  Understanding the self-organization of the most promising internal transport
barrier in fusion plasmas needs a long-time nonlinear gyrokinetic global
simulation. The Neighboring Equilibrium Update method, which solves the
secularity problem in a perturbative simulation and speeds up the numerical
computation by more than 10 times. It is found that the internal transport
barrier emerges at the magnetic axis due to inward propagated turbulence
avalanche, and its outward expansion is the catastrophe of self-organized
structure induced by outward propagated avalanche.
