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Standing sausage modes in flare loops are important for interpretingquasi-periodic pulsations (QPPs) in solar flare lightcurves. We propose aninversion scheme that consistently uses their periods $P$ and damping times$\tau$ to diagnose flare loop parameters. We derive a generic dispersionrelation governing linear sausage waves in pressure-less straight tubes, forwhich the transverse density inhomogeneity takes place in a layer of arbitrarywidth $l$ and is of arbitrary form. We find that $P$ and $\tau$ depend on thecombination of $[R/v_{\rm Ai}, L/R, l/R, \rho_{\rm i}/\rho_{\rm e}]$, where $R$is the loop radius, $L$ is the looplength, $v_{\rm Ai}$ is the internalAlfv\'en speed, and $\rho_{\rm i}/\rho_{\rm e}$ is the density contrast. Forall the density profiles examined, $P$ and $\tau$ experience saturation when$L/R \gg 1$, yielding an inversion curve in the $[R/v_{\rm Ai}, l/R, \rho_{\rmi}/\rho_{\rm e}]$ space with a specific density profile when $L/R$ issufficiently large. When applied to a spatially unresolved QPP event, thescheme yields that $R/v_{\rm Ai}$ is the best constrained, whereas $l/R$corresponds to the other extreme. For spatially resolved QPPs, while $L/R \gg1$ cannot be assumed beforehand, an inversion curve remains possible due toadditional geometrical constraints. When a spatially resolved QPP eventinvolves another mode, as is the case for a recent event, the full set of$[v_{\rm Ai}, l, \rho_{\rm i}/\rho_{\rm e}]$ can be inferred. We conclude thatthe proposed scheme provides a useful tool for magneto-seismologicallyexploiting QPPs.

Standing Sausage Modes In Nonuniform Magnetic Tubes: An Inversion Scheme For Inferring Flare Loop Parameters