obtained in the electrostatic shock (ES) field in front side of the foil. According to this point of view, self organized multistage ion acceleration formalism is proposed and confirmed by the 1D3V particle in cell simulation results. In this formalism, ions may be re-accelerated repeatedly in the developing ES field.
