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A cathode spot model is used to analyze the instability phenomena of a vacuum arc. The current below which no real solution exists is believed to be an unstable region. When the current decreases below 19 A, the electrons returning to the sheath region from the plasma region were found to dominate over the positive ions and, thus, the cathode electric field has an imaginary solution. An electrostatic probe was used to confirm these findings, and the analytical results were similar to measurement results. The present cathode spot model may be valid for volatile materials.