helicity

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helicity

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helicity (countable and uncountable, plural helicities)

1. The quality of being helical.
2. (physics, fluid mechanics, electrodynamics) Any of certain measures of the extent to which vortex lines (in fluid flow) or field lines (in a magnetic or electromagnetic field) kink and twist and/or link and coil around one another.
   • 1991, E. Levich, L. Shtilman, “Helicity Fluctuations and Coherence in Developed Turbulence”, in D. Schertzer, S. Lovejoy, editors, Non-Linear Variability in Geophysics: Scaling and Fractals, Kluwer Academic Publishers, page 18:

     The conjecture made in Tsinober and Levich (1983) was that coherent structures should possess a significant coherent helicity.

   • 1995, G. E. Marsh, “2: Helicity and Electrodynamic Field Topology”, in Terence William Barrett, Dale M. Grimes, editors, Advanced Electromagnetism: Foundations, Theory and Applications, World Scientific, page 62:

     The helicity associated with the writhing number is obtained by observing that a torus with twist number ±1 may be distorted into a figure-8 configuration which appears untwisted. […] Note that at each step the total helicity, consisting of the sum of twist, kink, and link helicities, is conserved.

   • 2001, Mitchell A. Berger, “Measures of Topological Structure in Magnetic Fields”, in Renzo L. Ricca, editor, An Introduction to the Geometry and Topology of Fluid Flows, Springer, page 249:

     Thus the total helicity H equals the sum of the entries in a matrix H_ij. If N is large then there will be many more mutual helicity terms. In this case ignoring the self helicities (if they are difficult to observe) may only give a small error.

   • 2016, Eric G. Blackman, “Magnetic Helicity and Large Scale Magnetic Fields: A Primer”, in Andre Balogh, Andrei Bykov, Jonathan Eastwood, Jelle Kaastra, editors, Multi-scale Structure Formation and Dynamics in Cosmic Plasmas, Springer,, page 72:

     Now conservation of helicity is maintained: the writhe of the loops in the second panel is compensated for by the opposite sign of the twist helicity along the loops.

3. (physics, quantum mechanics) The quantized spin component of a moving particle along the direction of its motion.
   • 1989, John Taylor, 17: Gauge theories in particle physics, Paul Davies, The New Physics, Cambridge University Press, 1992, 1st Paperback Edition, page 467,

     To understand this name, note that the helicity is, roughly speaking, the spin in the direction of motion.

   • 1999, Gustavo Castelo Branco, Luís Lavoura, João Paulo Silva, CP Violation, Oxford University Press, page 12:

     The experiment was particularly ingenious because, as the neutrino hardly interacts with matter, some way of indirectly measuring its helicity had to be devised.

   • 2010, Franz Mandl, Graham Shaw, Quantum Field Theory, Wiley, page 151:

     Interpreted in terms of helicity, this means that if the incident electron has positive helicity, then the outgoing electron has positive helicity for forward scattering, and negative helicity for backward scattering.

• hydrodynamical helicity
• magnetic helicity

• chirality
• linking number
• vorticity