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Title: Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect

Abstract

To study runaway electron generation in disruptions, we have extended the three-dimensional (two-dimensional in momentum space; one-dimensional in the radial direction) Fokker-Planck code, which describes the evolution of the relativistic momentum distribution function of electrons and the induced toroidal electric field in a self-consistent manner. A particular focus is placed on the hot-tail effect in two-dimensional momentum space. The effect appears if the drop of the background plasma temperature is sufficiently rapid compared with the electron-electron slowing down time for a few times of the pre-quench thermal velocity. It contributes to not only the enhancement of the primary runaway electron generation but also the broadening of the runaway electron distribution in the pitch angle direction. If the thermal energy loss during the major disruption is assumed to be isotropic, there are hot-tail electrons that have sufficiently large perpendicular momentum, and the runaway electron distribution becomes broader in the pitch angle direction. In addition, the pitch angle scattering also yields the broadening. Since the electric field is reduced due to the burst of runaway electron generation, the time required for accelerating electrons to the runaway region becomes longer. The longer acceleration period makes the pitch-angle scattering more effective.

Authors:
;  [1];  [2]
  1. Department of Engineering, Kyoto University, Kyoto 615-8540 (Japan)
  2. National Institutes for Quantum and Radiological Science and Technology, Aomori 039-3212 (Japan)
Publication Date:
OSTI Identifier:
22600118
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DISTRIBUTION; DISTRIBUTION FUNCTIONS; ELECTRIC FIELDS; ELECTRON TEMPERATURE; ENERGY LOSSES; FOKKER-PLANCK EQUATION; INCLINATION; ION TEMPERATURE; ONE-DIMENSIONAL CALCULATIONS; PLASMA; RELATIVISTIC RANGE; RUNAWAY ELECTRONS; SCATTERING; SLOWING-DOWN; TAIL ELECTRONS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Nuga, H., E-mail: nuga@p-grp.nucleng.kyoto-u.ac.jp, Fukuyama, A., and Yagi, M.. Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect. United States: N. p., 2016. Web. doi:10.1063/1.4953606.
Nuga, H., E-mail: nuga@p-grp.nucleng.kyoto-u.ac.jp, Fukuyama, A., & Yagi, M.. Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect. United States. doi:10.1063/1.4953606.
Nuga, H., E-mail: nuga@p-grp.nucleng.kyoto-u.ac.jp, Fukuyama, A., and Yagi, M.. 2016. "Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect". United States. doi:10.1063/1.4953606.
@article{osti_22600118,
title = {Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect},
author = {Nuga, H., E-mail: nuga@p-grp.nucleng.kyoto-u.ac.jp and Fukuyama, A. and Yagi, M.},
abstractNote = {To study runaway electron generation in disruptions, we have extended the three-dimensional (two-dimensional in momentum space; one-dimensional in the radial direction) Fokker-Planck code, which describes the evolution of the relativistic momentum distribution function of electrons and the induced toroidal electric field in a self-consistent manner. A particular focus is placed on the hot-tail effect in two-dimensional momentum space. The effect appears if the drop of the background plasma temperature is sufficiently rapid compared with the electron-electron slowing down time for a few times of the pre-quench thermal velocity. It contributes to not only the enhancement of the primary runaway electron generation but also the broadening of the runaway electron distribution in the pitch angle direction. If the thermal energy loss during the major disruption is assumed to be isotropic, there are hot-tail electrons that have sufficiently large perpendicular momentum, and the runaway electron distribution becomes broader in the pitch angle direction. In addition, the pitch angle scattering also yields the broadening. Since the electric field is reduced due to the burst of runaway electron generation, the time required for accelerating electrons to the runaway region becomes longer. The longer acceleration period makes the pitch-angle scattering more effective.},
doi = {10.1063/1.4953606},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = 2016,
month = 6
}
  • Hot tail runaway electron generation is caused by incomplete thermalization of the electron velocity distribution during rapid plasma cooling. It is an important runaway electron mechanism in tokamak disruptions if the thermal quench phase is sufficiently fast. Analytical estimates of the density of produced runaway electrons are derived for cases of exponential-like temperature decay with a cooling rate lower than the collision frequency. Numerical simulations, aided by the analytical results, are used to compare the strength of the hot tail runaway generation with the Dreicer mechanism for different disruption parameters (cooling rate, post-thermal quench temperature, and electron density) assuming thatmore » no losses of runaway electrons occur. It is seen that the hot tail runaway production is going to be the dominant of these two primary runaway mechanisms in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)].« less
  • The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay timemore » in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.« less
  • To take into account highly non-Maxwellian tail distributions expected in fusion and/or auxiliary heated plasmas, a self-consistent scheme of separating the non-Maxwellian tail particles from the Maxwellian bulk in the quasilinear Fokker--Planck equation is proposed. The resulting equation for tail particles is the same as that for a minority species, but with a different boundary condition at low energies. Transport fluxes of energetic particles can then be calculated as a minority species that can be easily added onto existing transport theory for the bulk species. Expressions for neoclassical fluxes of tail particles in the banana regime are obtained in termsmore » of the solution of a steady-state minority tail distribution which takes the place of the Maxwell distribution of a bulk species. The existence of a solution is demonstrated, and simple model analytic solutions are given.« less
  • A simple zero dimensional model for a tokamak disruption is developed to evaluate the avalanche multiplication of a runaway primary seed during the current quench phase of a fast disruptive event. Analytical expressions for the plateau runaway current, the energy of the runaway beam, and the runaway energy distribution function are obtained allowing the identification of the parameters dominating the formation of the runaway current during disruptions. The effect of the electromagnetic coupling to the vessel and the penetration of the external magnetic energy during the disruption current quench as well as of the collisional dissipation of the runaway currentmore » at high densities are investigated. Current profile shape effects during the formation of the runaway beam are also addressed by means of an upgraded one-dimensional model.« less