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The stabilization of ``rigid'' flute and ballooning modes $m = 1$ in anaxisymmetric mirror trap with the help of an ideally conducting lateral both inthe presence and in the absence of end MHD anchors is studied. The calculationswere performed for an anisotropic plasma in a model that simulates the pressuredistribution during the injection of beams of fast neutral atoms into themagnetic field minimum at a right angle to the trap axis. It was assumed thatthe lateral wall has the shape of a cylinder with a variable radius, so that onan enlarged scale it repeats the shape of the plasma column.  It has been found that for the effective stabilization of the listed modes byan ideally conducting lateral wall, the parameter beta ($\beta$, the ratio ofthe plasma pressure to the magnetic field pressure) must exceed some criticalvalue $\beta_{\text{crit}}$. When combined with a conducting lateral wall andconducting end plates imitating MHD end stabilizers, there are two criticalbeta values and two stability zones $0<\beta<\beta_{\text{ crit}1}$ and$\beta_{\text {crit}2}<\beta<1$ that can merge, making the entire range ofallowable beta values $0<\beta<1$ stable.  The dependence of the critical betas on the degree of plasma anisotropy, themirror ratio, and the width of the vacuum gap between the plasma and thelateral wall is studied. In contrast to the works of other authors devoted tothe plasma model with a sharp boundary, we calculated the boundaries of thestability zone for a number of diffuse radial pressure profiles and severalaxial magnetic field profiles.

Stabilization of the $m=1$ mode in a long-thin mirror trap with high-beta anisotropic plasmas