Self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity

Abstract

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Characteristics of constrained turbulent transport in flux-driven toroidal plasmas

“…Their fluctuations cause complex structures and dynamics not only in configuration space, e.g. turbulent spreading [20][21][22][23], avalanches and bursts [24][25][26][27][28][29], finescale pressure corrugations, referred to as staircase [30][31][32][33][34][35][36], etc. but also in velocity space, e.g.…”

“…Here, process 2 is a notable event which constitutes a quasi-deterministic, nonpower tail component in the size-PDF, which extracts larger turbulent free energy in the system through larger structure than that of linear, and plays a role to initiate an E × B shear layer pattern in process 3. Note that process 3 is considered to be the same as the E × B staircase discussed above and in [30][31][32][33][34][35][36]. It is also noted that processes 1 and 2 exhibit different spatial scales but provide similar radial correlation lengths, effectively from meso-scale to macro-scale.…”

On the Quantization of AB Phase in Nonlinear Systems

“…The goal of this work is entirely focused on aspects of the nonlinear AB phase around Dirac cones induced by general power law nonlinearity [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. In this way, it becomes possible to answer whether the previously obtained AB phase quantization is unique to Kerr nonlinearity and if so, why there is such uniqueness.…”

Destruction of Anderson localization by subquadratic nonlinearity

“…= Γ(q m1,m2 +1) and simultaneously relaxing the condition that the exponents q m1,m2 , while non-negative, must be necessarily integer. This leads to an iteration algorithm [9,10], according to which one can expand the algebraic form in eq. ( 9) by iterating on the number of fractional exponents to be allowed in eq.…”

“…Clearly, all such combinations would equally contribute to the series expansion in eq. (10). Then to account for these contributions one has to sum over the indexes m 1 and m 2 .…”