60 lines
3.2 KiB
Matlab
60 lines
3.2 KiB
Matlab
function ret = initialVelocitySampling(this, MOTObj)
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n = this.NumberOfAtoms;
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% Calculate Calculate Capture velocity --> Introduce velocity cutoff
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MOTObj.CaptureVelocity = 1.05 * MOTObj.calculateCaptureVelocity(this, [-this.OvenDistance,0,0], [1,0,0]);
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this.VelocityCutoff = MOTObj.CaptureVelocity(1); % Should be the magnitude of the 3-D velocity vector but since here the obtained capture
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% velocity is only along the x-axis, we take the first term which is the x-component of the velocity.
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[ReducedClausingFactor, NormalizationConstantForAngularDistribution] = this.calculateReducedClausingFactor();
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this.ReducedClausingFactor = ReducedClausingFactor;
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VelocityDistribution = @(velocity) sqrt(2 / pi) * sqrt(Helper.PhysicsConstants.Dy164Mass/(Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperatureinKelvin))^3 ...
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* velocity.^3 .* exp(-velocity.^2 .* (Helper.PhysicsConstants.Dy164Mass / (2 * Helper.PhysicsConstants.BoltzmannConstant ...
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* this.OvenTemperatureinKelvin)));
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c = integral(VelocityDistribution, 0, this.VelocityCutoff);
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this.ReducedFlux = c * this.ReducedClausingFactor * this.calculateFreeMolecularRegimeFlux();
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ret = zeros(n,3);
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SampledVelocityMagnitude = zeros(n,1);
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SampledPolarAngle = zeros(n,1);
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SampledAzimuthalAngle = zeros(n,1);
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MostProbableVelocity = sqrt((3 * Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperature) / Helper.PhysicsConstants.Dy164Mass); % For v * f(v) distribution
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if MostProbableVelocity > this.VelocityCutoff
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MaximumVelocityAllowed = this.VelocityCutoff;
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else
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MaximumVelocityAllowed = MostProbableVelocity;
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end
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NormalizationConstantForVelocityDistribution = this.velocityDistributionFunction(MaximumVelocityAllowed);
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parfor i = 1:n
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% Rejection Sampling of speed
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y = rand(1);
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x = this.VelocityCutoff * rand(1);
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while y > ((NormalizationConstantForVelocityDistribution)^-1 * this.velocityDistributionFunction(x)) %As long as this loop condition is satisfied, reject the corresponding x value
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y = rand(1);
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x = this.VelocityCutoff * rand(1);
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end
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SampledVelocityMagnitude(i) = x; % When loop condition is not satisfied, accept x value and store as sample
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% Rejection Sampling of polar angle
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w = rand(1);
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z = this.ExitDivergence * rand(1);
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while w > ((NormalizationConstantForAngularDistribution)^-1 * 2 * pi * this.angularDistributionFunction(z) * sin(z)) %As long as this loop condition is satisfied, reject the corresponding x value
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w = rand(1);
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z = this.ExitDivergence * rand(1);
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end
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SampledPolarAngle(i) = z; %When loop condition is not satisfied, accept x value and store as sample
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% Sampling of azimuthal angle
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SampledAzimuthalAngle(i)= 2 * pi * rand(1);
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ret(i,:)=[SampledVelocityMagnitude(i)*cos(SampledPolarAngle(i)), SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*cos(SampledAzimuthalAngle(i)), ...
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SampledVelocityMagnitude(i)*sin(SampledPolarAngle(i))*sin(SampledAzimuthalAngle(i))];
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end
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