We present the results of N _ { 2 } H ^ { + } ( J = 1 - 0 ) observations toward Serpens South , the nearest cluster-forming , infrared dark cloud . The physical quantities are derived by fitting the hyperfine structure of N _ { 2 } H ^ { + } . The Herschel and 1.1-mm continuum maps show that a pc-scale filament fragments into three clumps with radii of 0.1 - 0.2 pc and masses of 40 - 230 M _ { \odot } . We find that the clumps contain smaller-scale ( \sim 0.04 pc ) structures , i.e. , dense cores . 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-width tend to be large , presumably due to protostellar outflow feedback and stellar radiation . 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 the clump support . The clumps exhibit no free-fall , but low-velocity infall , and thus the clumps should be supported by additional forces . The most promising force is the globally-ordered magnetic field observed toward this region . We propose that the Serpens South filament was close to magnetically-critical and ambipolar diffusion triggered the cluster formation . We find that the northern clump , which shows no active star formation , has a mass and radius comparable to the central cluster-forming clump , and therefore , it is a likely candidate of a pre-protocluster clump . The initial condition for cluster formation is likely to be a magnetically-supported clump of cold , quiescent gas . This appears to contradict the accretion-driven turbulence scenario , for which the turbulence in the clumps is maintained by the accretion flow .