Self-Organized Evolution of the Internal Transport Barrier in Ion-Temperature-Gradient Driven Gyrokinetic Turbulence

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 is proposed, 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.

Figure 1

Equilibrium and heating profiles.

Figure 2

Formation of the ITB in ITG turbulence. (a) Profiles of $T_i$ and $E_r$ at different times. Open circles: $T_i$ at $t=10$ found by a simulation without NEU. (b) The temperature gradient, $-T_i^{\prime }(r,t)$. The ITB emerges around $r\approx 0.16a$ at $t\le 10\times 0.44\mathrm{ms}$, and its center expands to $r\approx 0.24a$ at $t\approx 50\times 0.44\mathrm{ms}$. (c) The turbulent thermal conductivity ${\chi }_i(r,t)$, which also signifies the turbulence intensity.

Figure 3

Dynamics of the ITB formation. (a)–(e) Emergence at $r=0.16a$. (f)–(j) Expansion at $r=0.28a$. $t_{\text{trans}}$: transition time (different for the two columns). (a),(f) ${\chi }_i$. The turbulence is reduced within the mesoscale region marked by the two horizontal lines. (b),(g) Ion pressure gradient ($p_i^{\prime }$). (c),(h) $E_r$ profile. (d),(i) The ${\chi }_i$-gradient relation; open circles: $L$ state; solid stars: $H$ state; open squares: transition time. (e),(j) $E_r$ and its contributions before ($t=t_{-}$) and after ($t_{+}$) transition; the effect of the toroidal rotation is negligible here.