What should be the diameter of tungsten filament used as cathode?
The cathode  in an x-ray tube consists of a filament and a focusing cup. The filament is the source of electrons within the x-ray tube. It is a coil of tungsten wire about 2 mm in diameter and 1 cm or less in length. Filaments typically contain about 1% thorium, which greatly increases the release of electrons from the heated wire.
Ref: Oral Radiology, Principles and Interpretation / Stuart C. White, Michael J. Pharoah - 7th ed - pg - 4
1 mm in diameter
2 mm in diameter
1 cm in diameter
2 cm in diameter