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.

I thought alpha particles were electrons. Beta particles were 2 protons and 2 neutrons and Gamma rays were just energy.

O well I'll take your word for it though.

Nope.  An alpha particle is the nucleus of a Helium atom;  Two protons and Two neutrons.  A beta particle is a high energy electron.  A gamma ray is like a very high energy light source.  

The emission of gamma rays is like the emission of light from an excited electron.  When you put a metal ion into a fire, the electrons get excited up to the next energy level, then fall back down emitting a characteristic wavelength of light.  When a nucleus undergoes decay, it winds up in an excited state.  The nucleus then gives off a gamma ray of a VERY specific energy as it falls back down into the ground state.  So excited electrons give off light when they go back to ground, and excited nuclei give off a very short wavelength of light known as a gamma ray when they fall back down to ground.