Speaker
Description
P. Buratti (1, 2), W. Bin (3), A. Cardinali (2), C. Castaldo (1), F. Napoli (1), M. Guerini Rocco (3, 4) and B. Moshref (5)
(1) ENEA, NUC Department, Via E. Fermi 45, 00044 Frascati, Italy
(2) INAF-IAPS, via Fosso del Cavaliere 100, I-00133 Rome, Italy
(3) ISTP-CNR, Via R. Cozzi 53, 20125 Milan, Italy
(4) Department of Physics, University of Milano-Bicocca, Milan, 20126, Italy
(5) Department of Physics, University La Sapienza of Rome, 00185 Roma, Italy
Interactions between plasma waves and relativistic electrons has received renewed interest in the context of runaway electron control in tokamaks. Scattering and slowing-down upon wave emission or absorption can in fact reduce the maximum electron energy, whereas coulombian collisions are ineffective. Some results from tokamaks will be presented, and a possible astrophysical implication will be pointed out.
Details of wave emissions became accessible due to the availability of digitizers with sampling rates of several GHz, faster than relevant waves frequencies. Both broadband and coherent spectra were observed. Coherent waves of the lower-hybrid type were identified in the Frascati Tokamak Upgrade [1], with electron gyrofrequency to plasma frequency ratio $\Omega_{ce} / \omega_{pe}$ ~ 3, whereas whistler waves were identified in DIII-D plasmas with $\Omega_{ce} / \omega_{pe}$ ~ 1 [2]. Experimental results stimulated stability analyses of plasma waves driven by runaway electrons considering hot plasma Maxwellian background [3]. The former FTU team is presently collecting a wealth of new experimental data at TCV.
Broadband wave spectra were often observed on FTU in conjunction with bursty emission. Clear evidence of rapid pitch-angle scattering during wave emission bursts was found [4]. Observed radio bursts assumed in most cases the shape of limit cycles, with growth time of wave amplitude much shorter than the interleaving quiescent periods. The concurrence of wave emission and pitch-angle scattering strongly indicates that the anomalous Doppler instability is occurring. Anomalous means that an energetic electron increases its perpendicular momentum while emitting a plasma wave; this is possible provided that the energy variation associated to the loss of particle parallel momentum upon emission is sufficient to supply both wave emission and perpendicular motion.
Repetitive bursts can be modeled as follows: the momentum distribution of relativistic electrons becomes more and more beamed during quiescent periods, until the anomalous Doppler instability is triggered by anisotropy of the electron momentum distribution and transfers energy from parallel motion to waves and to perpendicular motion. As such pitch-angle scattering reverts the momentum distribution from beamed to nearly isotropic, the instability drive fades and a new quiescent period starts.
Possible astrophysical implications of this mechanism stem from the fact that synchrotron cooling is weak for relativistic electrons with beamed distribution along an ambient (ordered) magnetic field; electrons can then accumulate large energies, and, if the anomalous Doppler instability occurs, such electrons do release very energetic flares during the rapid pitch-angle scattering phase. Linear stability calculations are relatively simple for electron-ion the tokamak plasma, as the cold plasma approximation can be applied for real part of the dispersion tensor. Such approximation has to be removed when considering relativistic astrophysical plasmas; furthermore a substantial population of positrons should be included in this case.
[1] W. Bin et al, Phys Rev. Lett. 129, 045002 (2022)
[2] D.A. Spong et al, Phys. Rev. Lett. 120, 155002 (2018)
[3] C. Castaldo et al, Nucl. Fusion 64 086003 (2024)
[4] P. Buratti et al, Plasma Phys. Controlled Fusion 63, 095007 (2021)
