# Tokamak Transformer Properties

1. Sep 10, 2010

### teroenza

Hello all,
I am a layman who is interested in nuclear fusion via magnetic confinement (the Tokamak setup). I recently read in a book about how the (a) transformer in the device could operate only for some number of "volt-seconds" before it had to be "recharged". This requires an additional outside source to keep the plasma temp. up in the meantime. I have never heard of this property of transformers. Is this something unique to this type of device, or a fundamental concept I missed?

Thank you

Google books page link, the specific text is on page 128

Last edited by a moderator: May 4, 2017
2. Sep 10, 2010

### Bob S

For the usual Faraday induction law the voltage on the secondary is:

V = - A·dB/dt (volts)

where V is the output voltage (per turn), A is the coil area, and dB/dt is the rate of change of the primary magnetic field. Rewriting this and integrating, we get

∫V·dt = - A·∫dB , or

V·Δt = - A·ΔB (volt seconds).

The volt-seconds limit is when the ΔB reaches the maximum due to current limit, or the iron saturates. This is why sometimes 60-Hz transformers will not work properly on 50-Hz power.

Bob S

3. Sep 11, 2010

### teroenza

Thank you for your reply. So the saturation of the iron must be dealt with somehow, and this would cause the mentioned interruption?

4. Sep 11, 2010

### Bob S

To maintain a constant poloidal voltage per turn, or poloidal electric field, you need a constant dB/dt (constantly increasing B), which means a constantly increasing excitation current. Running out of excitation current or out of iron relative permeability μ will cause the volt-seconds accumulation to stop. ITER needs over ~200 (~270?) volt seconds.

Bob S

5. Sep 11, 2010

### teroenza

And when the volt-second accumulation stops, this interrupts the operation of the transformer long enough to require the additional input to retain temperature and confinement? Also, you speak of ITER "needing" 200-270 volt-seconds. Do you mean that its transformer is "good for" or can sustain the conditions for that period of time before needing to be "recharged"? Finally, I know this is more complicated than I currently understand, but if an excitation current is needed for the poloidal field, why is a transformer necessary for that current (as opposed to directly energizing those coils).

Thank you

6. Sep 11, 2010

### Bob S

The idea for the poloidal electric field (volt-seconds) is the basic concept for the betatron accelerator. In the betatron, a constantly changing magnetic field f produces an azimuthal electric field. The same magnet in the betatron produces a vertical magnetic field to force the electrons into a circular orbit. So there are two separate functions of the magnetic field in a betatron: 1) the magnetic field forces the charged particles into a circular orbit, and 2) a changing magnetic field produces an azimuthal electric field to accelerate the charged particles. This latter effect is limited by volt-seconds. Read about betatrons by downloading the book "Principles of Particle Accelerators" (free) at