Statistical equilibrium spatial density in planar channeling

The calculation of the particle spatial probability density for planar channeling is carried out as a function of incident angle for statistical equilibrium using the continuum model. A computer code is given for the numerical computation of the spatial density. In addition, the channeled particle trajectory wavelength vs. amplitude is also obtained. An approximation is found which results in a simple analytic expression for the spatial density and gives reasonable agreement with numerical calculations. For more accurate calculations a normalization procedure has been obtained which allows a set of universal curves to be developed that have only two parameters, a normalized incident angle and a normalized planar spacing. Using the curves presented, the statistical equilibrium spatial density or channeled particle wavelength vs. amplitude can be easily obtained for any case for which the continuum model can be applied