**AAS 197, January 2001**

*Session 89. Large Scale Structure and Galaxy Clusters*

Oral, Wednesday, January 10, 2001, 10:30am-12:00noon, Town and Country
[Previous] |
[Session 89] |
[Next]

## [89.06] Thermal conduction in the stochastic magnetic fields in clusters of galaxies

*L.M. Malyshkin (Princeton University), R.M. Kulsrud (Princeton University, PPPL)*

We consider two effects that reduce electron thermal
conduction in the stochastic magnetic fields in clusters of
galaxies. First, the parallel conduction along magnetic
field lines may be reduced because the heat conducting
electrons become trapped and detrapped between regions of
strong magnetic field (magnetic mirrors). This problem
reduces to a simple but realistic model for parallel
diffusion of mono-energetic electrons based on the fact that
when there is a reduction of diffusion, it is controlled by
a subset of the mirrors, the principle mirrors. The
reduction of parallel diffusion can be considered as
equivalent to an enhancement of the pitch angle scattering
rate. Therefore, in deriving the full perturbed
electron-electron and electron-proton collision integral, we
modify the pitch angle scattering term, and then find the
effective parallel thermal conductivity as a function of the
ratio of the magnetic field decorrelation length l_{0} to
the electron mean free path at the electron thermal speed
V_{T}=\sqrt{2kT/m_{e}}.

The second effect is that conducting electrons have to
travel along tangled magnetic field lines, and as a result,
they have to go larger distances between hot and cold
regions of space. This effect leads to further reduction of
electron thermal conduction, which is given by the product
of (l_{0}/X_{0})^{2} and a function of a single parameter
\beta=2(X_{0}/l_{0})\,\langle B\rangle\big/\langle\delta
B\rangle. Here, X_{0} is the cluster size (or the
temperature gradient scale), \langle B\rangle is the mean
magnetic field component (assumed to be homogeneous), and
\langle\delta B\rangle is the averaged absolute value of
the random field component. We discuss the application of
our final results to clusters of galaxies.

Leonid Malyshkin would like to thank the Department of
Astrophysical Sciences at Princeton University and Professor
Bruce Draine for financial support.

[Previous] |
[Session 89] |
[Next]