Velocity distribution for Molecular beam vs. gas In the book: https://g.co/kgs/JRBLeA (Atomic Physics by C.J. Foot) on page 152 there's a table in the end that compares gas' velocity distribution and that for a molecular beam. I am unable to account for the extra velocity/speed factor in the latter. 

I understand that the former has a Maxwell Boltzmann distribution.
The text mention, on the same page, that this extra factor is attributed to the observation that faster atoms a more likely to effuse through a hole of area A compared to slower atoms. I don't understand why this should be so. First of all, if you have an atom beam (say) traveling with a particular velocity, how do you associate the concept of temperature to this?
 A: You probably know how to derive an expression for the pressure in the context of the kinetic gas theory.  If we use this line of argument, but we were interested only in the collisions between the molecules and the small area (=hole) within the wall, we have to ask: If a particle exists the hole during the time interval $[0, dt]$, where does it come from? 
Assuming that the particle has velocity $v$, and that no collision takes place in the time interval $[0, dt]$ the particles must come from the volume which is ${\bf ds} = {\bf v}\cdot dt$ away from the hole. Or, more precisely, they must come from a volume $V = {\bf A} \cdot {\bf ds} = A \, v dt \cdot \cos{\theta}$, where $\theta$ is the angle of the veclocity to the normal direction of the hole. The key point here is that particles with a "larger" velocity are allowed to be further way at time $t=0s$. Thus, "very fast" particles have a non-zero probability to exit the hole, no matter where they are at time $t=0s$, while "slow" particles must come from the direct surrounding of the hole. Proper derivations can be found in statistical physics textbooks.

[...] if you have an atom beam [...] traveling with a particular velocity, how do you associate the concept of temperature to this?

If we take about a gas having temperature $T$ we implicitly assume a random velocity distribution, where the atoms possess different velocities. Also, temperature uses the concept of an ensemble of particles -- we are unable to associate a temperature with a single particle, which happens to have the kinetic energy $k_B T$. So, if we use a velocity filter to generate a beam of particles with the velocity range $v + [0, dv]$, we should not use the term temperature to describe it.
However, it is conceptional fine to use the small hole in the wall of the container to generate a beam of particles, which is used probe the distribution of the ensemble inside the container.
