  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.
