A technical limitation of accelerators having an accelerating field that does not vary with time is that at voltages of a few MeV/meter, air breaks down, allowing the formation of conducting paths to ground. At low electric field values, air is a good insulator; electrons attach to atoms faster than they are knocked loose by collisions. However, when the electric field strength becomes high enough, electrons are knocked loose by collisions faster than they recombine with atoms. When such breakdown occurs, there can be arcing through the air, and the electrodes of the accelerator will discharge. The mechanism for lightning is similar; when enough charge collects in localized regions of clouds, the resulting high fields cause creation of conducting paths to ground via ionization of the atoms in the atmosphere.

Notice that the conducting surfaces of the Cockroft-Walton are smooth, avoiding sharp points in favor of larger radiuses of curvature. Charge collects at points, making the electric field near the surface of those places larger than elsewhere. Given the same electric potential, the electrodes with smoother shapes are less susceptible to breakdown.

There is a model demonstrating this explicitly in The Feynman Lectures (ISBN 0-201-02117-X Addison-Wesley Publishing Company), the gist of which is repeated here. Suppose there are two conducting spheres connected by a conducting wire, as shown in the figure below.

To be complete, there are two large electrostatic accelerators used in the Fermilab accelerating complex.The Cockroft-Walton is the first stage of acceleration for the entire complex of accelerators, taking H- ions up in energy to 750 KeV before they are injected into the Linear accelerator.The Pellatron is a 4.3 MV electrostatic accelerator used to produce a high current beam of electrons (.5 amps in 2005). This electron beam is used for the specific purpose of cooling antiprotons in the Recycler Ring, and is used only in one section of that storage ring. The electron beam is transported from the Pelletron into a section of the Recycler Ring,where it then co-propagates with the antiprotons for about 20 meters, so as to cool the antiprotons. The electron beam then returns to the Pelletron to complete the circulation path.

Electrostatic accelerators provide steady electric fields for acceleration via charged electrodes.Somehow the electrodes must be charged up. Van de Graaf accelerators, one of the earliest types of electrostatic accelerators, charged up the electrode via a moving belt; the belt carried charges and deposited them on the conductor. A Pelletron is an electrostatic accelerator with an improved belt design; it has a moving belt made of metal pellets connected with nylon links to carry the charge.