Statistical description of turbulent transport for flux driven toroidal plasmas

Anderson, Johan; Imadera, Kenji; Kishimoto, Y.; Li, J.Q.; Nordman, Hans

doi:10.1088/1741-4326/aa686b

Cited by 7 publications

(14 citation statements)

References 18 publications

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“…It is noted that the temperature profile is self-organized into an exponential function form with a fast time scale, so that the free energy of the instability, e.g. ε T (r) ≡ R/L T and/ or η i (r) ≡ L n /L T in the ITG mode case and/or η i -mode case, tends to be a radially constant value [13,14,17]. When the density profile is given by an exponential function form as n(r) ∝ exp (−r/L n (r)), the ion temperature is relaxed into the same function form as T i (r) ∝ exp (−r/L T (r)) since no density relaxation takes place due to the adiabatic electron response in the present simulation.…”

Section: Properties Of E × B Shear Flows In Full-f Flux-driven Gyroki...mentioning

confidence: 99%

“…the linear ITG mode unstable region, is believed to be the origin of such a staircase structure. Based on this hypothesis, we first discuss the characteristics of the ITG mode in a toroidal geometry based on the first order ballooning theory [12][13][14]17], and investigate the formation mechanism based on such ITG mode in section 4.1. In the zeroth order for 1/n (n: toroidal mode number), the linear eigenvalue problem is reduced to a 1D differential equation [10].…”

Section: Properties Of E × B Shear Flows In Full-f Flux-driven Gyroki...mentioning

confidence: 99%

“…On the other hand, such a meso-scale ITG mode is believed to be hardly survived in the quasi-steady turbulent state due to the generation of zonal flows and is disintegrated into smaller scale eddies [16]. However, in recent flux-driven simulations with moderate magnetic shear and both the effects of zonal flows and equilibrium mean flow, mode structures which ranging from meso-scale (∆r ≈ √ ρ i L) to macro-scale scale (∆r ≈ L) are induced intermittently, causing transport bursts in thermal transport across magnetic flux surfaces [8,17,18]. Although such an extended structure is readily disintegrated by zonal flows, the repetitive occurrence of the process is found to provide a constraint on the transport, leading to a stiffness in the profile formation [7,8,[19][20][21] and a selfsimilarity in the relaxation [13].…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, we study these topics through simulations computed based on gyrokinetic-based numerical experiment of tokamak (GKNET), a five-dimensional (5D) gyrokinetic code [8,17]. It is found that such a quasi-regular long-lived meso-scale E × B flow pattern is induced incorporated with the self-organization of global profile where the ion temperature profile tends to a specific function form and evolves keeping a self-similarity as discussed in above.…”

Section: Introductionmentioning

confidence: 99%

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A mechanism for the formation and sustainment of the self-organized global profile andE × Bstaircase in tokamak plasmas

et al. 2018

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The mechanism for the formation and sustainment of a self-organized global profile and the 'E × B staircase' are investigated through simulations of a flux-driven ion temperature gradient (ITG) turbulence based on GKNET, a 5D global gyrokinetic code. The staircase is found to be initiated from the radially extended ITG mode structures with nearly up-down symmetry during the saturation phase, and is established as it evolves into a quasi-steady turbulence, leading to a self-organized global temperature profile and to meso-scale isomorphic profiles of the radial electric field and the temperature gradient. It is found that the quasi-regular E × B shear flow pattern is primarily originated from an even-symmetrical zonal flow produced by the extended ITG mode, which flow pattern exhibits an in-phase relation with the mean flow variation induced by the temperature relaxation. Consequently, the staircase is initiated through the profiles of total electric field and temperature gradient with a self-organized manner. Since the sign of E × B shear flow at the central part are opposite to that at both edges, it disintegrates the ITG mode into smaller scale eddies. Meanwhile, smaller scale eddies tend to be aligned radially by spontaneous phase matching, which can provide the growth of mode amplitude and the formation of radially extended mode structures, leading to the bursty heat transport. This process is repeated quasi-periodically, sustaining self-organized structures and the E × B staircase. Moreover, the equilibrium mean field is found to be of specific importance in causing the structures and dynamics from meso-to macro scales in toroidal plasmas.

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Section: Properties Of E × B Shear Flows In Full-f Flux-driven Gyroki...mentioning

confidence: 99%

Section: Properties Of E × B Shear Flows In Full-f Flux-driven Gyroki...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A mechanism for the formation and sustainment of the self-organized global profile andE × Bstaircase in tokamak plasmas

et al. 2018

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“…Fourier-based analysis methods have been widely used, e.g. power spectral for frequency and wavenumber, wavelet, bi-coherence and also tricoherence, etc [13,28,[37][38][39]. Moreover, the test particle tracing method and other techniques including fractional equation, step size function, correlation for space and time, etc have been used [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation

et al. 2020

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Flux-driven ion temperature gradient (ITG) turbulence and associated transport regulated by non-local and non-diffusive processes are investigated based on GKNET simulations in a global toroidal geometry. Among these processes, the instantaneous formation of radially extended quasi-coherent structure, which leads to the transport burst, is found to play an important role in causing global profile formation and relaxation. To elucidate the characteristics of such a transport process, we introduce the size probability distribution function (size-PDF) P (S) to analyze heat flux eddies in the real space, with S the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, P (S) is found to be fitted by three piecewise power laws which transitions at two typical sizes, S a and S b , as P ∝ S −2/3 (S ⩽ S a ), P ∝ S −2 (S a ⩽ S ⩽ S b ), and P ∝ S −4 (S ⩾ S b ), where S a ∼ 50 and S b ∼ 200 in squared gyro-radius unit ρ 2 i for the system with a/ρ i ∼ 225 (a: the minor radius). On the other hand, the size-PDF in the bursting phase exhibits non-power-law irregular humps which corresponds to the quasi-coherent structures for S ⩾ S b reaching to S max ∼ 1500. Such a coherent structure is ascribed to the spontaneous alignment of smaller scale eddies through phase matching in radial direction, which is classified as a quasi-deterministic process. Resultantly, a large amount of free energy is extracted from the system due to subsequent growth of the event, by which a self-organized profile is established. The coherent structure is then readily disintegrated by self-generated zonal flows, followed by the energy transferred to smaller eddies. Finally, turbulent transport in the steady state of a flux-driven system is found to be regulated by the mixture of such quasi-deterministic process and probabilistic processes, which leads to stiffness and resilience in the profile formation and self-similarity in the relaxation.

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Gyrokinetic entropy balances and dynamics in toroidal flux-driven ITG turbulence

2021

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Overall entropy balances and radial dynamics for thermodynamic entropy and conventional fluctuation entropy are investigated by means of newly derived coupled equations and the full-f gyrokinetic simulations for toroidal flux-driven ion-temperature-gradient turbulence. When the equations are integrated over the radial direction, in the quasi-steady state, fluctuation entropy production due to collisional dissipation in velocity space and thermodynamic entropy reduction due to energy input/output in real space are found to be balanced through the generation of a heat flux and associated phase mixing. The cross-correlation analysis indicates that collisional dissipation occurs after the formation of fine-scale structures by phase mixing, while there exists an in-phase relationship between thermodynamic entropy production due to profile relaxation and heat flux. However, when the radial dynamics are retained in the equations, this relationship is found to be violated in regions exhibiting heat avalanches. This is because the thermodynamic entropy is dominated by advection, leading to a time lag between heat flux and temperature variation.

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Statistical description of turbulent transport for flux driven toroidal plasmas

Cited by 7 publications

References 18 publications

A mechanism for the formation and sustainment of the self-organized global profile andE × Bstaircase in tokamak plasmas

A mechanism for the formation and sustainment of the self-organized global profile andE × Bstaircase in tokamak plasmas

Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation

Gyrokinetic entropy balances and dynamics in toroidal flux-driven ITG turbulence

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