Hasegawa–Wakatani and Modified Hasegawa–Wakatani Turbulence Induced by Ion-Temperature-Gradient Instabilities

Sarto, D. Del; Ghizzo, A.

doi:10.3390/fluids2040065

Cited by 5 publications

(5 citation statements)

References 41 publications

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“…In all simulations presented here, the diffusion coefficient D (ψ) is zero everywhere excepted in a small region (5% of the total space) on the boundary limit in the poloidal flux to maintain the stability of your numerical scheme when strong turbulence emerges. Such approach is kinetic in nature and can be reduced to the Hasegawa-Wakatani in a two-field model (see [35] for more details).…”

Section: Hamilton-jacobi Model For Ion Temperature Gradient (Itg) Turmentioning

confidence: 99%

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

Ghizzo

Sarto

2019

Plasma

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We address the mechanisms underlying low-frequency zonal flow generation in a turbulent system through the parametric decay of collisionless trapped particle modes and its feedback on the stabilization of the system. This model is in connection with the observation of barrier transport in reduced gyrokinetic simulations (A. Ghizzo et al., Euro. Phys. Lett. 119(1), 15003 (2017)). Here the analysis is extended with a detailed description of the resonant mechanism. A key role is also played by an initial polarisation source that allows the emergence of strong initial shear flow. The parametric decay leads to the growth of a zonal flow which differs from the standard zero frequency zonal flow usually triggered by the Reynolds stress in fluid drift-wave turbulence. The resulting zonal flow can oscillate at low frequency close to the ion precession frequency, making it sensitive to strong amplification by resonant kinetic processes. The system becomes then intermittent. These new findings, obtained from numerical experiments based on reduced semi-Lagrangian gyrokinetic simulations, shed light on the underlying physics coming from resonant wave-particle interactions for the formation of transport barriers. Numerical simulations are based on a Hamiltonian reduction technique, including magnetic curvature and interchange turbulence, where both fastest scales (cyclotron and bounce motions) are gyro-averaged.

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Section: Hamilton-jacobi Model For Ion Temperature Gradient (Itg) Turmentioning

confidence: 99%

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

Ghizzo

Sarto

2019

Plasma

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“…In order to compute N ± ξk in terms of ξ ± k , we need to go back to Φ k and n k using (15)(16), compute the nonlinear terms (7-8) using those and combine them as in (14). They can then be written in the form: kr +ω + pr +ω + qr = 0 of the Hasegawa-Wakatani system for the case C = 1.0, κ = 0.2, ν = D = 10 −3 is shown corresponding to the wave vector k = (5, 5) that is shown explicitly.…”

Section: Nonlinear Termsmentioning

confidence: 99%

“…The model is well known to generate high levels of large scale zonal flows, especially for C 1 [8][9][10]. It has been studied in detail for many problems in fusion plasmas including dissipative drift waves in tokamak edge [11,12], subcritical turbulence [13], trapped ion modes [14], intermittency [15,16], closures [17][18][19], feedback control [20], information geometry [21] and machine learning [22]. Variations of the Hasegawa-Wakatani model are regularly used for describing turbulence in basic plasma devices [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Gürcan¹,

Anderson²,

Moradi³

et al. 2022

Preprint

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Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking where the phase differences between dominant modes converge to constant values as individual phases increase in time. This allows the system to have approximately constant amplitude solutions. Non-resonant triads show similar behavior only when one of its legs is a zonal wave number. However when an additional triad, which is a reflection of the original one with respect to the y axis is included, the behavior of the resulting triad pair is shown to be more complex. In particular, it is found that triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy to the subdominant mode which keeps growing exponentially, while those involving larger radial wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay to zero). In order to study the dynamics in a connected network of triads, a network formulation is considered including a pump mode, and a number of zonal and non-zonal subdominant modes as a dynamical system. It was observed that the zonal modes become clearly dominant only when a large number of triads are connected. When the zonal flow becomes dominant as a 'collective mean field', individual interactions between modes become less important, which is consistent with the inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation is discussed for the same parameters and various forms of the order parameter are computed. It is observed that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function of scale in direct numerical simulations.

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“…( 15) and ( 16), compute the nonlinear terms ( 7) and (8) using those, and combine them as in Eq. (14). They can then be written in the form…”

Section: Nonlinear Termsmentioning

confidence: 99%

“…7 The model is well known to generate high levels of large scale zonal flows, especially for C տ 1, [8][9][10] where C is the adiabaticity parameter. It has been studied in detail for many problems in fusion plasmas including dissipative drift waves in tokamak edge, 11,12 subcritical turbulence, 13 trapped ion modes, 14 intermittency, 15,16 closures, [17][18][19] feedback control, 20 information geometry, 21 and machine learning. 22 Variations of the Hasegawa-Wakatani model are regularly used for describing turbulence in basic plasma devices.…”

Section: Introductionmentioning

confidence: 99%

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa–Wakatani system

et al. 2022

View full text Add to dashboard Cite

The Hasegawa–Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices, is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking, where the phase differences between dominant modes converge to constant values as individual phases increase in time. This allows the system to have approximately constant amplitude solutions. Non-resonant triads show similar behavior only when one of its legs is a zonal wave number. However, when an additional triad, which is a reflection of the original one with respect to the y axis is included, the behavior of the resulting triad pair is shown to be more complex. In particular, it is found that triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy to the subdominant mode which keeps growing exponentially, while those involving larger radial wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay to zero). In order to study the dynamics in a connected network of triads, a network formulation is considered, including a pump mode, and a number of zonal and non-zonal subdominant modes as a dynamical system. It was observed that the zonal modes become clearly dominant only when a large number of triads are connected. When the zonal flow becomes dominant as a “collective mean field,” individual interactions between modes become less important, which is consistent with the inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation are discussed for the same parameters, and various forms of the order parameter are computed. It is observed that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function of scale in direct numerical simulations.

show abstract

Hasegawa–Wakatani and Modified Hasegawa–Wakatani Turbulence Induced by Ion-Temperature-Gradient Instabilities

Cited by 5 publications

References 41 publications

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa–Wakatani system

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