The **Ã**(**k**) are chosen according to the prescription

*P( A_i)* = [1 / (2) (

where *A*_i represents either the real or imaginary part of a
component of **Ã**. It is convenient to change to polar
coordinates and look at the amplitude and phase of *A*,

*P*(*A*,) d*A* d =
[*A* / ^2(*k*)]
exp[-*A*^2 / 2^2(*k*)]
d*A* {d / 2}. (10)

Therefore is uniformly
distributed between 0 and 2 and *A* is
drawn from a Rayleigh distribution. A Gaussian power spectrum was used,

^2(*k*) = *k*^2 exp(-*k*^2/*k*_0^2). (11)

This is equivalent to a Gaussian longitudinal magnetic field
autocorrelation function *f* =
exp(-*r*^2/2*r*_0^2), which defines the field scale
length *r*_0. With this definition the RM autocorrelation
function varies as 1-*r*^2/*r*_0^2 near the origin. The
scale *k*_0 is adjusted to vary the field correlation length
relative to that of the grid. Because the grid is only of finite size
only a small range of scale sizes can be investigated while keeping a
reasonable number of grid points per cell and a reasonable number of
cells in the box. The results were found to be similar for a range of
power spectra, although none of the power spectra had power on a large
range of scales.

I have smoothed the maps with a Gaussian observing beam of FWHM
*w*. A simple analytic approximation to the reduction in
contrast is

_S = _0/(1+*w*^2/*r*_0^2),
(12)

where *r_0* is the field scale length, _0 the map's
intrinsic contrast and _S the observed
contrast after smoothing. For the observations of Kim et al. (1990)
analysed below, *w* = 1 arcmin 40 kpc.

\centerline{\hbox{\psfig{figure=/hemlock/tribble/papers/halo/fig1.ps}}}

**Fig 1.** A simulation of the Coma radio halo at 1 arcmin=40 kpc
resolution, for a magnetic field scale length of 40 kpc. The scale is
in arcmin, the solid contours are the higher values and the dashed
contours the lower values.

I present models that have the same overall profile as the Coma radio
halo, approximated as a circular Gaussian of FWHM 16 arcmin (Kim et al.
1990), and smoothed to 1 arcmin resolution, for a variety of field
scale sizes. These models assume a spectral index *n=1* which is
a compromise between the slightly flatter spectral index of
*n*0.7 at the
centre of the halo and the value of *n*1.3 for the
halo as a whole (Kim et al. 1987). This approximation isn't a serious
concern as Section 2 shows that the variation
of contrast with spectral index is reasonably small over the range of
interest. Examples are shown in Figs. 1, 2 and 3. These maps are
constructed by periodically extending a half size emission map, shaping
to the desired profile and smoothing to 1 arcmin resolution. The
emission contrast is then corrected from a rectangular to a Gaussian
emission distribution along the line of sight.

\centerline{\hbox{\psfig{figure=/hemlock/tribble/papers/halo/fig2.ps}}}

**Fig 2.** A simulation of the Coma radio halo at 1 arcmin=40 kpc
resolution, for a magnetic field scale length of 25 kpc.

- On to section 4