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We present the results of N$_2$H$^+$ ($J=1-0$) observations toward SerpensSouth, the nearest cluster-forming, infrared dark cloud. The physicalquantities are derived by fitting the hyperfine structure of N$_2$H$^+$. TheHerschel and 1.1-mm continuum maps show that a pc-scale filament fragments intothree clumps with radii of $0.1-0.2$ pc and masses of $40-230M_\odot$. We findthat the clumps contain smaller-scale ($\sim 0.04$ pc) structures, i.e., densecores. We identify 70 cores by applying CLUMPFIND to the N$_2$H$^+$ data cube.In the central cluster-forming clump, the excitation temperature and line-widthtend to be large, presumably due to protostellar outflow feedback and stellarradiation. However, for all the clumps, the virial ratios are evaluated to be$0.1-0.3$, indicating that the internal motions play only a minor role in theclump support. The clumps exhibit no free-fall, but low-velocity infall, andthus the clumps should be supported by additional forces. The most promisingforce is the globally-ordered magnetic field observed toward this region. Wepropose that the Serpens South filament was close to magnetically-critical andambipolar diffusion triggered the cluster formation. We find that the northernclump, which shows no active star formation, has a mass and radius comparableto the central cluster-forming clump, and therefore, it is a likely candidateof a {\it pre-protocluster clump}. The initial condition for cluster formationis likely to be a magnetically-supported clump of cold, quiescent gas. Thisappears to contradict the accretion-driven turbulence scenario, for which theturbulence in the clumps is maintained by the accretion flow.

The Dynamical State of The Serpens South Filamentary Infrared Dark Cloud