Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach

Kolesnikov, R. A.; Krommes, John A.

doi:10.1103/physrevlett.94.235002

Cited by 20 publications

(27 citation statements)

References 17 publications

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“…[4,6,7,8,18,19,20,21,22,23]. In some cases, the requirement that the dynamics has Hamiltonian form has been used to guide the construction [6,20] and has led to the identification of new and physically important terms.…”

Section: Introductionmentioning

confidence: 99%

“…[24] The Hamiltonian structure of fluid models has also been shown to be important for the consistent calculation of zonal flow dynamics. [6,7,8] Several fluid models have been proposed to study electromagnetic plasma dynamics (see [12,25,26] for reviews). Some of these models have been instrumental in advancing our understanding of magnetic reconnection.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hamiltonian formulation and analysis of a collisionless fluid reconnection model

Tassi¹,

Morrison²,

Waelbroeck³

et al. 2008

Plasma Phys. Control. Fusion

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The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie-Poisson bracket. The bracket is used to obtain new independent families of invariants, so-called Casimir invariants, three of which are directly related to Lagrangian invariants of the system. The Casimirs are used to obtain a variational principle for equilibrium equations that generalize the Grad-Shafranov equation to include flow. Dipole and homogeneous equilibria are constructed. The linear dynamics of the latter is treated in detail in a Hamiltonian context: canonically conjugate variables are obtained; the dispersion relation is analyzed and exact thresholds for spectral stability are obtained; the canonical transformation to normal form is described; an unambiguous definition of negative energy modes is given; and thresholds sufficient for energy-Casimir stability are obtained. The Hamiltonian formulation also is used to obtain an expression for the collisionless conductivity and it is further used to describe the linear growth and nonlinear saturation of the collisionless tearing mode.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hamiltonian formulation and analysis of a collisionless fluid reconnection model

Tassi¹,

Morrison²,

Waelbroeck³

et al. 2008

Plasma Phys. Control. Fusion

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“…T eq = 1 is assumed for simplicity. At first, we analyse the basic feature of the growing intermittency based on equations (4)- (6). Equations (4)- (6) can be expressed as the following second order differential equation with respect to G: …”

Section: An Extended Predator-prey Modelmentioning

confidence: 99%

“…A theoretical model which primarily describes the intermittency, has been extensively studied in terms of predator-prey approach [5]. A dynamical systems approach which predicts the Dimits shift is also proposed in slab geometry [6].…”

Section: Introductionmentioning

confidence: 99%

A model of GAM intermittency near critical gradient in toroidal plasmas

Miki¹,

Kishimoto

Miyato

et al. 2008

J. Phys.: Conf. Ser.

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Abstract.We have constructed a four-field minimal model that describes the growing intermittency of turbulence associated with the geodesic acoustic mode (GAM) observed in our toroidal Landau-fluid simulations [K Miki et al. 2007 Phys. Rev. Lett. 99, 145003]. The intermittent dynamics are well reproduced by the model for the reference parameters used in the simulation. The model can also reproduce characteristics of turbulent transport associated with the GAM, such as a single burst leading to a full quench of turbulence and also a steady state turbulence mixed with steady zonal flows and GAMs. Investigating the behaviour of the solution trajectories around the fixed points in four-dimensional phase space, we study the comprehensive properties of the model and identify the bifurcation property between Dimits shift and steady state turbulence regimes, which correspond to different eigen-states.

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“…18 Such a reduction process is very useful for obtaining a finite set of dynamical equations from an infinite-dimensional system, while retaining the Hamiltonian properties of the latter. Potential uses for this Hamiltonian truncation procedure include constructing low-dimensional models for describing specific physical mechanisms [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and obtaining semi-discrete schemes for numerical integration of partial differential equations, as an alternative to techniques used or derived, for example, in references [43][44][45][46][47][48][49][50]. Second, as a collateral effect of beatification, all Casimir invariants ii of a system become linear in the dynamical variables.…”

Section: Introductionmentioning

confidence: 99%

Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories

2017

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A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson bracket and replaces it with a fixed dependence on a chosen state in phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.

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Transition to Collisionless Ion-Temperature-Gradient-Driven Plasma Turbulence: A Dynamical Systems Approach

Cited by 20 publications

References 17 publications

Hamiltonian formulation and analysis of a collisionless fluid reconnection model

Hamiltonian formulation and analysis of a collisionless fluid reconnection model

A model of GAM intermittency near critical gradient in toroidal plasmas

Beatification: Flattening the Poisson bracket for two-dimensional fluid and plasma theories

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