Slow Transition of Energy Transport in High-Temperature Plasmas

Abstract

A new slow transition process for energy transport in magnetically confined plasmas is reported. The slow transition is characterized by the change between two metastable transport conditions characterized by a weak and a strong electron temperature (T e ) dependence of normalized heat flux. These two branches are found to merge at the critical T e gradient. In metastable transport, the derivative of normalized heat flux to the T e gradient, @ Q e =n e =@ ÿrT e , is positive, while it becomes negative during the transition phase. The time for the transition increases as the normalized T e gradient is increased and exceeds the transport time scale characterized by the global energy confinement time. High-temperature plasmas, which are seen in nature or confined in laboratory experimental devices, are very often far from equilibrium. One of the noticeable features is that the observed temperature profiles are realized as a balance between the flux of energy and turbulence-driven transport. A sudden and distinctive jump in the profiles has been found, e.g., the H-mode phenomena in tokamak plasmas [1]. The concept of a profile transition has been employed in order to understand the formation and dynamics of a self-sustained radial profile in inhomogeneous plasmas [2]. The transitions in the profiles in H-mode plasmas are caused by the S-curve property (cusp-type catastrophe) in the gradient-flux relation, showing a feature analogous to the first-order phase transition [3,4]. As the second-order phase transition exists in terrestrial matter, it is possible that the other type of transition exists in the process of transport barrier formation in plasmas [4]. We here report the discovery of a new, slowly evolving transition between two transport branches that have different electron temperature (T e ) dependences, in toroidal plasmas.Heat transport in a magnetically confined toroidal plasma is strongly governed by turbulence. The mechanism of the H-mode transition has been studied both experimentally [5,6] and theoretically [7][8][9][10]. The bifurcation of the radial electric field and the associated suppression of turbulence are the key parameters to explain the fast transition between L mode and H mode [2,[7][8][9]. This transition mechanism appears as various phenomena such as the electric pulsation observed in the toroidal helical plasma and the internal transport barrier [11]. In parallel with these rapidly evolving phenomena, slow evolutions into the state of improved plasma confinement have also been observed in a slowly developing edge transport barrier [12] and in other confinement improved modes. Improved Ohmic confinement mode [13], counter-neutral beam injection improved mode [14], pellet enhanced performance mode [15], radiatively improved mode [16] associated with the change of density profiles without a clear fast transition. Although these improved modes associated with the slow transition are as important as the improved mode with a fast transition, the mechanism of the slow transition has been studie...

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“…The slow transition to the improved transport mode [3], which is often observed in other types of improved modes or internal transport barrier (ITB) plasmas [4], is categorized as a type of second-order transition in contrast to a first-order transition such as the L/H transition [5][6][7]. In helical plasma, associated with the transition from ion-root to electron-root, an electron internal transport barrier (ITB) appears, when the heating power of the ECH exceeds a threshold power [8][9][10][11][12].…”

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

“…The source term P (t) generally consists of a number of harmonic components in a perturbative experiment of which two have been explicitly stated, i.e., P (t) = P 0 + A 1 cos (f 1 t) + A 2 cos (f 2 t) + h.o.c., (4) where P 0 is the average power of the perturbation. The higher order components (h.o.c.)…”

“…The total contributions on the different harmonics can be calculated using (4) by substituting the harmonic number, e.g., k = 7 Θ (ρ, 7) = G (1) (ρ, 7) U (7) + 18 k1=−11…”

“…These quantities are generally analyzed in 1D as a function of the dimensionless normalized minor radius ρ, which is permissible due to the device geometry, magnetic field configuration, and relevant time scales of transport [3]. This radial transport is then analyzed in steady-state [4] or in the transient phase, often using a perturbation [2,5,3,6].…”

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“…The transitions in the profiles in H-mode plasmas are caused by the S-curve property (cusp-type catastrophe) in the gradientflux relation, showing a feature analogous to first-order phase transition [2]). The slow transition to the improved transport mode [3,4], which is often observed in other types of improved modes or internal transport barrier (ITB) plasmas [10], is categorized as a type of second-order transition in contrast to a first-order transition such as the L/H transition [5][6][7]. In the helical plasma, associated with the transition from ion-root to electron-root, an electron ITB appears, when the heating power of the ECH exceeds a threshold power [8][9][10][11][12].…”