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Biconic cusps

The biconic cusp was an early method for modeling plasma confinement.[1] They were studied at the Courant Institute by Harold Grad in the late 1950s and early 1960s.


The magnetic fields in this system were made by electromagnets placed close together. This was a theoretical construct used to model how to contain plasma. The fields were made by two coils of wire facing one another. These electromagnets had poles which faced one another and in the center was a null point in the magnetic field. This was also termed a zero point field. These devices were explored theoretically by Dr. Harold Grad at NYU's Courant Institute in the late 1950s and early 1960s.[2][3][4] Because the fields were planar symmetric this plasma system was simple to model.

Particle behavior[edit]

Simulations of these geometries revealed the existence of three classes of particles.[5] The first class moved back and forth far away from the null point. These particles would be reflected close to the poles of the electromagnets and the plane cusp in the center. This reflection was due to the magnetic mirror effect.[6][7] These are very stable particles, but their motion changes as they radiate energy over time. This radiation loss arose from acceleration or deceleration by the field and can be calculated using the larmor formula.[8] The second particle moved close to the null point in the center. Because particles passed through locations with no magnetic field, their motions could be straight, with an infinite gyroradius. This straight motion caused the particle to make a more erratic path through the fields. The third class of particles was a transition between these types. Biconic cusps were recently revived because of its similar geometry to the Polywell fusion reactor.[9]


  1. ^ Containment in a cusped Plasma System, Dr. Harold Grad, NYO-9496
  2. ^ J Berowitz, H Grad and H Rubin, in proceedings of the second United Nations International conference on peaceful uses of atomic energy, Geneva, 1958, Vol 31, Page 177
  3. ^ Grad, H. Theory of Cusped Geometries, I. General Survey, NYO-7969, Inst. Math. Sci., N.Y.U., December 1, 1957
  4. ^ Berkowitz, J., Theory of Cusped Geometries, II. Particle Losses, NYO-2530, Inst. Math. Sci., N.Y.U., January 6, 1959.
  5. ^ The motion of a charged particle near a zero field point. New York: New York University: Courant Institute of Mathematical Sciences,. 1961.  |first1= missing |last1= in Authors list (help)
  6. ^ M. P. Srivastava and P. K. Bhat (1969). Motion of a charged particle in superposed Heliotron and biconical cusp fields. Journal of Plasma Physics, 3, pp 255-267. doi:10.1017/S0022377800004359.
  7. ^ F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, New York, 1984), Vol. 1, pp. 30–34. ISBN 978-0-306-41332-2
  8. ^ J. Larmor, "On a dynamical theory of the electric and luminiferous medium", Philosophical Transactions of the Royal Society 190, (1897) pp. 205–300 (Third and last in a series of papers with the same name)
  9. ^ Low Beta Confinement in a Polywell Modeled with conventional point cusp theories, Physics of Plasma 18.112501 (2011)

Further reading[edit]

Biconic cusp simulation work


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