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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

    http://www.google.com/url?sa=t&sour...-cSxBA&usg=AFQjCNG_R_1TVNZD-9KTusPR3vJO_T9_eA.

    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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