Spatiotemporal Evolution of Runaway Electron Momentum Distributions in Tokamaks

Abstract

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

Physics of runaway electrons in tokamaks

“…Another interesting observation in DIII-D is that the measured growth rate depends on the energy range being measured. The growth rate was measured at different energies in DIII-D and was found to be closer to theory at higher energies, which is a sign of enhanced RE dissipation at low energies in QRE discharges [76]. This suggests that, at least in these experiments, neither synchrotron damping, nor drift orbit losses are responsible for anomalous RE dissipation in, but rather a factor acting on lower energy REs.…”

Dynamics of positrons during relativistic electron runaway

“…2015; Paz-Soldan et al. 2017) and create positrons in collisions with electrons and ions. The created positrons are also accelerated by the electric field, in the opposite direction with respect to the electrons, and if the electric field is sufficiently strong, a substantial fraction of them will run away (Fülöp & Papp 2012).…”

First Direct Observation of Runaway-Electron-Driven Whistler Waves in Tokamaks

“…Experiment and diagnostics -The whistler experiments were performed on the DIII-D tokamak device in very low density Ohmic plasmas [19,20]. DIII-D is a D-shaped cross section tokamak with major radius R 0 = 1.7m, minor radius <a> = 0.6m.…”