Modeling Velocity Distribution in Matlab

[msgreyson]

I'm having some hang ups while trying to model what is probably a fairly simply velocity distribution in matlab.

It's just an effusive atomic beam exiting from a small circular aperture with negligible thickness. I have figured out the equations to use for the speed distribution of the atoms leaving the aperture, and the angle at which they leave, which matches our experimental setup.

Probability(speed) goes as A(speed^2)exp(-speed^2/B)exp(-C/speed)
Probability(angle) goes as cos(theta)

Ultimately, I'm trying to find an expression for the probability distribution of the longitudinal and transverse atom velocities relative to the direction of propagation of the atom beam. I think I'm having issues conceptualizing it since it seems to me that the velocity distribution in any direction will depend on both the angle and the speed of the atom.

Just considering the longitudinal velocity distribution, I can easily model the speeds without applying the angles. Applying the angular distribution should, I think, cause the longitudinal distribution to widen but ultimately stay in the same place, since the highest probability of angle to to continue going straight in the longitudinal direction. Yet simply multiplying the two probabilities moves the curve to the realm of higher velocities in the longitudinal.

Perhaps it's an issue of indexing in my coding or something along those lines. But if anyone is willing to offer advice or has any questions that might nudge me in a useful direction as to the physics here, it would be greatly appreciated.

 

[BigJDubs]

Thanks!The way I would approach this problem is to use a Monte Carlo simulation. Essentially, you generate a large sample of atom speeds and angles, and then calculate the corresponding longitudinal and transverse velocities. You can then plot the histograms of the longitudinal and transverse velocities to get a good approximation of the velocity distribution. You can also use the Monte Carlo method to calculate the expected value of the longitudinal and transverse velocities given the speed and angular distributions.