VITESS Supermirror-Ensemble

This module simulates an ensemble of mirror or supermirror (SM) planes of up to 50 elements. This can be used for the simulation of more complicated optical systems, with branch geometry. For example one can use 4 elements as a normal guide and put one transparent element into this tilted by an angle relative to the main (beam) axis and use it as polarizer. Both sides of the supermirror plates reflect.
Shapes and positions of the SM elements have to be given in the file "geometry and reflectivity data". Size and shape of each element are defíned by giving the four corners in a plane perpendicular to the beam. The center of each mirror is then moved to his final position; then two rotations are executed to get the mirror in the right orientation. A triangular shape can also be treated: 3 'corners' have to be co-linear for that.

The algorithm calculates the angle of inclination for each trajectory and decides about reflection or transmission depending on the reflectivity. The reflectivity model that is used for the sm_ensemlbe module depends on the format of the parameter file. If the file format is the old one, then for angles below theta_c, a reflectivity of 1 is assumed, for angles above thetaCSM, reflectivity of 0 is used. These parameters are used in the old file format. For angles between theta_c and thetaCSM, the reflectivity decreases linearly from 1 to R.
If the new file format is used, then only the m number is given for spin-up and spin-down neutrons, respectively. The module then calculated the reflectivity according to the empirical model describing the reflectivity behaviour of Swiss Neutronics mirrors. See below for details about the two file formats.

Visualisation of neutron paths or collision points is available. The module will visualize only the first 10000 trajectories or points.

### Parameters for module 'sm_ensemble'

Parameter Unit> | Description | Command Option
geometry and reflectivity data file | In this file shape, position, orientation, angular spread, 'up' and 'down' reflectivity curves and absorption of the mirrors have to be given | -P
File format | For differences between the old and the new file formats, see below. Its best to stick to the new format if a specific subtrate material is chosen. | -F
Subtrate coating | Choose between available materials Silicon or Sapphire for a proper description of neutron absorption. Choose Other for a general approximation. Beware that OTHER only works with the old file format! | -S
Modify color | Choose this option if the module should increase the color variable by 1 each time the trajectory undergoes a reflection within the mirror stack. | -R
spin quantisation direction | direction of spin quantisation in accordance with input data (e.g.source module) | -Q
output frame X',Y',Z' [cm] | The position of the output frame origin in the original frame. It represents the translation vector applied to shift the origin of the original (input) frame to the new (output) position. | -r, -s, -t
output angle horizontal, vertical [deg] | A rotation about the Z axis and then a rotation about the (new)Y axis defines a new orientation for the neutrons written to the output. | -h, -v
Visualisation window | Horizontal and vertical coordinates of the custom visualisation window. | -w, -W, -a, -A
Cutoff probability | The minimum probability still used for the custom visualisation | -b
stop at collisions | At this number of collisions it stops and writes out the trajectory for custom visualisation. This can be used for localising the coordinates of the 1th, 2nd, 3rd, etc. collisions. | -M
visualisation | If 'yes' (1), it writes out the collisions into a file "collisions.dat". Else: it visualises the trajectories | -T
device | Choose the device for visualisation: 1 - display, 2 - file, 3 - display+file | -o

#### Figure 1: geometry definitions

### Parameter file describing the mirrors in module 'sm_ensemble'

### Old format

Parameter Unit> | Description | Values
on/off | defines if the wall is active (1) or not (0) (i.e. you can switch it off) at most 50 walls can be active | 1: on 0: off
yi, zi i=1,..,4 [cm] | defines shape and size of a mirror element: the positions of the corners of a quadrangle are given in a plane perpendicular to the beam you can also form a triangle if 3 'corners' are co-linear(cf. figure above) | any
X Y Z [cm] | X,Y,Z defines the position of the mirror: The element (defined by y1 to z4) is supposed to arranged around the origin (0,0,0). This point of the mirror is now translated to its rigth place in the final geometry by a shift by the vector (X,Y,Z). | 1: on 0: off
H/° V/° [deg] | Rotation angles which define the final normal vector of the mirror. It is first rotated (in a horizontal plane) about the z-axis by an angle 'H'. Then it is rotated (in a vertikal plane) about the new y-axis by an angle 'V'. | -180° to 180°
h/° v/° [deg] | is the full width of a rectangular distribution expected for the variations in the plane orientation. For each trajectory a deviation from the average orientation in the given range is determined by a Monte Carlo choice. | theoretically -180° to 180°
thetaC [rad] | angle up to which 1 Å neutrons are totally reflected, corresponding to m=1 | typically: 0.00173
theta_csm [rad] | angle up to which 1 Å neutrons are reflected, corresponding to the m-value | m*0.00173
R_csm | reflectivity for theta_csm: theta_c < theta < theta_csm R decreases linearly from 1 to R_csm theta < theta_c : R = 1.0 theta > theta_csm: R = 0.0 | 0 ... 1
µ*d | wavelength dependent part of the attenuation (in case óf transmission) d is the thickness of the mirror in cm µ is the macroscopic attenuation (in 1/cm) for 1 Å neutrons | > 0.0 0.017 for Si
µ_incoh*d | wavelength independent part of the attenuation (in case óf transmission) d is the thickness of the mirror in cm µ_incoh is the macroscopic attenuation (in 1/cm) | > 0.0 0.020 for Si
wall | name given by the user to the walls (no real input) | any text

### New format

The new format makes use of the available empirical description of the mirror reflectivities valid for mirror coatings produced by Swiss Neutronics. Apart from geometrical information, in this format only the thickness d and the m-number for spin-up and spin-down neutrons has to be given. This format can only be used if sapphire or silicon is chosen as mirror subtrate!

Parameter Unit> | Description | Values
on/off/no transmission | defines if the wall is not active (0), active (1), or active without transmission, i.e. all trajectories that are not reflected are absorbed (2) at most 50 walls can be active | 0: off 1: on 2: no transmission
yi, zi i=1,..,4 [cm] | defines shape and size of a mirror element: the positions of the corners of a quadrangle are given in a plane perpendicular to the beam you can also form a triangle if 3 'corners' are co-linear(cf. figure above) | any
X Y Z [cm] | X,Y,Z defines the position of the mirror: The element (defined by y1 to z4) is supposed to arranged around the origin (0,0,0). This point of the mirror is now translated to its rigth place in the final geometry by a shift by the vector (X,Y,Z). | 1: on 0: off
H/° V/° [deg] | Rotation angles which define the final normal vector of the mirror. It is first rotated (in a horizontal plane) about the z-axis by an angle 'H'. Then it is rotated (in a vertikal plane) about the new y-axis by an angle 'V'. | -180° to 180°
h/° v/° [deg] | is the full width of a rectangular distribution expected for the variations in the plane orientation. For each trajectory a deviation from the average orientation in the given range is determined by a Monte Carlo choice. | theoretically -180° to 180°
Thickness [cm] | Thickness d of the mirror element | typically: 0.01 - 0.5cm
m spin-up | m value for the spin-up neutrons. Critical angle is then 0.1*m*λ. | typically: 0 - 7
m spin-down | m value for the spin-down neutrons. Critical angle is then 0.1*m*λ. | typically: 0 - 7

## Examples:

### Example 1: Polarizing V Cavity

A V type cavity is a transmission polarization device, by which a wide neutron band with large divergence can be polarized. Here it is realized as a single V cavity using an FeSi supermirror, which shows total reflectivity up to m=1 and zero reflectivity above m=4 for spin-up and total reflectivity up to m=0.6 and zero reflectivity above m=0.7 for spin-down neutrons (cf. figure and table).

#### Figure 2: V cavity and reflectivity curves of the FeSi coating of its polarizing mirrors

### Old format

    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0  -0.2496   0.0   -90.715    0.0   0.0   0.0     0.00173   0.00692   0.78     0.000144   0.0009      0.001038   0.001211   0.60    0.000144   0.0009   ----- pol mirror 1 -----
    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0   0.2496   0.0    90.715    0.0   0.0   0.0     0.00173   0.00692   0.78     0.000144   0.0009      0.001038   0.001211   0.60    0.000144   0.0009   ----- pol mirror 2 -----
    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0  -0.4992   0.0    90.000    0.0   0.0   0.0     0.00173   0.00173   0.99   100.00    100.00         0.00173    0.00173    0.99  100.00     100.00     ----- left side    -----
    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0   0.4992   0.0    90.000    0.0   0.0   0.0     0.00173   0.00173   0.99   100.00    100.00         0.00173    0.00173    0.99  100.00     100.00     ----- right side   -----
    1      20.0  0.9984  -20.0  0.9984  -20.0  -0.9984   20.0  -0.9984   20.0   0.0000   1.5    90.000  -90.0   0.0   0.0     0.00173   0.00519   0.88   100.00    100.00         0.00173    0.00519    0.88  100.00     100.00     ----- up           -----
    1      20.0  0.9984  -20.0  0.9984  -20.0  -0.9984   20.0  -0.9984   20.0   0.0000  -1.5    90.000   90.0   0.0   0.0     0.00173   0.00519   0.88   100.00    100.00         0.00173    0.00519    0.88  100.00     100.00     ----- down         -----
    on/off  y1   z1        y2   z2        y3    z3        y4    z4         X      Y       Z      H/°      V/°   h/°   v/° Up: theta_c  theta_csm  R_csm   µ*d      µ_incoh*d  Down: theta_c theta_csm  R_csm     µ*d    µ_incoh*d         wall

### New format

    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0  -0.2496   0.0   -90.715    0.0   0.0   0.0     0.03	4	0.6  	 ----- pol mirror 1 -----
    1      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0   0.2496   0.0    90.715    0.0   0.0   0.0     0.03	4	0.6	 ----- pol mirror 2 -----
    2      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0  -0.4992   0.0    90.000    0.0   0.0   0.0     0.03 	1	1	 ----- left side    -----
    2      20.0  1.5     -20.0  1.5     -20.0  -1.5      20.0  -1.5      20.0   0.4992   0.0    90.000    0.0   0.0   0.0     0.03	1	1	 ----- right side   -----
    2      20.0  0.9984  -20.0  0.9984  -20.0  -0.9984   20.0  -0.9984   20.0   0.0000   1.5    90.000  -90.0   0.0   0.0     0.03	3	3	 ----- up           -----
    2      20.0  0.9984  -20.0  0.9984  -20.0  -0.9984   20.0  -0.9984   20.0   0.0000  -1.5    90.000   90.0   0.0   0.0     0.03	3	3	 ----- down         -----
    on/off  y1   z1        y2   z2        y3    z3        y4    z4         X      Y       Z      H/°      V/°   h/°   v/°     d	m up	m down	   wall

### Example 2: Extraction System

The following example shows the realization of a bi-spectral extraction system consisting of 3 vertical m=3 supermirrors and 2 horizontal m=2 supermirrors. The vertical mirrors are 0.77° and 0.19° inclined (relative to the beamline) in the direction shown in the figure.
5 numbers have to be given to define the reflectivity curve (s. Table below), both for up- and down-neutrons. Note that apart from the second mirror, all others do not transmit neutrons.

#### Figure 3: Bispectral extraction system

### Old format

    1     323.5     5.0  -323.5     5.0  -323.5     -5.0   323.5    -5.0    323.5    -7.347  0.00   90.77    0.00    0.00  0.00     0.00173   0.00519   0.88   200.0     200.0            0.00173  0.00519  0.88   200.0   200.0       --left---
    1     323.5     5.0  -323.5     5.0  -323.5     -5.0   323.5    -5.0    323.5    -1.347  0.00   90.77    0.00    0.00  0.00     0.00173   0.00519   0.88     0.00024   0.00150        0.00173  0.00519  0.88   0.00024    0.00150   --center---
    1     252.5     5.0  -252.5     5.0  -252.5     -5.0   252.5    -5.0    394.5     2.163  0.00   90.19    0.00    0.00  0.00     0.00173   0.00519   0.88   200.0     200.0            0.00173  0.00519  0.88   200.0   200.0       --right---
    1       3.0   323.5    -3.0   323.5   -11.74  -323.5    +0.87  -323.5   323.5     0.0    5.0    00.00  -90.00    0.00  0.00     0.00173   0.00346   0.95   200.0     200.0            0.00173  0.00346  0.95   200.0   200.0       --top---
    1       3.0   323.5    -3.0   323.5   -11.74  -323.5    +0.87  -323.5   323.5     0.0   -5.0    00.00  -90.00    0.00  0.00     0.00173   0.00346   0.95   200.0     200.0            0.00173  0.00346  0.95   200.0   200.0       --bot---
    on/off  y1      z1      y2      z2      y3       z3      y4      z4        X       Y      Z       H/°      V/°    h/°   v/° Up: theta_c  theta_csm  R_csm   µ*d      µ_incoh*d  Down: theta_c theta_csm R_csm   µ*d    µ_incoh*d     wall

### New format

    2     323.5     5.0  -323.5     5.0  -323.5     -5.0   323.5    -5.0    323.5    -7.347  0.00   90.77    0.00    0.00  0.00     0.05	5	5       --left---
    1     323.5     5.0  -323.5     5.0  -323.5     -5.0   323.5    -5.0    323.5    -1.347  0.00   90.77    0.00    0.00  0.00     0.05	3	3      --center---
    2     252.5     5.0  -252.5     5.0  -252.5     -5.0   252.5    -5.0    394.5     2.163  0.00   90.19    0.00    0.00  0.00     0.05	3	3       --right---
    2       3.0   323.5    -3.0   323.5   -11.74  -323.5    +0.87  -323.5   323.5     0.0    5.0    00.00  -90.00    0.00  0.00     0.05   	3  	3        --top---
    2       3.0   323.5    -3.0   323.5   -11.74  -323.5    +0.87  -323.5   323.5     0.0   -5.0    00.00  -90.00    0.00  0.00     0.05	2	2        --bot---
    on/off  y1      z1      y2      z2      y3       z3      y4      z4        X       Y      Z       H/°      V/°    h/°   v/° Thickness	m up	m down     wall

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Last modified: Fri Jul 4 16:51:30 MEST 2003, G. Zs.