- Is the filament connected in this manner with the cathode as shown below?
Yes
- Now I know it isn't possible but I somehow connect an Ammeter at the battery end as shown below. Will I be able to get the current that has passed??
Yes. You will be able to measure the current flowing in the loop comprising the two power supplies, the X-ray diode, and the ground connection. It may be safer to install the ammeter in one of the ground connections, then it is at ground potential and so easier to read. It will read the same current as one connected where you show.
If yes then how? electrons are produced in the filament and are not flowing from the cathode of the battery to the anode physically. If the answer is No, then how is the current calculated that is passed??
Electrons are 'boiled off' (a metaphor summarising a lot of physics) the filament due to its high temperature. Electrons ARE accelerated through the electric field towards the anode. X-rays are produced as the electrons hit the anode and decelerate rapidly, releasing most of the kinetic energy they accumulated in their flight to the anode as heat. That's why the anode is shown as a very chunky lump of metal for heatsinking and high thermal capacity, and in some X-ray tubes will actually rotate to spread the heat load along a line on the anode rather than at a point. If you get an X-ray from one of these machines, you will hear a 'wheeee' just before the shot, which is the anode spinning up.
The diode current flows round the entire loop of both power supplies and the X-ray diode.
The cathode shown here is the 'directly heated' type. Most low voltage thermionic tubes use an 'indirect' cathode, where the cathode is electrically insulated from the heater. This means the entire cathode is at the same potential, so the cathode to other electrodes potential difference is consistent. When a cathode is directly heated, there is a potential drop along the filament, and the potential difference to other electrodes changes with position on the filament. With a low voltage tube, that can lead to a large fractional spread of electron energies at the anode. When there's 100 kV across the tube, a few volts difference due to a directly heated cathode is an insignificant fraction.
