Methods and devices for producing an electron beam

An electron gun, comprising:

• a paraelectric cathode including:
• a paraelectric layer, of paraelectric material, having a proximal face and a distal face, said paraelectric layer sandwiched between:
• on said proximal face, a back electrode;
• and
• on said distal face, a front electrode including at least one hole,
• said hole providing fluid communication between said distal face of said paraelectric layer and a volume distal to said front electrode.