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Abstract Transport equations for electron thermal energy in the high- β e intracluster medium (ICM) are developed that include scattering from both classical collisions and self-generated whistler waves. The calculation employs an expansion of the kinetic electron equation along the ambient magnetic field in the limit of strong scattering and assumes whistler waves with low phase speeds V w ∼ v te / β e ≪ v te dominate the turbulent spectrum, with v te the electron thermal speed and β e ≫ 1 the ratio of electron thermal to magnetic pressure. We find: (1) temperature-gradient-driven whistlers dominate classical scattering when L c > L / β e , with L c the classical electron mean free path and L the electron temperature scale length, and (2) in the whistler-dominated regime the electron thermal flux is controlled by both advection at V w and a comparable diffusive term. The findings suggest whistlers limit electron heat flux over large regions of the ICM, including locations unstable to isobaric condensation. Consequences include: (1) the Field length decreases, extending the domain of thermal instability to smaller length scales, (2) the heat flux temperature dependence changes from T e 7 / 2 / L to V w nT e ∼ T e 1 / 2 , (3) the magneto-thermal- and heat-flux-driven buoyancy instabilities are impaired or completely inhibited, and (4) sound waves in the ICM propagate greater distances, as inferred from observations. This description of thermal transport can be used in macroscale ICM models.
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Wave Generation and Energetic Electron Scattering in Solar Flares
Abstract We conduct two-dimensional particle-in-cell simulations to investigate the scattering of electron heat flux by self-generated oblique electromagnetic waves. The heat flux is modeled as a bi-kappa distribution with aT∥>T⊥temperature anisotropy maintained by continuous injection at the boundaries. The anisotropic distribution excites oblique whistler waves and filamentary-like Weibel instabilities. Electron velocity distributions taken after the system has reached a steady state show that these instabilities inhibit the heat flux and drive the total distributions toward isotropy. Electron trajectories in velocity space show a circular-like diffusion along constant energy surfaces in the wave frame. The key parameter controlling the scattering rate is the average speed, or drift speedvd, of the heat flux compared with the electron Alfvén speedvAe, with higher drift speeds producing stronger fluctuations and a more significant reduction of the heat flux. Reducing the density of the electrons carrying the heat flux by 50% does not significantly affect the scattering rate. A scaling law for the electron scattering rate versusvd/vAeis deduced from the simulations. The implications of these results for understanding energetic electron transport during energy release in solar flares are discussed.
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- Award ID(s):
- 2109083
- PAR ID:
- 10443869
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 954
- Issue:
- 1
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 21
- Size(s):
- Article No. 21
- Sponsoring Org:
- National Science Foundation
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