Effect of bremsstrahlung radiation emission on fast electrons in plasmas

Abstract

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...

Effect of Partially Screened Nuclei on Fast-Electron Dynamics

“…During the simulation of the decay phase, the weak electric field E = 2E c was used, which is well below the effective critical field if reduced screening effects are taken into account. To isolate the effect of reduced screening, avalanche runaway generation (which is unimportant on the simulation timescale [31]) was neglected, and bremsstrahlung (which can sometimes be an important energy-loss mechanism [35,36]) does not affect the dynamics significantly at the energies considered.…”

Analysis of Avalanche Runaway Generation after Disruptions with Low-<i>Z </i>and Noble Gas Species

“…1-2 of Ref. [48], showing that the maximum energy limit is less sharp in the Boltzmann case and the electron distribution function exhibits a broader spectrum in both energy and angular directions. Figure 3 of Ref.…”

“…Figure 3 of Ref. [48] has shown the maximum reachable energy is about twice the energy obtained using the mean force operator.…”

“…Note that in out TQ model, the energy exchange between hot and cold (Maxwellian) electrons has already been retained by Eqs. (48) and (49). In Fig.…”

“…(29) has been used in both test-particle [45] and Fokker-Planck simulations [47], the treatment of bremsstrahlung as a continuous slowing down of the electrons loses its discrete picture when the emitted photons can have energies of the same order as the incident electrons. Recently, Embréus, et al [48] have analyzed the bremsstrahlung emission of runaway electrons as binary interactions using the Boltzmann-type kinetic operator. Although such a kinetic treatment is beyond the scope of this work, the comparison of the Boltzmann and mean force operators has been illustrated in Figs.…”