When a filament breaks that should not be the end of your world, a little dexterity and a little patience and within 20 minutes or so your should be back in action.  

Remove the cathode from the microscope CARE IT IS PROBABLY VERY HOT.

 Looking across the top of the cathode, using a hand lens as shown in the diagram, judge the angle between the lens and the cap when just visualising the tip of the “broken” filament.  Judge the angle required to just see the filament tip through the cathode aperture.

 Remove the cathode cap from the filament holding base.

  Place the cathode cap open side down in a beaker of 3 to 1 Ammonium hydroxide in water and ultrasonic for about 15 minutes until clean internally.

 See “Cleaning a Cathode Assembly” for more details of this procedure and safety guide lines.

Clean the base unit having removed the old filament once every three filament changes along with the anode.  Clean the two units separately as important faces should not be in contact with the beaker base or any other component as they must not become scratched.  

Fit a new filament and if the height adjusting devices have not been moved, replace the cathode cap and centre the filament as accurately as possible using a binocular microscope as your guide.   If the height setting devices have been moved set the cap well away from its lowest position and put it in place.  Gradually lower the cap using the data obtained about viewing angle to determine the filament to cap distance.  When satisfied lock the cap height system and continue as above to align the filament.