To realize a high power microwave source of longtime operation with a low guiding magnetic field, an S-band, GW level multi-beam relativistic klystron amplifier (RKA) has been investigated by means of theoretical modeling, numerical simulation and experiment. Firstly, a four-cavity multi-beam RKA was optimized with a one-dimension large signal code, and optimal working parameters are obtained. Under the conditions of 530 kV voltage, 4.7 kA current, and 14 beams, a 1.1 GW averaged microwave power with efficiency 43% was generated with the code. Subsequently, the beam-wave interaction parameters obtained from the code were verified with a PIC code, and a 992 MW output microwave power with efficiency 37% was obtained. At last, a long time operation experiment was conducted. In such an experiment, a 934 MW averaged microwave power with 69 ns pulse width and 33% efficiency was generated under the conditions of 530 kV voltage, 5.4 kA current, 20 Hz repetition frequency for 1 s, 0.39 T guiding magnetic field and 1.7 kW input microwave power. In addition, for the experiment of 20 Hz repetition frequency and 10 min operating time, a 889 MW averaged microwave power was obtained with 42 ns averaged pulse width. The investigation results make a strong foundation for the S-band RKAs of low guiding magnetic field and longtime operation.