38 lines
1.3 KiB
Mathematica
38 lines
1.3 KiB
Mathematica
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function ret = angularDistributionFunction(this, theta)
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%This function calculate the angle distribution of atoms coming out
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%from a single channel.
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KnudsenNumber = this.MeanFreePath/this.NozzleLength;
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alpha=0.5 - (3*this.Beta^2)^-1 * ...
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((1 - (2*this.Beta^3) + ((2*this.Beta^2) - 1) * sqrt(1+this.Beta^2)) / ...
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(sqrt(1+this.Beta^2) - (this.Beta^2 * asinh((this.Beta^2)^-1))));
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eta0 = alpha;
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eta1 = 1 - alpha;
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delta = (eta0./sqrt(2*KnudsenNumber*(eta1-eta0)))./sqrt(cos(theta));
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F = 2/sqrt(pi)* (1-eta1)/eta0 * delta.* exp( -(delta*eta1/eta0).^2 );
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q = this.Beta^-1 * tan(theta);
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R = acos(q) - (q .* sqrt(1-q.^2));
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if abs(q) >= 1
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t = linspace(0,1,10000);
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S = sum(sqrt(1-t.^2).* ( erf(delta.*(1 + (t.*(eta1-eta0)./(q.*eta0)) ))-erf(delta)))*(t(2)-t(1));
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if S == 0 || isnan(S)
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ret = eta0*cos(theta);
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else
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ret = eta0*cos(theta)+ 2/sqrt(pi)*eta0*cos(theta) * (exp(delta.^2)/delta) * S;
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end
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else
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t = linspace(0,q,10000);
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S = sum(sqrt(1-t.^2).* ( erf(delta.*(1 + (t.*(eta1-eta0)./(q.*eta0)) ))-erf(delta)))*(t(2)-t(1));
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if isnan(S)
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S=0;
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end
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ret = 2/sqrt(pi)*eta0*cos(theta)*(exp(delta.^2)/delta) * (R./2*(erf(delta*eta1/eta0)-erf(delta)+F)+S)+eta0*cos(theta);
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end
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end
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