Radiation reaction induced non-monotonic features in runaway electron distributions

Hirvijoki, Eero; Pusztai, István; Decker, J.; Embréus, Ola; Stahl, Adam; Fülöp, Tünde

doi:10.1017/s0022377815000513

Cited by 25 publications

(46 citation statements)

References 21 publications

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“…Both radiative energy loss channels can therefore be significant at densities characteristic of disruptions and are included in this paper. The synchrotron radiation reaction force is given by [28,29]…”

Section: Radiation Lossesmentioning

confidence: 99%

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

Hesslow

Embréus

Wilkie

et al. 2018

Plasma Phys. Control. Fusion

108

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We derive a formula for the effective critical electric field for runaway generation and decay that accounts for the presence of partially ionized impurities in combination with synchrotron and bremsstrahlung radiation losses. We show that the effective critical field is drastically larger than the classical Connor-Hastie field, and even exceeds the value obtained by replacing the free electron density by the total electron density (including both free and bound electrons). Using a kinetic equation solver with an inductive electric field, we show that the runaway current decay after an impurity injection is expected to be linear in time and proportional to the effective critical electric field in highly inductive tokamak devices. This is relevant for the efficacy of mitigation strategies for runaway electrons since it reduces the required amount of injected impurities to achieve a certain current decay rate.

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Section: Radiation Lossesmentioning

confidence: 99%

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

Hesslow

Embréus

Wilkie

et al. 2018

Plasma Phys. Control. Fusion

108

View full text Add to dashboard Cite

show abstract

“…Further work highlighted the important role of synchrotron damping in elevating the threshold electric field above E C [7,8], and several experiments have since yielded evidence of the elevated threshold [9][10][11][12]. These observations motivated the development of a rigorous analytical theory [13] and computational tools [14][15][16][17][18][19] that clarified the importance of the effects of pitch-angle scattering and synchrotron damping. Alongside quantifying the enhancement of the threshold field, these works predict phase-space circulation around an attractor resulting in a pileup of REs at specific energies potentially resulting in nonmonotonic features in the RE distribution function (f e ).…”

mentioning

confidence: 99%

Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks

et al. 2017

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Novel spatial, temporal, and energetically resolved measurements of bremsstrahlung hard-x-ray (HXR) emission from runaway electron (RE) populations in tokamaks reveal nonmonotonic RE distribution functions whose properties depend on the interplay of electric field acceleration with collisional and synchrotron damping. Measurements are consistent with theoretical predictions of momentum-space attractors that accumulate runaway electrons. RE distribution functions are measured to shift to a higher energy when the synchrotron force is reduced by decreasing the toroidal magnetic field strength. Increasing the collisional damping by increasing the electron density (at a fixed magnetic and electric field) reduces the energy of the nonmonotonic feature and reduces the HXR growth rate at all energies. Higher-energy HXR growth rates extrapolate to zero at the expected threshold electric field for RE sustainment, while low-energy REs are anomalously lost. The compilation of HXR emission from different sight lines into the plasma yields energy and pitch-angle-resolved RE distributions and demonstrates increasing pitch-angle and radial gradients with energy. DOI: 10.1103/PhysRevLett.118.255002 Introduction.-Reaching mega-ampere currents and mega-electron volt (MeV) energies during fast shutdown events, runaway electrons (REs) pose perhaps the greatest operational risk to tokamak fusion reactors such as ITER [1][2][3][4]. Because of the severe potential for damage to the reactor walls, opportunities for empirical tuning of RE control actuators will be limited. Instead, a first-principles predictive understanding is needed, and present-day experiments fill a crucial need in validating theoretical predictions of RE dissipation.Classical theories for relativistic RE generation in tokamaks based on the effects of Coulomb collisions (small angle [5] and secondary avalanche [6]) determine the critical electric field (E C ) for the growth of RE populations. Further work highlighted the important role of synchrotron damping in elevating the threshold electric field above E C [7,8], and several experiments have since yielded evidence of the elevated threshold [9][10][11][12]. These observations motivated the development of a rigorous analytical theory [13] and computational tools [14][15][16][17][18][19] that clarified the importance of the effects of pitch-angle scattering and synchrotron damping. Alongside quantifying the enhancement of the threshold field, these works predict phase-space circulation around an attractor resulting in a pileup of REs at specific energies potentially resulting in nonmonotonic features in the RE distribution function (f e ). While important to the RE dissipation rate and thus the prospects for control, neither

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“…Inclusion of synchrotron radiation losses associated with the gyromotion of electrons in a straight magnetic field has been shown to be an important energy-loss mechanism [17][18][19][20][21]. Figure 1(b) shows that, in conjunction with bremsstrahlung losses, synchrotron losses (modeled as in [17]) shift the distribution towards lower energies but does not change its qualitative features. The difference between the Boltzmann and mean-force models is reduced in such cases, as the extent of the distribution when full bremsstrahlung effects are included is reduced by the synchrotron effect.…”

Section: Numerical Resultsmentioning

confidence: 98%

“…The difference between the Boltzmann and mean-force models is reduced in such cases, as the extent of the distribution when full bremsstrahlung effects are included is reduced by the synchrotron effect. When bremsstrahlung losses are ignored, and synchrotron emission alone is responsible for the energy loss by radiation, a non-monotonic runaway tail can also form (solutions to this problem have been characterized in [17,20]). However, for the present values of density, magnetic and electric fields this occurs at the significantly higher momentum [6,20] .…”

Section: Numerical Resultsmentioning

confidence: 99%

Effect of bremsstrahlung radiation emission on fast electrons in plasmas

2016

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Bremsstrahlung radiation emission is an important energy loss mechanism for energetic electrons in plasmas. In this paper we investigate the effect of spontaneous bremsstrahlung emission on the momentum−space structure of the electron distribution, fully accounting for the emission of finite −energy photons by modeling the bremsstrahlung interactions with a Boltzmann collision operator. We find that electrons accelerated by electric fields can reach significantly higher energies than predicted by the commonly used radiative stopping−power model. Furthermore, we show that the emission of soft photons can contribute significantly to the dynamics of electrons with an anisotropic distribution by causing pitch−angle scattering at a rate that increases with energy.Energetic electrons are ubiquitous in plasmas, and bremsstrahlung radiation is one of their most important energy loss mechanisms [1,2]. At sufficiently high electron energy, around a few hundred megaelectronvolts in hydrogen plasmas, the energy loss associated with the emission of bremsstrahlung radiation dominates the energy loss by collisions. Bremsstrahlung emission can also strongly affect electrons at lower energies, particularly in plasmas containing highly charged ion species.An important electron acceleration process, producing energetic electrons in both space and laboratory plasmas, is the runaway mechanism [3]. In the presence of an electric field which exceeds the minimum to overcome collisional friction [4], a fraction of the charged particles can detach from the bulk population and be accelerated to high energies, where radiative losses become important. Previous studies of laboratory plasmas [5, 6] and lightning discharges [7] have shown that the energy carried away by bremsstrahlung radiation is important in limiting the energy of runaway electrons. The effect of bremsstrahlung radiation loss on energeticelectron transport has also been considered in astrophysical plasmas, for example in the context of solar flares [8]. However, only the average bremsstrahlung friction force on test particles has been considered in these studies. In this paper, we present the first quantitative kinetic study of how bremsstrahlung emission affects the runaway-electron distribution function.Starting from the Boltzmann electron transport equation, we derive a collision operator representing bremsstrahlung radiation reaction, fully accounting for the finite energies and emission angles of the emitted photons. We implement the operator in a continuum kinetic-equation solver [9], and use it to study the effect of bremsstrahlung on the distribution of electrons in 2D momentum space. We find significant differences in the distribution function when bremsstrahlung losses are modeled with a Boltzmann equation (referred to as the 'Boltzmann' or 'full' bremsstrahlung model), compared to the model where only the average friction force is accounted for (the 'mean-force' model). In the former model, the maximum energy reached by the energetic electrons is significantly high...

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Radiation reaction induced non-monotonic features in runaway electron distributions

Cited by 25 publications

References 21 publications

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks

Effect of bremsstrahlung radiation emission on fast electrons in plasmas

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