2 
_T,
(7)
p = p_0 2 _T,
(7)
as long as the correlation length of the field is much smaller than the
size of the system. If the halo has many cells along the line of sight
then p ~ _T <<
1.
The observed polarization will be further reduced by two effects: line of sight depolarization and beam averaging. Line of sight depolarization (Burn 1966) only affects the polarization from a single cell---as the polarization position angles from different cells are random, rotating them relative to each other has no effect. In each cell the depolarization is due to half the total RM of the cell,
RM_cell 
10 (n_e /
2x10^-3 per cm^3) (B / 1
) (r_0 / 10
kpc)
rad / m^2, (8)
where n_e is the thermal electron density. At a wavelength of 20 cm each cell will suffer very little depolarization, even at the centre of the Coma cluster. There is a slight bias against depolarization in that the strongest emission comes from the cells with small B_z which are depolarized the least. Depolarization by averaging within the beam is expected have a similar effect to the smoothing of intensity. In these simple models, polarization at about the same level as the intensity contrast is expected.