Homemade particle accelerator Watching a documentary, I heard Michio Kaku telling that when he was young, he built a home-made particle accelerator. What I would like to know is if I, myself can do so? And how?
 A: Well, there are a lot of different types of particle accelerators.
Besides the already suggested cathode ray tube, another rather small accelerator would be a cyclotron. The first one was built by Lawrence and Livingston, "a device about 4.5 inches in diameter used a potential of 1,800 volts to accelerate hydrogen ions up to energies of 80,000 electron volts." I guess it would be possible to get a high voltage power source and hydrogen, but really building a working device would probably take a long time.
A: It is not so hard, but it won't be able to generate enough high energetic particles.
The best example for a particle accelerator is a CRT (cathode ray tube), which you can find in every CRT monitor or TV. It can generate around $40\rm\,keV$ electrons. (LHC generates $3.5\rm\,TeV$ protons, thus it is around a hundred million times stronger).
Only a particle accelerator isn't enough, if you want to make experiments with it, you need some analytic/measurements devices also. In the current accelerators, they are nearly so complex and costly as the main accelerating device.
There is also a device capable to be built in home, it is the Farnsworth fusor:

Maybe it is not a particle accelerator in the classical sense, it creates enough strong field to be able to fuse deuterons (although it is doing this with terrible efficiency, around $10^{-8}$). You can see a Farnsworth fusor scematic below: 

(source: fusor.net) 
There is a whole community of home fusors which can be found here.
A: Particle accelerator that can fit on a tabletop opens new chapter for science research
June 20, 2013 - sourced by University of Texas at Austin

The laser plasma accelerator has accelerated about half a billion
  electrons to 2 gigaelectronvolts over a distance of about 1 inch. It's
  a downsizing of a factor of approximately 10,000, and marks a major
  milestone in the advance toward the day when multi-gigaelectronvolt
  laser plasma accelerators are standard equipment in research
  laboratories around the world.

