Conductive electron heat flow along magnetic field lines

A novel approach that enables the study of parallel transport in magnetized plasmas is presented. The method applies to general magnetic fields with local or nonlocal parallel closures. Temperature flattening in magnetic islands is accurately computed. For a wave number k, the fattening time scales as χ τ ∼ k −α where χ is the parallel diffusivity, and α = 1 (α = 2) for non-local (local) transport. The fractal structure of the devil staircase temperature radial profile in weakly chaotic fields is resolved. In fully chaotic fields, the temperature exhibits self-similar evolution of the form T = (χ t) −γ/2 L (χ t) −γ/2 δψ , where δψ is a radial coordinate. In the local case, f is Gaussian and the scaling is sub-diffusive, γ = 1/2. In the non-local case, f decays algebraically, L(η) ∼ η −3 , and the scaling is diffusive, γ = 1.

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“…[2,14]. In these references, the flux is calculated by integrating the transport kernel along the field lines.…”

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confidence: 99%

“…However, more general closures, like those in Refs. [2,14], are straightforward to implement by first computing the Green's function numerically. It is also interesting to point out that, for non-integer 1 < α < 2, the Green's function in Eq.…”

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confidence: 99%

Local and Nonlocal Parallel Heat Transport in General Magnetic Fields

Del-Castillo-Negrete

Chacòn

2011

Phys. Rev. Lett.

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“…The similar form of this general expression for the parallel heat flow with previous collisionless expressions 12,13 was emphasized in Ref. 1. It was also shown there that Eq.…”

Section: ͑37͒mentioning

confidence: 49%

“…1 This paper presents an important extension of this theory by setting forth a parallel heat flux closure scheme that allows for more general magnetic geometry. This includes the important case of helical magnetic islands growing in axisymmetric toroidal equilibria of arbitrary aspect ratio and shaping.…”

Section: Introductionmentioning

confidence: 99%

Conductive electron heat flow along an inhomogeneous magnetic field

2003

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In this work a general closure for the conductive electron heat flux parallel to an inhomogeneous magnetic field is derived and examined. Free-streaming and collisional effects are present in the drift kinetic equation which is solved using an expansion of eigenfunctions of the bounce-averaged, pitch-angle scattering operator. For bounce times short compared to transit and collision times, the subsequent heat flow closure takes the form of an integral operator acting on electron temperature variations along magnetic field lines. The general closure agrees qualitatively with previous forms for the heat flux in homogeneous magnetic geometry and importantly, predicts a substantial reduction in the heat flow due to the trapping of particles in magnetic wells and the enhanced effect of collisions near the trapped/passing particle boundary.

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“…[1][2][3] This is in contrast to collisional transport theory which writes closures in terms of local gradients of fluid quantities. 4 In general, local forms for the closures are the result of collisions spatially localizing the generalized, integral expressions.…”

Section: Introductionmentioning

confidence: 69%

Nonlocal closures for plasma fluid simulations

et al. 2004

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The application of fluid models in studies of transport and macroscopic stability of magnetized, nearly collisionless plasmas requires closure relations that are inherently nonlocal. Such closures address the fact that particles are capable of carrying information over macroscopic parallel scale lengths. In this work, generalized closures that embody Landau, collisional and particle-trapping physics are derived and discussed. A gyro/bounce-averaged drift kinetic equation is solved via an expansion in eigenfunctions of the pitch-angle scattering operator and the resulting system of algebraic equations is solved by integrating along characteristics. The desired closure moments take the form of integral equations involving perturbations in the flow and temperature along magnetic field lines. Implementation of the closures in massively parallel plasma fluid simulation codes is also discussed. This implementation includes the use of a semi-implicit time advance of the fluid equations to stabilize the dominant closure terms which are introduced explicitly. Application of the nonlocal, parallel heat flow closure, q ʈ , in studies of temperature flattening across helical magnetic islands in toroidal geometry reveal a scaling of temperature versus critical island width for flattening of Tϳw d Ϫ1.5 . This result predicts more robust flattening at small island widths when compared to the diffusive scaling, Tϳw d Ϫ1.7 , which assumes a Braginskii-type parallel heat conductivity. Preliminary application of q ʈ to tokamak disruption simulations shows qualitative agreement of wall heat loads with experimental observations, smooth distribution in toroidal angle, and striation in the poloidal direction along the wall.

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Conductive electron heat flow along magnetic field lines

Cited by 43 publications

References 15 publications

Local and Nonlocal Parallel Heat Transport in General Magnetic Fields

Local and Nonlocal Parallel Heat Transport in General Magnetic Fields

Conductive electron heat flow along an inhomogeneous magnetic field

Nonlocal closures for plasma fluid simulations

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