  The MHD stabilization of ``rigid'' flute and ballooning modes with azimuthal
number $m = 1$ in an axisymmetric mirror trap by means of a perfectly
conducting lateral wall is studied both in the presence and in the absence of
the end MHD anchors. Numerical calculations were carried out for an anisotropic
plasma created by injection of a beam of neutral atoms into the minimum of the
magnetic field at the right angle to the trap axis. The stabilizing effect of
the conducting shell in the form of a straight cylinder is compared with a
proportional chamber, which, on an enlarged scale, repeats the shape of the
plasma column.
  It is confirmed that for effective wall stabilization of the rigid modes, the
plasma beta ($\beta$, the ratio of the plasma pressure to the magnetic field
pressure) must exceed some critical value $\beta_{\text{crit}}$. When
conducting lateral wall is combined with conducting end plates imitating MHD
end anchors, there are two critical beta values and, respectively, two
stability zones $\beta<\beta_{\text{ crit}1}$ and $\beta > \beta_{\text
{crit}2}$ that can merge, making the entire range of allowable beta values
$0<\beta<1$ stable.
  The dependence of the critical betas on the plasma anisotropy, mirror ratio,
and the width of the vacuum gap between the plasma and the lateral wall is
examined. In contrast to the earlier works of other authors focused on to the
stepwise plasma model, the stability margins are calculated for a number of
diffuse radial pressure profiles with different peakedness and several axial
magnetic field profiles.
