Apparatus for the study of creep in polymers

Braginskii, A.I.; Zelenev, Yu. V.

doi:10.1016/0032-3950(75)90240-3

Cited by 3 publications

(18 citation statements)

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“…We note that the Coloumb logarithm ln Λ ≈ 17 [30]. After Braginskii [31], we define the ion self-collision frequency ν ii by…”

Section: The Gyrokinetic Equation and Quasineutralitymentioning

confidence: 99%

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Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Hardman,

Parra,

Chong

et al. 2021

Preprint

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Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Hence, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes, due to the small electron-to-ion mass ratio and the large electron transit frequency. However, in gyrokinetic simulations of ion-gyroradius-scale modes, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations with narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating interesting parallels to neoclassical transport theory. The predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insights from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

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“…We note that the Coloumb logarithm ln Λ ≈ 17 [30]. After Braginskii [31], we define the ion self-collision frequency ν ii by…”

Section: The Gyrokinetic Equation and Quasineutralitymentioning

confidence: 99%

“…is the Lorentz collision operator resulting from electron-ion collisions, with the electronion collision frequency ν ei defined following Braginskii [31], i.e.,…”

Section: The Gyrokinetic Equation and Quasineutralitymentioning

confidence: 99%

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Hardman,

Parra,

Chong

et al. 2021

Preprint

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Section: Pacs Numbersmentioning

confidence: 99%

“…In diverse fields of plasma physics including astrophysics, inertial confinement fusion, and magnetohydrodynamics, classical thermal transport [1,2] provides the foundation for calculating heat flux [3][4][5][6][7]. The classical theories of thermal transport by Spitzer-Härm (SH) [1] and Braginskii [2] specify the heat flux by a local expression, in terms of the thermal conductivity κ and the electron temperature gradient (e.g., q SH = −κ∇T e ). This theory breaks down in the presence of large temperature gradients [8][9][10][11], turbulence [12], or return current instabilities [13][14][15][16]: classical theory does not include nonlocal effects where energetic electrons travel distances comparable with the temperature scale length before colliding.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…Local thermal transport theories [1,2] follow from a perturbative solution of a kinetic equation in terms of the collision parameter λ ei /L T 1, where λ ei is the electron-ion (ei) mean free path and L T = |∇ ln(T e )| −1 is the scale length of the temperature gradient. Nonlocal theories overcome limitations of classical theory by accounting for the range of electron-ion mean free paths associated with different electron velocities.…”

Section: Pacs Numbersmentioning

confidence: 99%

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Observation of Nonlocal Heat Flux Using Thomson Scattering

et al. 2018

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Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Hardman

Parra

Chong

et al. 2022

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Due to the small electron-to-ion mass ratio and the large electron transit frequency, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes. However, in gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal magnetic fields, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations with narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, in axisymmetric toroidal magnetic geometry, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating parallels in structure and physical processes to neoclassical transport theory. By examining initial-value simulations of fastest-growing eigenmodes, the predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insights from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

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Apparatus for the study of creep in polymers

Cited by 3 publications

References 0 publications

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Observation of Nonlocal Heat Flux Using Thomson Scattering

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

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