Diameter and length of filament with X-ray tube are?
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. The filament is mounted between two stiff support wires that carry an electrical current. These two mounting wires lead through the glass envelope and connect to both the high-voltage and the low-voltage electrical sources. The filament is heated to incandescence by the flow of current from the low-voltage source and emits electrons at a rate proportional to the temperature of the filament.
Reference: White and Pharoah's Oral Radiology Principles and Interpretation 7th edition page no 5
3 mm ; 2 cm
2 cm ; 3 mm
2 mm ; < 1 cm
4 mm ; 1 cm