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Tokamak Transformer Properties

  1. Sep 10, 2010 #1
    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

    http://books.google.com/books?id=pPqq7EvBDZkC&lpg=PA154&dq=plasma%20physics%20Eliezer&pg=PA128#v=onepage&q=transformer&f=false [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 10, 2010 #2
    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
  4. Sep 11, 2010 #3
    Thank you for your reply. So the saturation of the iron must be dealt with somehow, and this would cause the mentioned interruption?
  5. Sep 11, 2010 #4
    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
  6. Sep 11, 2010 #5
    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
  7. Sep 11, 2010 #6
    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


    and reading about betatrons in Chapter 11. Now, after reviewing the equations for the betatron accelerator, apply them to ITER.

    Bob S
  8. Sep 12, 2010 #7
    Thank you for your reply, and also for the download site. The book I linked to did not go deep enough for me to explore the topic further, the book you provided seems to do the trick.
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