Module Elliptic Guide

# VITESS Module Elliptic Guide

The module guide_elliptic simulates the neutron flight path through a mirrored guide calculating the intensity loss for each reflection (in dependence of the neutron wavelength and the incident angle). While the regular Guide module is designed to handle all possible wall shapes, this module is explicitly designed to deal with guides, which are elliptic in one or both planes. No segmentation is used in this guide, thus for all shapes, for which an input file is used, the conventional guide module should be used.

### Input parameters

If the elliptic shape is chosen, there are two combinations of parameters that allow a complete definition of the shape: - Length, major and minor axis, in this case the ellipse is symmetric wrt to its center - Length, entrance & exit width and distance from exit to focus

For linear or constant shape, the entrance & exit width (height) and length have to be specified. Note that for a constant shape, the width (height) at entrance and exit must agree.

See below for the full list of parameters.

Parameter Unit | Description | Command option
Horizontal / vertical shape | shape of the guide: constant: Same cross section throughout the whole guide. linear : linearly converging or diverging between entrance and exit. elliptic: The guide is described by a true ellipse in the corresponding plane. | -H, -V
Output shape file | The output shape file is used to store the width and height of the guide as a function of length for future purposes | -O
Ellipse axes in horizontal plane [m] | Major and minor ellipse axis in the x-y plane, where the major axis is along the x-axis. | -a, -b
Ellipse axes in vertical plane [m] | Major and minor ellipse axis in the x-z plane, where the major axis is along the x-axis. | -A, -B
entrance width, height [cm] | size of the guide entrance (in y- and z-direction) | -w, -u
exit width, height [cm] | size of the guide exit (in y- and z-direction) | -W, -H
Length of guide [m] | Guide length | -l
Distance to focus [m] | Distance to focal point in horizontal and vertical plane. Note that the focal points are allowed to differ. | -d -D
left, right, top/bottom plane | reflectivity file for the coating of the guide on the inner side (left), on the outer side (right), on the top and on the bottom plane. If no file for the bottom plane is given, the file of the top plane is used for the bottom. | -i, -I, -j, -J
Add to color | Add value to neutron color on each reflection. | -A

### Mathematical description

The basis for the mathematical description of an elliptic guide is the ellipse equation: sqrt(x²/a² + y²/b²) = 1, where a and b is the major and minor axis, respectively. This equation is used to determine the interaction position between the guide and a neutron trajectory and the reflection angle. For both parabolic and straight trajectories, the intersection equation is solved analytically (see Analytical calculation of quartic equations). In case the axes of the ellipse are not given by the input parameters, they are calculated from the entrance and exit width, the length of the guide and the distance to the focal point. Back to VITESS overview
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