The ideal rectangular axial structure of the eigenfunction of the curvature driven trapped particle mode, localized in the central cell of a tandem mirror is critically examined and revised. The search for a physical damping mechanism which can truncate the short wavelength part of the spectrum of the ideal eigenfunction has led to the halo coupling of the trapped particle mode. The radial coupling of the trapped particle mode to the halo plasma can excite acoustic modes which are strongly damped at short wavelengths. This mechanism can easily smooth out the ideal rectangular structure. Approximate results indicate a significant departure from the ideal rectangular structure and a corresponding reduction of the growth rate.