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Register a new userSuppression of electron thermal conduction by whistler turbulence in a sustained thermal gradient
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Added by
Gareth Roberg-Clark
Publication date
2017
fields
Physics
and research's language is
English
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The dynamics of weakly magnetized collisionless plasmas in the presence of an imposed temperature gradient along an ambient magnetic field is explored with particle-in-cell simulations and modeling. Two thermal reservoirs at different temperatures drive an electron heat flux that destabilizes off-angle whistler-type modes. The whistlers grow to large amplitude, $delta B / B_{0} simeq 1$, and resonantly scatter the electrons, significantly reducing the heat flux. A surprise is that the resulting steady state heat flux is largely independent of the thermal gradient. The rate of thermal conduction is instead controlled by the finite propagation speed of the whistlers, which act as mobile scattering centers that convect the thermal energy of the hot reservoir. The results are relevant to thermal transport in high $beta$ astrophysical plasmas such as hot accretion flows and the intracluster medium of galaxy clusters.
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Understanding the thermodynamic state of the hot intracluster medium (ICM) in a galaxy cluster requires a knowledge of the plasma transport processes, especially thermal conduction. The basic physics of thermal conduction in plasmas with ICM-like conditions has yet to be elucidated, however. We use particle-in-cell simulations and analytic models to explore the dynamics of an ICM-like plasma (with small gyroradius, large mean-free-path, and strongly sub-dominant magnetic pressure) driven by the diffusive heat flux associated with thermal conduction. Lin- ear theory reveals that whistler waves are driven unstable electron heat flux, even when the heat flux is weak. The resonant interaction of electrons with these waves then plays a critical role in scattering electrons and suppressing the heat flux. In a 1D model where only whistler modes that are parallel to the magnetic field are captured, the only resonant electrons are moving in the opposite direction to the heat flux and the electron heat flux suppression is small. In 2D or more, oblique whistler modes also resonate with electrons moving in the direction of the heat flux. The overlap of resonances leads to effective symmetrization of the electron distribution function and a strong suppression of heat flux. The results suggest that thermal conduction in the ICM might be strongly suppressed, possibly to negligible levels.
Transport equations for electron thermal energy in the high $beta_e$ 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 $V_wsim{v}_{te}/beta_ell{v}_{te}$ dominate the turbulent spectrum, with $v_{te}$ the electron thermal speed and $beta_egg1$ the ratio of electron thermal to magnetic pressure. We find: (1) temperature-gradient-driven whistlers dominate classical scattering when $L_c>L/beta_e$, 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 $V_wnT_esim{T}_e^{1/2}$, (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.
Slow magnetoacoustic waves were first detected in hot ($>$6 MK) flare loops by the SOHO/SUMER spectrometer as Doppler shift oscillations in Fe XIX and Fe XXI lines. Recently, such longitudinal waves have been found by SDO/AIA in the 94 and 131 AA channels. Wang et al. (2015) reported the first AIA event revealing signatures in agreement with a fundamental standing slow-mode wave, and found quantitative evidence for thermal conduction suppression from the temperature and density perturbations in the hot loop plasma of $gtrsim$ 9 MK. The present study extends the work of Wang et al. (2015) by using an alternative approach. We determine the polytropic index directly based on the polytropic assumption instead of invoking the linear approximation. The same results are obtained as in the linear approximation, indicating that the nonlinearity effect is negligible. We find that the flare loop cools slower (by a factor of 2-4) than expected from the classical Spitzer conductive cooling, approximately consistent with the result of conduction suppression obtained from the wave analysis. The modified Spitzer cooling timescales based on the nonlocal conduction approximation are consistent with the observed, suggesting that nonlocal conduction may account for the observed conduction suppression in this event. In addition, the conduction suppression mechanism predicts that larger flares may tend to be hotter than expected by the EM-$T$ relation derived by Shibata & Yokoyama (2002)
Magnetic reconnection in solar flares can efficiently generate non-thermal electron beams. The accelerated electrons can, in turn, cause radio waves through kinetic instabilities as they propagate through the ambient plasma. We aim at investigating the wave emission caused by fast electron beams (FEBs) with characteristic non-thermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: bump-on-tail EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs close to the diffusion region. For this sake we utilized 2.5D fully kinetic Particle-In-Cell (PIC) code simulations in this study. We found that: (1) the bump-on-tail EVDFs are unstable to cause electrostatic Langmuir waves via bump-on-tail instabilities and then multiple harmonic transverse waves from the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs, on the other hand, can cause multi-harmonic electromagnetic electron cyclotron waves through electron cyclotron maser instabilities in diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters which control reconnection in solar flares by means of radio waves observations.
Galaxy clusters host a large reservoir of diffuse plasma with radially-varying temperature profiles. The efficiency of thermal conduction in the intracluster medium (ICM) is complicated by the existence of turbulence and magnetic fields, and has received a lot of attention in the literature. Previous studies suggest that the magnetothermal instability developed in outer regions of galaxy clusters would drive magnetic field lines preferentially radial, resulting in efficient conduction along the radial direction. Using a series of spherically-symmetric simulations, here we investigate the impact of thermal conduction on the observed temperature distributions in outer regions of three massive clusters, and find that thermal conduction substantially modifies the ICM temperature profile. Within 3 Gyr, the gas temperature at a representative radius of $0.3r_{500}$ typically decreases by ~10 - 20% and the average temperature slope between $0.3r_{500}$ and $r_{500}$ drops by ~ 30 - 40%, indicating that the observed ICM would not stay in a long-term equilibrium state in the presence of thermal conduction. However, X-ray observations show that the outer regions of massive clusters have remarkably similar radially-declining temperature profiles, suggesting that they should be quite stable. Our study thus suggests that the effective conductivity along the radial direction must be suppressed below the Spitzer value by a factor of 10 or more, unless additional heating sources offset conductive cooling and maintain the observed temperature distributions. Our study provides a smoking-gun evidence for the suppression of parallel conduction along magnetic field lines in low-collisionality plasmas by kinetic mirror or whistler instabilities.
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