# Helicon (physics)

A helicon is a low frequency electromagnetic wave that can exist in plasmas in the presence of a magnetic field. The first helicons observed were atmospheric whistlers,[1][2] but they also exist in solid conductors[3][4] or any other electromagnetic plasma. The electric field in the waves is dominated by the Hall effect, and is nearly at right angles to the electric current (rather than parallel as it would be without the magnetic field); so that the propagating component of the waves is corkscrew-shaped (helical) - hence the term “helicon,” coined by Aigrain. [5]

Helicons have the special ability to propagate through pure metals, given conditions of low temperature and high magnetic fields. Most electromagnetic waves in a normal conductor are not able to do this, since the high conductivity of metals (due to their free electrons) acts to screen out the electromagnetic field. Indeed, normally an electromagnetic wave would experience a very thin skin depth in a metal: the electric or magnetic fields are quickly reflected upon trying to enter the metal. (Hence the shine of metals.) However, skin depth depends on an inverse proportionality to the square root of angular frequency. Thus a low frequency electromagnetic wave may be able to overcome the skin depth problem, and thereby propagate throughout the material.

One property of the helicon waves (readily demonstrated by a rudimentary calculation, using only the Hall effect terms and a resistivity term) is that at places where the sample surface runs parallel to the magnetic field, one of the modes contains electric currents that “go to infinity" in the limit of perfect conductivity; so that the Joule heating loss in such surface regions tends to a non-zero limit.[6][7][8] The surface mode is especially prevalent in cylindrical samples parallel to the magnetic field, a configuration for which an exact solution has been found for the equations, [6][9] and which figures importantly in subsequent experiments.

The practical significance of the surface mode, and its ultra-high current density, was not recognized in the original papers, but came to prominence a few years later when Boswell[10][11] discovered the superior plasma generating ability of helicons – achieving plasma charge densities 10 times higher than had been achieved with earlier methods, without a magnetic field.[12]

Since then, helicons found use in a variety of scientific and industrial applications – wherever highly efficient plasma generation was required,[13] as in nuclear fusion reactors[14] and in space propulsion (where the Helicon double-layer thruster[15] and the Variable Specific Impulse Magnetoplasma Rocket[16] both make use of helicons in their plasma heating phase). Helicons are also utilized in the procedure of plasma etching,[17] used in the manufacture of computer microcircuits.[18]

A helicon discharge is an excitation of plasma by helicon waves induced through radio frequency heating. The difference between a helicon plasma source and an inductively coupled plasma (ICP) is the presence of a magnetic field directed along the axis of the antenna. The presence of this magnetic field creates a helicon mode of operation with higher ionization efficiency and greater electron density than a typical ICP. The Australian National University, in Canberra, Australia, is currently researching applications for this technology. A commercially developed magnetoplasmadynamic engine called VASIMR also uses helicon discharge for generation of plasma in its engine. Potentially, Helicon Double Layer Thruster plasma based rockets are suitable for interplanetary travel.

## Experiment

A simple experiment can be conducted with fairly affordable equipment, and may be found in university-level undergraduate advanced physics laboratory courses.[19][20] A metal such as 99.999% pure indium is commonly used: it is cooled using liquid helium to reach the conditions of low temperature, while the high magnetic field is accomplished using a superconducting solenoid. Ultimately, the experiment characterizes the resonance frequency and resonance width of the helicon standing waves. It can also be used to measure the magnetoresistance and Hall coefficients of the pure metal.

## References

1. ^ Storey, L. R. O. (9 July 1953) "An investigation of whistling atmospherics". Philosophical Transactions of the Royal Society A. 246 (908): 113. DOI: 10.1098/rsta.1953.0011.
2. ^ Darryn A. Schneider (1998). Helicon Waves in High Density Plasmas (Ph.D thesis). Australian National University.
3. ^ Bowers, R., Legéndy, C. R., and Rose, F. E. (November 1961) "Oscillatory galvanomagnetic effect in metallic Sodium". Physical Review Letters 7 (9): 339-341. DOI: 10.1103/PhysRevLett.7.339.
4. ^ B.W. Maxfield (1969). "Helicon Waves in Solids". American Journal of Physics. 37 (3): 241–269. Bibcode:1969AmJPh..37..241M. doi:10.1119/1.1975500.
5. ^ Aigrain, P. (1961) Proceedings of the International Conference on Semiconductor Physics (Publishing House of the Czechoslovak Academy of Science, Prague, 1961) p. 224.
6. ^ a b Legéndy, C. R. (September 1964) "Macroscopic theory of helicons". The Physical Review 135 (6A): A1713-A1724. DOI:10.1103/PhysRev.135.A1713.
7. ^ Goodman, J. M. and Legéndy, C. R. (May 1964) "Joule loss in a 'perfect' conductor in a magnetic field". Cornell University Materials Science Center Report No. 201.
8. ^ Goodman, J. M. (15 July 1968) "Helicon waves, surface-mode loss, and the accurate determination of the Hall coefficients of Aluminum, Indium, Sodium, and Potassium". Physical Review 171 (1): 641-658. DOI: 10.1103/PhysRev.171.641.
9. ^ Klozenberg, J. P., McNamara, B., and Thonemann, P. C. (March 1965) "The dispersion and attenuation of helicon waves in a uniform cylindrical plasma". Journal of Fluid Mechanics 21 (3): 545-563. DOI:10.1017/S0022112065000320.
10. ^ Boswell, R. W. (July 1970) "A study of waves in gaseous plasmas". Ph.D. Thesis, School of Physical Sciences, Flinders University of South Australia. (http://people.physics.anu.edu.au/~rwb112/hr/index.htm#Boswell_Thesis_directory)
11. ^ Boswell, R. W. (October 1984) "Very efficient plasma generation by whistler waves near the lower hybrid frequency". Plasma Physics and Controlled Fusion 26 (10): 1147–1162. DOI:10.1088/0741-3335/26/10/001.
12. ^ Boswell, R. W. and Chen F. F. (December 1997) "Helicons – the early years". IEEE Transactions on Plasma Science 25 (6): 1229–1244. DOI: 10.1109/27.650898.
13. ^ Chen, F. F. (December 1996) "Helicon plasma sources" in: High Density Plasma Sources: Design, Physics and Performance, Oleg A. Popov (ed) (Elsevier-Noyes) print ISBN 978-0-8155-1377-3, ebook ISBN 978-0-8155-1789-4.
14. ^ Marini, C., Agnello, R., Duval, B. P., Furno, I., Howling, A. A., Jacquier, R., Karpushov, A. N., Plyushchev, P., Verhaegh, K., Guittienne, Ph., Fantz, U., Wünderlich, D., Béchu, S., and Simonin, A. (January 2017) "Spectroscopic characterization of H2 and D2 helicon plasmas generated by a resonant antenna for neutral beam applications in fusion." Nuclear Fusion 57:036024 (9pp) DOI:10.1088/1741-4326/aa53eb
15. ^ Charles, C., Boswell, R. W., and Lieberman, M. A. (December 2006) "Xenon ion beam characterization in a helicon double layer thruster." Applied Physics Letters 89:261503 (3 pgs) DOI: 10.1063/1.2426881.
16. ^ Longmier, B. W., Squire, J. P., Cassady, L. D., Ballenger, M. G. Carter, M. D., Olsen, C., Ilin, A. V., Glover, T. W., McCaskill, G. E., Chang Diaz, F. R., Bering III, E. A., and Del Valle, J. (September 2011) “VASIMR® VX-200 Performance Measurements and Helicon Throttle Tables Using Argon and Krypton.” 32nd International Electric Propulsion Conference, held in Wiesbaden, Germany, September 11-15, 2011 (Wiesbaden: IEPC-2011-156).
17. ^ Boswell, R. W. and Henry D. (15 November 1985) "Pulsed high rate plasma etching with variable Si/SiO2 selectivity and variable Si etch profiles". Applied Physics Letters 47 (10): 1095–1097 DOI: 10.1063/1.96340.
18. ^ Poulsen, R. G. (1977) "Plasma etching in integrated circuit manufacture – A review" Journal of Vacuum Science and Technology 14 (1): 266 DOI: 10.1116/1.569137
19. ^ J.R. Merrill; D. Pierce; D. Giovanielli (1970). "A Helicon Solid-State Plasma Experiment for the Advanced Laboratory". American Journal of Physics. 38 (1): 417–420. Bibcode:1970AmJPh..38..417M. doi:10.1119/1.1976357.
20. ^ J.Harlow and J. Pitre (2011). Helicons in Metals (PDF) (Report). University of Toronto.