Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons

Pokol, Gergö; Kómár, Anna; Budai, Ádám; Stahl, Adam; Fülöp, Tünde

doi:10.1063/1.4895513

Cited by 14 publications

(20 citation statements)

References 18 publications

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“…For particles with purely parallel momentum, this condition determines the critical momentum p c ≡ (E −1) −1/2 above which electrons are continuously accelerated. For particles with very large momentum p ≫ 1, the condition (24) provides an asymptotic value ξ c = E −1 , such that K p > 0 for particles with ξ > ξ c . In this paper, the runaway region is defined as the region where the momentum force balance is positive, i.e.…”

Section: Evolution Of the Electron Distribution Functionmentioning

confidence: 99%

Numerical characterization of bump formation in the runaway electron tail

Decker

Hirvijoki

Embréus

et al. 2016

Plasma Phys. Control. Fusion

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Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham-Lorentz-Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting the electron acceleration. The effect of the ALD-force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker-Planck codes LUKE [Decker & Peysson, Report EUR-CEA-FC-1736, Euratom-CEA, (2004)] and CODE [Landreman et al, Comp. Phys. Comm. 185, 847 (2014)]. Under the action of the ALD force, we find that a bump is formed in the tail of the electron distribution function if the electric field is sufficiently large. We also observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could in turn pump energy from runaway electrons and alter their confinement.

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Section: Evolution Of the Electron Distribution Functionmentioning

confidence: 99%

Numerical characterization of bump formation in the runaway electron tail

Decker

Hirvijoki

Embréus

et al. 2016

Plasma Phys. Control. Fusion

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“…The large induced electric field will usually decay rapidly on a timescale of a few ms in response to the formation of a narrow runaway electron (RE) beam. With runaway electrons reaching energies of order tens of MeV, they can carry a significant fraction of the pre-disruption plasma current and can drive high frequency electromagnetic instabilities through resonant interactions [27][28][29][30]. Recently, low-frequency magnetic fluctuations in the range f ≈ 60 − 260 kHz, have been observed in the TEXTOR tokamak during induced-disruption studies with argon massive gas injection (MGI).…”

Section: B Tokamak Disruptionsmentioning

confidence: 99%

Numerical calculation of ion runaway distributions

et al. 2015

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“…In a spatially homogeneous plasma, the main processes influencing energetic-electron dynamics are: the presence of an accelerating electric field; magnetization (causing directed motion); Coulomb collisions; dynamic changes in plasma parameters such as the temperature; radiative losses (associated with synchrotron and fast-electron bremsstrahlung emission); and wave-particle interaction. The combined influence of these processes has been shown to lead to phenomena such as bump-on-tail formation [14,15] and local isotropization [16,17] in the high-energy tail of strongly anisotropic electron populations. Since analytic treatment is possible only in special cases, the evolution of the electron distribution function f must in general be studied using kinetic simulations.…”

Section: Introductionmentioning

confidence: 99%

NORSE: A solver for the relativistic non-linear Fokker–Planck equation for electrons in a homogeneous plasma

Stahl¹,

Landreman²,

Embréus³

et al. 2017

Computer Physics Communications

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Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentumspace dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted. Solves the Fokker-Planck equation for electrons in 2D momentum space in a homogeneous plasma (allowing for magnetization), using a relativistic non-linear electron-electron collision operator. Electric-field acceleration, synchrotronradiation-reaction losses, as well as heat and particle sources are included. Scenarios with time-dependent plasma parameters can be studied. Keywords Solution method:The kinetic equation is represented on a non-uniform 2D finite-difference grid and is evolved using a linearly implicit time-advancement scheme. A mixed finite-difference-Legendre-mode representation is used to obtain the relativistic potentials (analogous to the non-relativistic Rosenbluth potentials) from the distribution.

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Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons

Cited by 14 publications

References 18 publications

Numerical characterization of bump formation in the runaway electron tail

Numerical characterization of bump formation in the runaway electron tail

Numerical calculation of ion runaway distributions

NORSE: A solver for the relativistic non-linear Fokker–Planck equation for electrons in a homogeneous plasma

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