# VITESS Tool Generate Mirror Files

This tool generates reflectivity files that are used in the modules 'guide' and 'bender'. Two options are available: a linear decrease of reflectivity with scattering angle, or a description using an additional quadratic term. In both cases, an output filename has to be given. If no path is included in that filename, the generated reflectivity file will be written to the parameter directory.

### Quadratic Swiss Neutronics description

If this option is chosen, the only additional input parameter necessary is the m-value of the supermirror coating. The reflectivity is the calculated as

R = 1/2 R0 (1 - tanh((Q - m Qc,Ni)/W) (1 - a(Q - Qc) + b(Q - Qc)2)

where R0=0.99 and W, a, b and m2 are linear functions of m:

    W  = -0.0002*m +  0.0022
    a  =  0.1204*m +  5.0944  if m>3, else a=m
    b  = -7.6251*m + 68.1137  if m>3, else b=0
    m2 =  0.9853*m +  0.1978

The parameters used here are the results of fits to experimental data (H. Jacobsen). The reflectivity curve gained for m=4 is shown by the black line in figure 1.

### Linear description

If quadratic Swiss Neutronic description is answered with no, the parameters m, R0, Rm, Qc and W (s. table) have to be given in addition to the filename.
For W=0 the reflectivity curve consists of linear functions and a sharp cut-off at Q = m Qc,Ni. The red line in figure 1 shows an example for m=4.
For W > 0 and Q > Qc, the reflectivity R is calculated as

R = 1/2 R0 (1 - tanh((Q - m Qc,Ni)/W) (1 - a(Q - Qc))

using
a = (Rm - R0) / (m Qc,Ni - Qc)
The product m Qc,Ni must be greater or equal Qc, because m is meant to extent the Q range to values greater than Qc.
An example for m=4 and W=0.003 is shown by the green line in figure 1.

Parameter Unit | Description | typical values
R0 | reflectivity for 0 <= Q <=Qc | 0.99
m | factor of supermirror | 1 ... 4
Qc [Ang-1] | crit. momentum transfer | 0.0217
Rm | reflectivity for Q = m Qc(Ni) for a sharp cut-off (W=0) | 0.6 .... 0.95
W [Ang-1] | width of the cut-off range W=0 causes a sharp cut-off | 0 ... 0.004
mirror file | name of the file into which the reflectivity curve is written | -

Figure 1: Reflectivity curves obtained with the tool for m=4 using different options.

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