and transmission 
are given by the formulas:
There are two dedicated VITESS modules to simulate neutron polarisers:
polariser_he3 simulates a helium-3 polarizer.
polariser_sm simulates a (vertical) stack of nearly horizontal, rectangular, parallel plane mirrors with different reflectivity curves for up- and and down-neutrons.
It assumes an odd number of channels, absorption on the left and right side of the stack, a polarizing B field along the x-axis and identical reflectivities for all mirrors.
A stack of vertical mirrors can be realized using the frame module before and after this component.
For any other situation, the module sm_ensemble has to be used.
If the polarizer consists of only 1 mirror, it is easiest to use the module pol_mirror, which allows horizontal and vertical mirror orientation.
This module simulates a multichannel supermirror polarizer with flat channel
walls tilted by an angle relative to the neutron beam in order to reflect
all neutrons at least one time.
The polarization process at each reflection is treated quantummechanically:
qnew = 2. * atan(aDD/ aUU * tan(q/2.)) ;
where
aUU = sqrt(rupdata[datanumber]) ;
aDD = sqrt(rdowndata[datanumber]) ;
are the diagonal components of the polarization scattering matrix and rupdata[datanumber]
and rdowndata[datanumber] give the "Up" and "Down" reflectivities belonging
to the wavelength bin (numero 'datanumber') as read from the reflectivity
files.
The probability weight is multiplied by the probability of reflection in
function of the wavelength:
Prob =Prob * (sq(aUU * cos(q/2.)) + sq(aDD * sin(q/2.)) );
and this simplifies to Prob = Prob * RUp,Down in case of only "Up" or "Down" trajectories, when q is 0 or p.
The spin precessions are approximated classically i.e. we rotate the spin vectors belonging to the trajectories in order to simulate dephasing in function of flight time through the magnetic field.
| Parameter Unit |
Description |
Range or Values |
Command Option |
| parameter file | name of the parameter file | -P | |
| Up-reflectivity file | reflectivity data file for Up neutrons; format as guide reflectivity file | file for m=4 | -U |
| Down-reflectivity file | reflectivity data file for Down neutrons; format as guide reflectivity file | file for m=0.6 | -D |
| position X, Y, Z [cm] |
center position of the rectangular geometry polarizer | (48.0, 0.0, 0.5) | -a, -b, -c |
| vertical inclination [deg] |
rotation angle of the polarizer in vertical direction (0, 0 means parallel to X i.e. beam) | 0.6 deg | -V |
| output X, Y, Z [cm] |
position of the output frame (in the input frame) | (96.0, 0.0, 1.0) | -R, -E, -G |
| hor., vert. rotation angle [deg] |
rotation angle of the output frame in horizontal (first rotation) and vertical direction (0, 0 means parallel to original X) | 0.0, 1.2 deg | -h, -v |
| Parameter Unit |
Description |
Range or examples |
Command Option |
| dimension X, Y, Z [cm] |
length, width and height of the polarizer | 96, 6.0, 3.0 | |
| number of channels | number of channels in vertical direction | 1, 3, 5, ... | |
| wall width [cm] |
width of the wall between the channels | 0.05 | |
| guide field X, Y, Z [Gs] |
components of the guide field | all components ≥0, e.g. (1.0, 0.0, 0.0) | |
| analysis dir. X, Y, Z | direction vector components of the quantization direction | (1.0, 0.0, 0.0) |
This module simulates a He-3 gas polarizer/filter. Inside the cylindrical
He-3 gas chamber the field component is homogeneous. The guide field is added
to the total field.
The spin precessions are first approximated classically i.e. we first rotate
the spin vectors belonging to the trajectories in order to simulate dephasing
in function of flight time through the magnetic field. Then we use the known
quantummechanical formulas to define the new spin orientation if the "Up"
and "Down" mixed states weights will change due to the interaction with the
He-3 gas:
{ CartesianToSpherical(SpinVector, &theta, &phi);
pDown = sqrt(1.0 - polardata[datanumber]);
theta = 2.0 * asin(pDown * sin(theta/2.0)) ;
SphericalToCartesian(SpinVector, &theta, &phi);
}
where polardata[datanumber] gives the polarization belonging to the wavelength
bin (numero 'datanumber') as read from the 'polarization file'.
The probability weight is multiplied by the transmission in function of the
wavelength.
As result, the average polarization and transmission per wavelength
of the trajectories will depend on the wavelength as given in the polarization
and transmission files.
In the case of choosing the analytical option, the neutron polarization
and transmission
are given by the formulas:
where n and l are the He-3 particle density [cm-3] and the polarizer length [cm] resp.
and PHe is the He-3 polarization.
is the cross-section [barn], with En given in eV.
Alternatively, σ(λ) = 2945 barn * λ/Å
| Parameter Unit |
Description | Range or Values | Command option |
| wavelength dependence |
choice between analytical and numerical determination of the wavelength dependence of the polarization and transmission If 'wavelength dependence'='analytical' is chosen' the polarization and transmission file are generated from the He-3 polarization, its density and the tube length of the polarizer If 'wavelength dependence'='numerical' is chosen, the files containing polarization and transmission as a function of wavelenth are used. They have to be supplied by the user and must be in the form described below. Note that He-3 polarization, He-3 particle density and length of the polarizer are ignored in this case. |
'numerical' 'analytical' |
-a |
| polarization He3 [%] |
polarization of the He-3 gas | (needed for the analytical calculation of polarization and transmission)80% | -b |
| density He3 [cm-3] |
density of the He3 gas (needed for analytical calculation of polarization and transmission) |
2.7e19 (for 1 bar) |
-d |
| polarization xsection [barn] |
polarization cross-section of 1 Å neutrons in He-3 (usually calculated from the tabulated value for 1.798 Å neutrons) |
2945 | -c |
| polarization file |
Input file containing the wavelength dependent polarization of the given He-3 polarizer If 'wavelength dependence'='analytical' is chosen' it is generated in the beginning of the simulation from the He-3 polarization, its density and the polarizer tube length Otherwise, it has to be supplied by the user. It consists of polarization values (between 0 and 1) in a single column for wavelength values of 0.01, 0.02, 0.03, 0.04 ... 50 Å |
-P | |
| transmission file |
Input file containing the wavelength dependent transmission of the given He-3 polarizer If 'wavelength dependence'='analytical' is chosen' it is generated in the beginning of the simulation from the He-3 polarization, its density and the polarizer tube length Otherwise, it has to be supplied by the user. It consists of polarization values (between 0 and 1) in a single column for wavelength values of 0.01, 0.02, 0.03, 0.04 ... 50 Å |
-T | |
| position main X,Y,Z [cm] |
center position of the cylindrical He-3 gas chamber | 25 0 0 | -k, -l, -m |
| cylinder length, diameter [cm] |
length (along the beamline) and diameter of the cylindrical He-3 gas chamber | 10 10 | -X, -Y |
| guide field X, Y, Z [Gs] |
x-, y- and z-component of the guide field | 1 0 0 | -G, -H, -K |
| pol. field X, Y, Z [Gs] |
x-, y- and z-component of the magnetic field in the chamber, which is added to the guide field | 10 0 0 | -M, -N, -O |
| output X, Y, Z [cm] |
position of the output frame (in the input frame) | 50 0 0 | -p, -r, -s |
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Last modified: Tue Jul 23 17:27:04 MEST 2002, G.Zs.