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Perfecting the Magnetic Bottle

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Abstract

The last chapter had a lot of information in it, so let us recapitulate. To get energy from the fusion of hydrogen into helium as occurs in the sun and other stars, we have to make a plasma of ionized hydrogen and electrons and hold it in a magnetic bottle, since the plasma will be too much hot to be held by any solid material. The way a magnetic field holds plasma particles is to make them turn in tight circles, called Larmor orbits, so that they cannot move sideways across magnetic field lines. However, the ions and electrons can move along the field lines in their thermal motions without restraint. Consequently, the magnetic container has to be shaped like a doughnut, a torus, so that the field lines can go around and around without ever running into the walls. The field lines also have to be twisted into helices to avoid a vertical drift of the particles that occurs in a torus but not in a straight cylinder. Ideally, each field line will trace out a magnetic surface as it goes around many times without ever coming back exactly on itself. The plasma is then confined on nested magnetic surfaces which never touch the wall. This ideal picture will be modified in this and later chapters as we understand more about the nature of these invisible, nonmaterial containers.

Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

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Notes

  1. 1.

    Notes

    The data are from Bosch and Hale [1]. The vertical axis is actually reactivity in units of 1016 reactions/cm3/sec.

  2. 2.

    Such data were originally given by Post [2] and have been recomputed using more current data.

  3. 3.

    What is actually shown here is an equipotential of the electric field, which is the path followed by the guiding centers in an E  ×B drift. The short-circuiting occurs when the spacing becomes smaller than the ion Larmor radius, so that the ions can move across the field lines to go from the positive to the negative regions on either side of the equipotential. The curves are measured, not computed.

References

  1. H.S. Bosch, G.M. Hale, Nucl. Fusion 32, 611 (1992)

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  2. R.F. Post, Rev. Mod. Phys. 28, 338 (1956)

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  3. F.F. Chen, Observations of X-rays from the Stellarator (USAEC, Washington, DC, 1955) Tech Rept. 289, pp. 297–302

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  4. D. Mosher, F.F. Chen, Convective losses in a thermionic plasma with shear. Phys. Fluids 13, 1328 (1970)

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  5. L. Spitzer, R. Härm, Phys. Rev. 89, 977 (1953), summarized in Physics of Fully Ionized Gases, 2nd edn, by L. Spitzer, Jr. (Wiley-Interscience, New York, 1962)

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Chen, F.F. (2011). Perfecting the Magnetic Bottle. In: An Indispensable Truth. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7820-2_5

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