7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Formation, Propagation and Conversion of Transport Barriers Triggered byDynamical Critical Gradient in Tokamak Plasmas
Xiaobo Li1, Zhibin Guo1 and P.H. Diamond2
1
State Key Laboratory of Nuclear Physics and Technology, Fusion Simulation Center, School ofPhysics, Peking University, Beijing, 100871, People’s Republic of China
2
Department of Physics, University of California San Diego, La Jolla, California 92093, USAe-mail: Tharukin@pku.edu.cn
Magnetically confined plasma system is well-knownfor its multi-confinement states. Typical scenarios
include the L-mode (L: low confinement), the H-mode(H: high confinement) and the I-mode (I: improved), etal[1, 2]. An ‘order parameter’ depicting the confinement
state is the transport barrier, measured by the shearing
rate of the mean E×B flow. The transport barrier could
occur near the core or the edge, dubbed as internal/edge
transport barrier (ITB/ETB). It is a key structure formaintaining the high confinement state of magneticallyconfined plasma systems. Transitions between different
type of transport barriers, (typically, the ITB and theETB), cause the conversions of different confinement
states. The synergism between the global dynamics (i.e.,propagation) and the local dynamics (i.e., transition) is
critical to understanding the transition mechanisms ofdifferent confinement states.
Plasma profiles tend to stay near a critical gradient,
known as self-organized criticality (SOC), which gives
rise to profile stiffness[3]. This stiffness strongly
constrains the transition of confinement states, especiallyin the plasma core region that lacks boundary conditions.
To form a transport barrier, the profile stiffness needs tobe weakened, breaking the old SOC state andestablishing a new one. The experimental evidence
suggested that the profile stiffness is correlated with therotational flow, i.e., by increasing the flow shear, theprofile stiffness could be softened[4]. Thus, the criticalgradient should dynamically align with the flow
evolution rather than being an adjustable parameter.
In this work, we propose a 1D reduced model with adynamical critical gradient (DCG) to study the formation,propagation, and conversion of the transport barriers. In
contrast to the commonly adopted static critical gradient,
an evolving critical gradient self-consistently softens theprofile stiffness, so as to facilitate the generation oftransport barriers. This is especially crucial to the ITBformation. Numerically, we show that the inhomogeneityof turbulent and neoclassical diffusivities can induce theglobal wave front propagation of the transport barrier.
When the heating power ramps quickly, the ITB
propagates unidirectionally to the edge region andconverts into an ETB. For slow power ramping, thepropagating ITB will bifurcate into bidirectional
wavefronts and finally convert into a steady DTB(double transport barrier) state. Our model uncovers thevital role of a dynamical ‘profile-stiffness’ in depicting
the global dynamics of the transport barrier.

𝜖! ="
#!

, 𝐿 ! = −𝑑 ln 𝑇/𝑑𝑟

Figure 1. Stiffness with different mean flow shear Ev.

References[1] F. Wagner et al., Phys. Rev. Lett. 53, 1453 (1984)[2] D. Whyte et al., Nuclear Fusion 50, 105005 (2010)[3] X. Garbet et al., Plasma Physics and Controlled
Fusion 46, 1351 (2004)[4] P. Mantica et al., Phys. Rev. Lett.107.135004(2011)

Figure 2. Spatiotemporal evolutions of
turbulence, zonal flow, and mean flowin the cases of w/o DCG (a-c) and w/
DCG (d-f) under a slow power ramp,and w/ DCG (g-i) under a quick power
ramp. The input power is increased
from 5 × 10$% to 1 × 10$& with aduration of Δ𝑡 = 5 × 10% for the slow
ramp, and Δ𝑡 = 2 × 10% for the quick
ramp.