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The intracavity photon density and the initial population-inversion density are assumed to be Gaussian spatial distributions in the rate equations of a laser-diode end-pumped actively Q-switched intracavity-frequency-doubling laser. In addition, the influence of the pump rate, the thermal effect in the gain medium and the change of the photon density along the cavity axis have been taken into account. These coupled rate equations are solved numerically, and the dependences of pulse width, single-pulse energy and peak power on incident pump power are obtained for the generated-green-laser pulses. In the experiment, a laser-diode end-pumped actively Q-switched Nd:YVO4/KTP laser with acoustic-optic-modulator is realized and the experimental results agree with the numerical solutions.