Abstract
The present study is conducted to investigate Fokker-Planck equation in action-angle variables. The formalism is applied for the impedance of the pillbox RF cavity with 100 MHz frequency which is designed at ILSF based on MAX-lab design. The beam instability is discussed as a function of current and storage ring circumference. The Robinson instability occurs for dipole mode if the storage ring circumference is equal to 528 m and the current is more than 410 mA. Moreover, for current of 400 mA, the storage ring circumference values including 525 m, 527.90 m and 530.97 m lead to Robinson instability.
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