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/*******************************************************************************
* McXtrace, x-ray tracing package
* Copyright, All rights reserved
* DTU Physics, Kgs. Lyngby, Denmark
* Synchrotron SOLEIL, Saint-Aubin, France
*
* Component: SAXSEllipticCylinders
*
* %Identification
* Written by: Martin Cramer Pedersen (mcpe@nbi.dk)
* Date: May 2, 2012
* Origin: KU-Science
*
* A sample of monodisperse cylindrical particles with elliptic cross section in
* solution.
*
* %Description
* A component simulating the scattering from a box-shaped, thin solution
* of monodisperse, cylindrical particles with elliptic cross section.
*
* Example: SAXSEllipticCylinders( xwidth = 0.01, yheight = 0.01, zdepth = 0.01, SampleToDetectorDistance = 0.48, DetectorRadius = 0.1 )
*
* %Parameters
* 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 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 x-rays).
* DetectorRadius: [m] Radius of the detector (for focusing the scattered x-rays).
*
* %End
*******************************************************************************/
DEFINE COMPONENT SAXSEllipticCylinders
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
%{
double Prefactor;
double Absorption;
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
%{
double l0;
double l1;
double l_full;
double l;
double l_1;
double Formfactor1;
double Formfactor2;
double Intensity;
double SolidAngle;
double qx;
double qy;
double qz;
double q;
double k;
double dl;
double kx_i;
double ky_i;
double kz_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);
Intersect = box_intersect(&l0, &l1, x, y, z, kx, ky, kz, xwidth, yheight, zdepth);
if (Intersect) {
if (l0 < 0.0) {
fprintf(stderr, "Photon already inside sample %s - absorbing...\n", NAME_CURRENT_COMP);
ABSORB;
}
// Compute properties of photon
k = sqrt(pow(kx, 2) + pow(ky, 2) + pow(kz, 2));
l_full = l1 - l0;
dl = rand01() * (l1 - l0) + l0;
PROP_DL(dl);
l = dl - l0;
// Store properties of incoming photon
kx_i = kx;
ky_i = ky;
kz_i = kz;
/* Generate new direction of photon */
randvec_target_circle(&kx, &ky, &kz, &SolidAngle, 0, 0, SampleToDetectorDistance, DetectorRadius);
NORM(kx, ky, kz);
kx *= k;
ky *= k;
kz *= k;
/* Compute q */
qx = kx_i - kx;
qy = ky_i - ky;
qz = kz_i - kz;
q = sqrt(pow(qx, 2) + pow(qy, 2) + pow(qz, 2));
/* Compute scattering */
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));
SCATTER;
}
%}
MCDISPLAY
%{
box(0, 0, 0, xwidth, yheight, zdepth,0, 0, 1, 0);
%}
END
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