The role of the Kubo number in two-component turbulence

Qin, Gang; Shalchi, A.

doi:10.1063/1.4821026

Cited by 7 publications

(4 citation statements)

References 36 publications

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“…Depending on V, one finds therefore two regimes, the weak turbulence regime for D V D ω , such that the expansion of the solution for D in (21c) yields D ≈ D V , which scales like V 2 , and a Bohm strong turbulence regime such that D ≈ √ D V D ω and is therefore linear in V [84]. The ratio D V /D ω , which can be interpreted as a Kubo number [85,86], governs this transition. As a possible closure of the system, we enforce the diffusion coefficient D to be in the weak turbulence regime.…”

Section: Diffusive Transport Driven By the Local Dynamics: Closure Co...mentioning

confidence: 99%

Self-consistent cross-field transport model for core and edge plasma transport

Baschetti

Bufferand²,

Ciraolo³

et al. 2021

Nucl. Fusion

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The 2D mean-field plasma edge transport description of plasma wall interaction is completed by a κ-ε model as in Reynolds Average Navier Stokes simulations for neutral fluids. The local evolution of the turbulent kinetic energy κ and its dissipation rate ε are revisited and slightly modified. It is shown that the κ-ε extends the quasilinear approach by self-consistently determining κ and the relevant time κ/ε leading to the diffusion coefficient κ 2 /ε. The κ-ε evolution is also shown to be equivalent to both coupled Ginzburg-Landau amplitude equations and predator-prey systems where κ is the prey and ε the predator. The dissipation process ε we enforce describes the small scale dissipation of Kolmogorov cascades. It depends on a free parameter akin to a velocity V . The chosen closure relates V to the the parallel connection time and the normalized Scrape-Off layer width qρ * , q is the safety factor and ρ * the ratio of the characteristic Larmor radius and plasma minor radius. A 1D model with κ-ε self-organized transport is used for comparison to empirical scaling laws of SOL width and energy confinement time in L-mode plasmas. Shortfalls of the scaling laws are analyzed. Possible changes of the closure for V are discussed. The 1D model is also used to test the transport response to a dependence of V to large scale velocity shear. Spontaneous confinement improvement when increasing the heating power 1 is observed with the development of an interface barrier at the separatrix. Plasma-wall interaction simulations for TCV and WEST are analyzed. A single scalar free parameter tunes the cross field transport. Experimental midplane and divertor profiles are compared to the simulations. Remarkable agreement is observed. The SOL width determined by the simulation for WEST is close to the experimental value with less than 20 % difference, while the scaling law for L-mode is off my more than a factor 3. The turbulent transport described by the κ-ε is not homogeneous, but ballooned as experimentally observed together with cross-field transport in the divertor SOL on the low field side, and nearly none in the private flux region.

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Section: Diffusive Transport Driven By the Local Dynamics: Closure Co...mentioning

confidence: 99%

Self-consistent cross-field transport model for core and edge plasma transport

Baschetti

Bufferand²,

Ciraolo³

et al. 2021

Nucl. Fusion

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“…These efforts require, as input, a model of the spectrum of magnetic fluctuations generated by the plasma turbulence, and a wide variety of such turbulent magnetic field models have been used. Sophisticated numerical field line following algorithms and complementary analytical approaches have been used to study realizations of slab turbulence models with magnetic field fluctuations (Schlickeiser 1989; Shalchi & Kourakis 2007 a , b ; Shalchi 2010 b ), two-dimensional (2-D) turbulence models with (Shalchi & Kourakis 2007 a , b ; Guest & Shalchi 2012), composite models including slab plus 2-D components with (Bieber, Wanner & Matthaeus 1996; Giacalone & Jokipii 1999; Shalchi & Kourakis 2007 a , b ; Qin & Shalchi 2013) and full 3-D models with , including both isotropic (Zimbardo et al. 1995; Giacalone & Jokipii 1999; Shalchi 2010 a ; Ragot 2011) and anisotropic distributions of magnetic fluctuations (Chandran 2000; Zimbardo, Veltri & Pommois 2000; Zimbardo, Pommois & Veltri 2006; Shalchi & Kolly 2013; Ruffolo & Matthaeus 2013).…”

Section: Impact Of Magnetic Field Line Wandermentioning

confidence: 99%

The development of magnetic field line wander by plasma turbulence

Howes

Bourouaine

2017

J. Plasma Phys.

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Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

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“…1995). Recently, several models were developed to study the separation of the magnetic field lines, implementing various models of turbulence, including slab turbulence (Schlickeiser 1989; Shalchi & Kourakis 2007 a , b ; Shalchi 2010 b ), two-dimensional turbulence (Shalchi & Kourakis 2007 a , b ; Guest & Shalchi 2012), composite models including slab plus two-dimensional components (Bieber, Wanner & Matthaeus 1996; Shalchi & Kourakis 2007 a , b ; Qin & Shalchi 2013) and other three-dimensional models including MHD turbulence (Zimbardo et al. 1995; Zimbardo, Veltri & Pommois 2000; Maron, Chandran & Blackman 2004; Zimbardo, Pommois & Veltri 2006; Shalchi 2010 a ; Ragot 2011; Beresnyak 2013; Ruffolo & Matthaeus 2013; Shalchi & Kolly 2013).…”

Section: Introductionmentioning

confidence: 99%

“…Advanced models implementing nonlinear calculations of FLRW theory were developed later to estimate the diffusion of the field line wandering (Matthaeus et al 1995). Recently, several models were developed to study the separation of the magnetic field lines, implementing various models of turbulence, including slab turbulence (Schlickeiser 1989;Shalchi & Kourakis 2007a,b;Shalchi 2010b), two-dimensional turbulence (Shalchi & Kourakis 2007a,b;Guest & Shalchi 2012), composite models including slab plus two-dimensional components (Bieber, Wanner & Matthaeus 1996;Shalchi & Kourakis 2007a,b;Qin & Shalchi 2013) and other three-dimensional models including MHD turbulence (Zimbardo et al 1995;Zimbardo, Veltri & Pommois 2000;Maron, Chandran & Blackman 2004;Zimbardo, Pommois & Veltri 2006;Shalchi 2010a;Ragot 2011;Beresnyak 2013;Shalchi & Kolly 2013). In the latter works, the superdiffusive behaviour of the magnetic field lines has been confirmed in three-dimensional MHD simulations for scales comparable to or less than the injection scale l 0 , but for scales much larger than l 0 the field lines follow a diffusive law.…”

Section: Introductionmentioning

confidence: 99%

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

Bourouaine

Howes

2017

J. Plasma Phys.

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The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time $t_{2}$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time $t\lesssim t_{2}$ for strong turbulence, and at $t\gtrsim t_{2}$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval $t_{2}<t\leqslant 13t_{2}$. Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form $\langle (\unicode[STIX]{x1D6FF}r)^{2}\rangle =A(z/L_{\Vert })^{p}$ ($L_{\Vert }$ is the correlation length parallel to the magnetic background field $\boldsymbol{B}_{\mathbf{0}}$, $z$ is the distance along $\boldsymbol{B}_{\mathbf{0}}$ direction), providing functional forms of the amplitude coefficient $A$ and power-law exponent $p$ as a function of the nonlinearity parameter.

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The role of the Kubo number in two-component turbulence

Cited by 7 publications

References 36 publications

Self-consistent cross-field transport model for core and edge plasma transport

Self-consistent cross-field transport model for core and edge plasma transport

The development of magnetic field line wander by plasma turbulence

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

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