The nonlinear dynamics and structure of plasmas with tightly twisted magnetic field lines have been studied using a toroidal plasma device. Stepwise magnetohydrodynamic (MHD) relaxation occurs, resulting in a discontinuous change in the pitch of magnetic field lines. This discrete nature of the pitch stems from the instability of kink (torsional) modes. The MHD relaxation stabilizes kink modes by selecting (self-organizing) appropriate pitches. The self-organized state displays the characteristic of a ‘dissipative structure’ in that it is accompanied by enhanced energy dissipation; the global resistance of the plasma current is substantially enhanced. The magnetic energy, which is generated by the internal plasma current, first changes into fluctuation energy through the kink instability, and then it goes mainly to ion thermal energy through viscous dissipation of the fluctuating flow. The viscosity dissipates the fluctuation energy with conservation of helicity. The self-organization of the stabilized magnetic field is characterized by the preferential conservation of the helicity.