Well I am not sure if you are able to get your hands on an alpha emitter since they can be quite expensive and due to the safety issues radioactive sources might not be readily available to an average user.
However I can tell you a little bit about the science behind this demo. Alpha particles are charged particles - they have 2 protons and two neutrons and no electrons. So the effective charge is 2+. Due to this fact, alpha particles interact with matter and pick up electrons really quickly - their path lenght is on the order of a few centimeters.
So the point of making "the cloud" as you call it, is to have a very dense (hence visible) gas. When alpha particles go through this gas they pick up electrons from the collisions with the gas molecules and the electron transfers occur. That's what you would observe in this case as trails of alpha particles.