Multilongitudinal mode instability in ring Nd:YAG lasers is theoretically analyzed. After we review the way in which the standard two-level laser theory applies to this laser we extend the theoretical treatment to include transverse effects. We do this by taking into account the finite transverse section of the active medium and by assuming a Gaussian transverse distribution for the intracavity field. Finally we demonstrate that multimode emission develops whenever the intracavity field waist

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... ameter is almost equal to the active rod diameter. We conclude that continuous-wave diode-pumped Nd:YAG lasers with low cavity losses are good candidates for the observation of the Risken-Nummedal-Graham-Haken instability.