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The quantum-limited linewidth of a laser cavity is enhanced above theSchawlow-Townes value by the Petermann factor K, due to the non-orthogonalityof the cavity modes. The average Petermann factor $<K>$ in an ensemble ofcavities with chaotic scattering and broken time-reversal symmetry iscalculated non-perturbatively using random-matrix theory and the supersymmetrytechnique, as a function of the decay rate $\Gamma$ of the lasing mode and thenumber of scattering channels N. We find for $N\gg 1$ that for typical valuesof $\Gamma$ the average Petermann factor $<K>\propto \sqrt{N}\gg 1$ isparametrically larger than unity.Comment: 7 pages, 2 figures, europhys.sty (macro included

Large Petermann factor in chaotic cavities with many scattering channels