VITESS Tool Generate Reflectivity Files

This tool generates reflectivity files as they are used in the modules 'guide' and 'bender'. Five options are available: two of them only use the m-value as input, two transfer if from another file format and one calculates it from 5 input parameters. In all 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 output directory.


VITESS reflectivity file format

VITESS uses a special file format: The file contains the probability of reflection in dependence of the incident angle for neutrons with a wavelength of 1 Å. Each row contains 10 data points covering 0.01 deg, i.e. each point gives the probability average over an angular interval of 0.001 deg. The first row contains values for 0.000 to 0.009 deg, the second for 0.010-0.019 deg a.s.o.). The number of data points may vary between 2 and 1000.


Linear 5 parameter description

The reflectivity curve of a supermirror is determined by the 5 parameters m, R0, Rm, Qc and W (s. table).
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))

with the slope a given by

    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.


Linear 2020 Approach

To facilitate the use of reflectivity functions, the attempt was made to describe the whole curve only by the parameter m. This was first done by H. Jacobsen [1] using the Quadratic Swiss Neutronics description (see below) to describe reflectivity curves measured by SwissNeutronics.
Advances in coating technology between 2010 and 2020 could reduce the descent in R(Q) and achieved a nearly constant slope again, so that the formula above can used to describe the reflectivity curve by only one parameter. Data delivered by Swissneutronics, S-DH and Mirrortron for their products with nominal coating mn were fitted using the equation above and the resulting parameters averaged resuting in 
        R0 = 0.995
        W  = 0.00157
        Rm = Min(R0, 1.096 - 0.0758*mn)
        m  = mn + 0.14

Quadratic Swiss Neutronics description

As for the Linear 2020 Approach, the only input parameter necessary is the m-value of the supermirror coating. The reflectivity is calculated as

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

where R0 is constant and W, a, b and m are linear functions of mn [1]: 
        R0 = 0.99
        W = -0.0002*mn +  0.0022 
        a =  0.1204*mn +  5.0944  if mn > 3, else a = mn 
        b = -7.6251*mn + 68.1137  if mn > 3, else b = 0 
        m =  0.9853*mn +  0.1978
The parameters used here are the results of fits to experimental data. The reflectivity curve gained for m=4 is shown by the black line in figure 1.
Note that this describes well the reflectivity of high m coatings produced around 2010, while a smaller descent with a constant slope in Q as used in the 'Linear 2020 approach' could be achieved afterwards.

R(m) and R(Q) files

If the reflectivity curve exists as 2 column file R(Q) or R(m) with Q or m resp. in the first and the reflectivity R in the 2nd column, it can be transferred to the VITESS reflectivity file format.
Note that R(Q) can also be used in the module guide, but not in guide_ideal or bender. R(m) needs to be transferred in any case.


Parameter description

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 -

Plot of reflectivity curves


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


Literature

[1] H. Jacobsen, K. Lieutenant, C. Zendler, K. Lefmann, Bi-spectral extraction through elliptic neutron guides, Nucl. Instr. Meth. Phys. Res. A 717 (2013) 69-76.


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