PPPL
QUIZ: INTRODUCTION TO MAGNETIC CONFINEMENT
The fundamental concepts of magnetic confinement of plasmas are reviewed.

(click on a question to show/hide answers)
1. What is a tokamak?
  • 1.  A tokamak is a device for timing fluctuations in plasma transparency. The word is derived from the “tik-tok” sound emanating from the rather clumsy clocks (by today's standards) that were used in the early 1950s.

    2.  A tokamak is a nominally axisymmetric, toroidal magnetic confinement device used for confining plasmas to high temperature, high density, and for a sufficiently long time.

    3.  A tokamak is a type of “bot” used in automated warehouses to transport shipping boxes. (The word “bot” is also used to describe an automated or semi-automated tool used to edit Wikipedia; see the Wikipedia article.)

    4.  A tokamak is an abbreviation of the difficult-to-pronounce word, “tokamatroneomous”, which refers to a disfunction of automated feedback control systems for artificially enhanced, artificially intelligent humanoids, which are presently under-development in a secret government research facility being built on Mars.

    [#q12]

    (click here to show/hide answer)

      The correct answer is 2
      Charged particles feel the effects of electic and magnetic fields, and magnetic fields can be created by electric currents. The idea of the tokamak is to create a magnetic field that “confines” the plasma to an enclosed region. The “toroidal” magnetic field is produced by external current-carrying coils, and the “poloidal” magnetic field is produced by currents internal to the plasma. See the Wikipedia article on tokamaks.
2. What is a stellarator?
  • 1.  A stellarator is a gyroscopic “star machine” used to stabilize the vertical position of rockets on launch.

    2.  A stellarator is a non-axisymmetric, toroidal, magnetic confinement device used for confining plasmas to high temperature, high density, and for a sufficiently long time.

    3.  A stellarator is plasma that machine that performs superbly, e.g. “that was a stellar plasma”. The word stellar means “of or relating to the stars, or brilliant”.

    [#q13]

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      The correct answer is 2
      A stellarator is an toroidal magnetic confinement device used for confining plasmas to high temperature, high density, and for a sufficiently long time. The majority of the magnetic field is produced , i.e. by current-carrying coils. Consequently, stellarators are more stable than tokamaks, because a perturbation to the internal plasma current does not significantly perturb the magnetic field; however, this comes at a cost. To produce the “rotational-transform” required for confinement, stellarators must be non-axisymmetric and this degrades the particle confinement, and so stellarators, historically, have higher transport than compared to tokamaks (which is bad); but stellarators come in many shapes, and modern design insights allow the particle transport to be reduced (which is good).
3. What is “rotational-transform” ?
  • 1.  The rotational transform, ${\cal M}$, is a mathematical term describing the “diagonality” of a linear transformation of coordinates.

    2.  The rotational-transform, $\iota\!\!\!$-, quantifies the ratio of how many times a magnetic fieldline traverses the torus the short way around (poloidally) divided by how many times a magnetic fieldline traverses the torus the long way around (toroidally).

    3.  The rotational-transform, $q$, quantifies how many times an electron spirals about a nucleus before the electic attraction to the proton results in a fusion collision.

    4.  The rotational-transform, RT, measures the de-acceleration of magnetic fieldlines as they lose magnetic momentum from collisions with electric fieldlines.

    [#q14]

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      The correct answer is 2
      To cancel particle drifts caused by inhomogeneities of the toroidal magnetic fields, the magnetic fieldlines must wrap around the torus helically, and the rotational-transform measures how “tightly” (i.e. the pitch) the magnetic field lines twist. This quantity is important for determining the stability of the plasma equilibrium. Rotational-transform is the inverse of $q$, the so-called “safety-factor”.
4. Why are tokamaks and stellarators toroidal?
  • 1.  Generally, a torus, $\Gamma$, is an $n$-dimensional hypersurface, embedded in an $n-1$ subdimension, for which $\forall {\bf x} \in \Gamma$, then ${\bf x} \in \Gamma-1$. By reducing the dimensionality of space, improved compressional confinement is achieved.

    2.  Charged particles move freely along the magnetic fieldlines, and to prevent “end-losses” the magnetic fieldlines cannot leave the confinement region.

    3.  A basic theorem of topological geometry shows that any volume with minimal surface area to enclosed volume must be a torus.

    [#q15]

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      The correct answer is 2
      The simplest approximation to charged particle trajectories in strong magnetic fields is that the charged particle just follows along a magnetic fieldline; so, to confine charged particles we must first “confine” the magnetic fieldlines. Magnetic fields are “divergence-free”, which means that there are no magnetic “monopoles”, which more simply means that magnetic fieldlines have no beginning and no end. A torus is a doubly periodic, two-dimensional surface embedded in three-dimensional space. The simplest torus is something that looks like a donut. Not just any old donut, but specifically a donut with a hole in the middle. It is easy enough to imagine drawing an infinitely long line on a donut that wraps around helically and never crosses another line (but which may “bite its own tail” after some number of turns).
5. What is “flux surface” ?
  • 1.  A flux surface is a surface of constant electro-magnetic oscillations.

    2.  A flux surface is the initial position of the plasma before it submerges into the magnetic field for de-activation.

    3.  A flux surface is a two-dimensional, toroidal surface on which the magnetic field is tangential.

    [#q19]

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      The correct answer is 3
      For the most part, tokamaks and stellarators must have a large volume of space “filled” with flux surfaces. Flux surfaces are surfaces on which magnetic fieldlines wrap around for ever, while never leaving the confinement region. As charged particles, for the most part, move freely in the direction parallel to the magnetic field, the most important challenge of magnetic confinement is to create magnetic fields that never leave the confined volume. This is achieved by constructing magnetic fields with fieldlines that lie on flux surfaces.
6. What is the “energy confinement time” ?
  • 1.  The energy confinement time quantifies how long energy is confined.

    2.  The question makes no sense: energy can neither be created nor destroyed, and energy cannot be “confined”. (Energy can, however, be transformed into mass.)

    3.  The correct expression is “magnetic energy decay time”, which quantifies the creation and dissipation time of the magnetic field.

    [#q29]

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      The correct answer is 1
      The thermal energy of a plasma decreases by heat conduction, and also by particle losses. Let $P_L$ denote the energy loss of the plasma per unit volume and per unit time (i.e. power loss / volume ), the “loss time”, $\tau$, also called the “energy confinement time”, is defined \begin{eqnarray} P_L \equiv \frac{3 n T}{\tau}, \end{eqnarray} where $n$ is the plasma density and $T$ is the plasma temperature.
      [1] K. Miyamoto, Plasma Physics for Nuclear Fusion, The MIT Press (1980)