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/*******************************************************************************
* McStas, neutron ray-tracing package
* Copyright 1997-2003, All rights reserved
* Risoe National Laboratory, Roskilde, Denmark
* Institut Laue Langevin, Grenoble, France
*
* Component: SANSEllipticCylinders
*
* %I
* Written by: Martin Cramer Pedersen (mcpe@nbi.dk)
* Date: October 17, 2012
* Origin: KU-Science
*
* A sample of monodisperse cylindrical particles with elliptic cross section in
* solution.
*
* %D
* A component simulating the scattering from a box-shaped, thin solution
* of monodisperse, cylindrical particles with elliptic cross section.
*
* %P
* R1: [AA] First semiaxis of the cross section of the
* elliptic cylinder.
* R2: [AA] Second semiaxis of the cross section of the
* elliptic cylinder.
* Height: [AA] Height of the elliptic cylinder.
* Concentration: [mM] Concentration of sample.
* DeltaRho: [cm/AA^3] Excess scattering length density of the
* particles.
* AbsorptionCrosssection: [1/m] Absorption cross section of the sample.
* xwidth: [m] Dimension of component in the x-direction.
* yheight: [m] Dimension of component in the y-direction.
* zdepth: [m] Dimension of component in the z-direction.
* SampleToDetectorDistance: [m] Distance from sample to detector (for
* focusing the scattered neutrons).
* DetectorRadius: [m] Radius of the detector (for focusing the
* scattered neutrons).
*
* %E
*******************************************************************************/
DEFINE COMPONENT SANSEllipticCylinders
SETTING PARAMETERS (R1 = 20.0, R2 = 40.0, Height = 100.0, Concentration = 0.01, DeltaRho = 1.0e-14, AbsorptionCrosssection = 0.0,
xwidth, yheight, zdepth, SampleToDetectorDistance, DetectorRadius)
DEPENDENCY " @GSLFLAGS@ "
NOACC
/*X-ray Parameters (x, y, z, kx, ky, kz, phi, t, Ex, Ey, Ez, p)*/
SHARE
%{
#include <gsl/gsl_sf_bessel.h>
%}
DECLARE
%{
// Declarations
double Prefactor;
double Absorption;
double q;
double NumberDensity;
%}
INITIALIZE
%{
// Rescale concentration into number of aggregates per m^3 times 10^-4
NumberDensity = Concentration * 6.02214129e19;
// Computations
if (!xwidth || !yheight || !zdepth) {
printf("%s: Sample has no volume, check parameters!\n", NAME_CURRENT_COMP);
}
Prefactor = NumberDensity * pow(PI * Height * R1 * R2, 2) * pow(DeltaRho, 2);
Absorption = AbsorptionCrosssection;
%}
TRACE
%{
// Declarations
double t0;
double t1;
double l_full;
double l;
double l1;
double Formfactor1;
double Formfactor2;
double Intensity;
double SolidAngle;
double qx;
double qy;
double qz;
double v;
double dt;
double vx_i;
double vy_i;
double vz_i;
double ProjectedRadius;
char Intersect = 0;
// Variables needed for integration over alpha
int i;
const int NumberOfStepsInAlpha = 30;
double Alpha;
const double AlphaMin = 0.0;
const double AlphaMax = PI / 2.0;
const double AlphaStep = (AlphaMax - AlphaMin) / (1.0 * NumberOfStepsInAlpha);
// Variables needed in integration over beta
int j;
const int NumberOfStepsInBeta = 30;
double Beta;
const double BetaMin = 0.0;
const double BetaMax = PI / 2.0;
const double BetaStep = (BetaMax - BetaMin) / (1.0 * NumberOfStepsInBeta);
// Computation
Intersect = box_intersect(&t0, &t1, x, y, z, vx, vy, vz, xwidth, yheight, zdepth);
if (Intersect) {
if (t0 < 0.0) {
fprintf(stderr, "Neutron already inside sample %s - absorbing...\n", NAME_CURRENT_COMP);
ABSORB;
}
// Compute properties of neutron
v = sqrt(pow(vx, 2) + pow(vy, 2) + pow(vz, 2));
l_full = v * (t1 - t0);
dt = rand01() * (t1 - t0) + t0;
PROP_DT(dt);
l = v * (dt - t0);
// Store properties of incoming neutron
vx_i = vx;
vy_i = vy;
vz_i = vz;
// Generate new direction of neutron
randvec_target_circle(&vx, &vy, &vz, &SolidAngle, 0, 0, SampleToDetectorDistance, DetectorRadius);
NORM(vx, vy, vz);
vx *= v;
vy *= v;
vz *= v;
// Compute q
qx = V2K * (vx_i - vx);
qy = V2K * (vy_i - vy);
qz = V2K * (vz_i - vz);
q = sqrt(pow(qx, 2) + pow(qy, 2) + pow(qz, 2));
// Compute scattering
l1 = v * t1;
Intensity = 0.0;
for (i = 0; i < NumberOfStepsInAlpha; ++i) {
Alpha = (i + 0.5) * AlphaStep;
for (j = 0; j < NumberOfStepsInBeta; ++j) {
Beta = (j + 0.5) * BetaStep;
ProjectedRadius = sqrt(pow(R1 * sin(Beta), 2) + pow(R2 * cos(Beta), 2));
Formfactor1 = gsl_sf_bessel_J1(q * ProjectedRadius * sin(Alpha)) / (q * ProjectedRadius * sin(Alpha));
Formfactor2 = sin(q * Height * cos(Alpha) / 2.0) / (q * Height * cos(Alpha) / 2.0);
Intensity += 2 / PI * sin(Alpha) * Prefactor * pow(2 * Formfactor1 * Formfactor2, 2) * AlphaStep * BetaStep;
}
}
p *= l_full * SolidAngle / (4.0 * PI) * Intensity * exp(- Absorption * (l + l1) / v);
SCATTER;
}
%}
MCDISPLAY
%{
box(0, 0, 0, xwidth, yheight, zdepth,0, 0, 1, 0);
%}
END
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