X-ray source with multiple grids

An x-ray source comprising:

• a vacuum enclosure;
• an anode disposed in the vacuum enclosure;
• a plurality of field emitters disposed in the vacuum enclosure, each field emitter configured to generate an electron beam;
• a plurality of first grids, each first grid associated with a corresponding one of the field emitters and configured to control field emission from the corresponding field emitter;
• and
• a second grid disposed between the plurality of first grids and the anode.

A method of operating an x-ray source, comprising:

• applying a voltage to a first grid to control field emission from a field emitter to generate an electron beam;
• directing the electron beam toward an anode to generate x-rays;
• and
• applying voltages to a second grid and a third grid disposed between the first grid and the anode to alter an electric field between the first grid and the anode.