A problem proposed by E. Hart to determine whether there are locally high or low neutron densities at the corners of a cubical cavity in a graphite lattice. To simplify the computations consider an infinite two dimensional lattice with a square cavity that has a point source of neutrons at the center (see Figure 1).

The free streaming of neutrons in a cylindrical cavity is investigated. Using experimental data for the flux distribution along the walls, the direct beam hole loss and leakage into the target from the lattice is estimated for the MTA system.

An empirical relation is presented which represents a boundary between no vacuum sparking and possible vacuum sparking. Metal electrodes and r.f. or d.c. voltages are used. The criterion fits several orders of surface gradient, voltage, gap, and frequency. Current due to field emission is considered necessary for sparking but in addition, energetic particles are required to initiate a cascade process which increases the field emission currents to the point of sparking. An elementary cascade process is outlined, but the data upon which it is based is not fully stated.