Jets are ubiquitous in the universe[1,2]. The radio jet is a beamed plasma flow with relativistic speed accelerated by a supermassive black hole in some galaxies. Recent observations of the relativistic jet in the elliptical galaxy M87 have discovered a triple-ridge sub-structure in the jet at a distance of one thousand Schwartzchild radius from the black hole [3,4]. The triple-ridge structure may be the first strong evidence of the spine-sheath structure consisting of the fast spine region (jet spine) and relatively slow sheath region (jet sheath), which was hypothetically introduced to explain observational features in various unresolved relativistic jets [5,6]. However, the formation mechanism of such a spine-brightened jet is quite enigmatic. Here we report that the combination of the magnetic pinching force induced by an electron-scale shear-instability called Mushroom instability[7] and the high-energy electron ejections by the subsequent magnetic reconnection leads to the drastic accumulation of high-energy electrons in the center of the cylindrical jet. The concentration of high-energy electrons towards the jet center indicates the appearance of bright jet-spine as observed in M87. Thus, the electron-scale, microscopic processes would play an important role in the structure formation and generation of high-energy components in the relativistic jets. Rererences: [1] Frank, A. etal. Jets and Outflows from Star to Cloud: Observations ConfrontTheory. InBeuther, H., Klessen, R. S., Dullemond, C. P. & Henning, T. (eds.) Protostars and Planets VI, 451 (2014). [2] Blandford, R., Meier, D. & Readhead, A. Relativistic Jets from Active Galactic Nuclei. ARA&A 57, 467–509 (2019). [3] Asada, K., Nakamura, M. & Pu, H.-Y. Indication of the Black Hole Powered Jet in M87 by VSOP Observations. ApJ833, 56 (2016). [4] Hada, K. The Structure and Propagation of the Misaligned Jet M87. Galaxies 5, 2 (2017). [5] Laing, R. A. & Bridle, A. H. Relativistic models and the jet velocity field in the radio galaxy3C 31. MNRAS 336, 328–352 (2002). [6] Ghisellini, G., Tavecchio, F. & Chiaberge, M. Structured jets in TeV BL Lac objectsand radiogalaxies. Implications for the observed properties. A&A 432, 401–410 (2005). [7] Alves, E. P., Grismayer, T., Fonseca, R. A. & Silva, L. O. Transverse electron-scale instability in relativistic shear flows. PhRvE 92, 021101 (2015).

Recent progress in super-computers has opened a new tool for the study of nonlinear dynamics in plasmas. This paper reviews the recent computer simulation studies for the self-organization and self-relaxation processes in MHD plasmas carried out by the Hiroshima group. Taylor's conjecture for the selective dissipation of magnetic energy keeping the total magnetic helicity constant is confirmed and the mechanisms for formation and maintenance of the reversed field pinch configuration are explained in terms of the self-relaxation of the plasma due to a driven magnetic reconnection triggered by ideal MHD helical kink unstable modes and their nonlinear couplings. § 1. IntroductionThe second law of thermodynamics predicts that the entropy of an isolated system increases monotonically_ At a glance, this law appears to imply that any structures in universe continuously decay and that the entire universe will eventually evolve to a state of complete randomness or uniformity. In our universe, however, a wide variety of structures does exist and continues to develop, as can be seen most clearly in the biological system_ 1 J Such a spontaneous generation and maintenance of structures is called a self organization process and can be widely observed in non-biological systems in nature. Formation of an ordered structure in fluids such as the Benard cell or a coherent oscillation reaction as the Belousov-Zhabotinsky reaction are the well-known examples.2l Recent progress in plasma physics has revealed that a plasma exhibits many such self-organization processes. In this paper, we present a review of the recent research on nonlinear dynamics associated with the self-organization processes in plasmas. Particular emphasis will be placed on the results of computer simulations that have made an important contribution to progress in this research.Self-organization in nature has attracted not only the poetic physicists, but also the nuclear fusion scientists who have been trying to find a magnetic field configuration, which can confine a high-temperature plasma in a stable and steady state. Since instabilities and resistive diffusions will disturb or modify the magnetic at