66 lines
3.5 KiB
Mathematica
66 lines
3.5 KiB
Mathematica
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function [LoadingRate, StandardError] = runSimulation(this)
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n = this.NumberOfAtoms;
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%% Calculate Background Collision Time --> Calculate Capture velocity --> Introduce velocity cutoff --> Calculate capture fraction
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this.CaptureVelocity = 1.05 * this.calculateCaptureVelocity([-this.OvenDistance,0,0], [1,0,0]); % Make 5% larger than the numerically obtained CV
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this.VelocityCutoff = this.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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VelocityDistributionFunction = @(velocity) sqrt(2 / pi) * (Helper.PhysicsConstants.Dy164Mass/(Helper.PhysicsConstants.BoltzmannConstant * this.OvenTemperatureinKelvin)) ...
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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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this.CaptureFraction = integral(VelocityDistributionFunction, 0, this.VelocityCutoff) / integral(VelocityDistributionFunction, 0, Inf);
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%% Calculate the Clausing Factor
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% Compute the angular distribution of the atomic beam
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ThetaArray = linspace(0.0001, pi/2, 1000);
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AngularDistribution = zeros(1,length(ThetaArray));
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parfor i = 1:length(ThetaArray)
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AngularDistribution(i) = this.angularDistributionFunction(ThetaArray(i));
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end
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% Numerically integrate the angular distribution over the full solid angle
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NormalizationConstant = 0;
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for j = 1:length(ThetaArray)
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if ThetaArray(j) <= this.NozzleExitDivergence
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NormalizationConstant = NormalizationConstant + (2 * pi * sin(ThetaArray(j)) * AngularDistribution(j) * (ThetaArray(2)-ThetaArray(1)));
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end
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end
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this.ClausingFactor = (1/pi) * NormalizationConstant; %The complete intergration will give pi * ClausingFactor.
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%Therefore, the Clausing Factor needs to be extracted from the
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%result of the above integration by dividing out pi
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this.AngularDistribution = AngularDistribution;
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this.NormalizationConstantForAngularDistribution = NormalizationConstant;
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%%
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% - sampling the position distribution
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this.InitialPositions = this.initialPositionSampling();
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% - sampling the velocity distribution
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this.InitialVelocities = this.initialVelocitySampling(this.VelocityCutoff, this.AngularDistribution, this.NormalizationConstantForAngularDistribution);
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%% Solve ODE
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progressbar = Helper.parforNotifications();
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progressbar.PB_start(n,'Message',['Simulating capture process for ' num2str(n,'%.0f') ' atoms:']);
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% calculate the final position of the atoms
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FinalDynamicalQuantities = zeros(n,9);
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Positions = this.InitialPositions;
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Velocities = this.InitialVelocities;
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parfor Index = 1:n
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ret = this.solver(Positions(Index,:), Velocities(Index,:));
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FinalDynamicalQuantities(Index,:) = ret(2);
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progressbar.PB_iterate();
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end
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clear Index
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%% Calculate the Loading Rate
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[LoadingRate, StandardError] = this.calculateLoadingRate(this.CaptureFraction, this.ClausingFactor, FinalDynamicalQuantities);
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%% Save
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%if this.DoSave
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%end
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end
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