Jenifer Haselgrove

Jenifer Haselgrove (now Jenifer Leech) (born 1931) is a British physicist and computer scientist. She is most noted for her formulation of ray tracing equations in a cold magneto-plasma, now widely known in the radio science community ^{[http://www.ursi.org/]} as Haselgrove's Equations. [K. G. Budden : "The Propagation of Radio Waves: The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere" Cambridge University Press, 1988.] [ J. M. Kelso : "Radio Ray Tracing in the Ionosphere" McGraw-Hill, 1964.]

Haselgrove developed her equations at Cambridge University in the 1950's, as a student under Kenneth Budden, by re-applying the earlier work of William Rowan Hamilton and Hamilton's principle in geometrical optics [ A. W. Conway and J. L. Synge, The Mathematical Papers of Sir William Rowan Hamilton Vol 1. Gemoetrical Optics, London, Cambridge University Press, 1931.] to radio propagation in a plasma. [ Haselgrove, J.: 1955, Ray Theory and a New Method for Ray Tracing, London Physical Society Report of Conference on the Physics of the Ionosphere. pp. 355–364.] Indeed, the application of Haselgrove's equations is often termed Hamiltonian ray tracing. Ray tracing is intrinsically an approximation that is often called geometric. It formulates as the Eikonal equation and is only applicable under certain conditions including that the plasma is slowly varying; nevertheless it has enormous practical use in radio science. Other radio propagation scientists have developed various techniques to explore radio propagation in such media, [ J. M. Kelso : "Radio Ray Tracing in the Ionosphere" McGraw-Hill, 1964.] but Haselgrove's formulation has seen the most widespread application, most likely because the resulting set of differential equations readily lend themselves to numerical solution on a computer. Haselgrove herself used the Cambridge computer, EDSAC, to study ray propagation in the Earth's ionosphere in the late 1950's. ^{[http://www.cl.cam.ac.uk/conference/EDSAC99/reminiscences/]} Historically the most well known code applying Haselgrove's equations is the Jones-Stephenson code [Jones, R. M. and Stephenson, J. J. A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere, U. S. Department of Commerce, OT Report 75-76, 1975.] which was developed in the 1970's and may be found at the US Department of Commerce website.

Today Haselgrove's equations are widely used in scientific investigations involving radio propagation in slowly varying plasmas, and therefore have found much applicability in exploration and utilization of the Earth's ionosphere. Here they have also been used to represent the radio propagation element of practical systems providing high frequency communication, direction finding and over-the-horizon radar. For a recent broad disccusion on ray tracing in the ionosphere see Bennett et al. [ J.A. Bennett, P. L. Dyson, R. J. Norman, Progress in Radio Ray Tracing in the Ionosphere, The Radio Science Bulletin, September 2004, pg 81. ] Other publications applying Haselgrove's equations have recently appeared. [ C.J. Coleman, On the simulation of backscatter ionograms, J.A.T.P. 59, 16, pg 20-89, 1997.] [ R. I. Barnes, Faraday Rotation in a cold, inhomogeneous magneto-plasma: A numerical comparison of ray and full wave analyses, Rad. Sci. 32, 1523-1532, 1997.] [ X. Huang and B. Reinisch, Real-time HF ray tracing through a tilted ionosphere, Radio Science, 41,5, 2006] [ L.J. Nickisch, M.A. Hausman and S.V. Fridman, Range rate-Doppler correlation for HF propagation in TID environments, Radio Science 41, 2006.]

Haselgrove was married to British mathematician C. Brian Haselgrove ^{[http://www-groups.dcs.st-andrews.ac.uk/~history/Biographies/Haselgrove.html]} and published several highly cited, technical articles with him. [ For instance, C. B. Haselgrove and Jenifer Haselgrove, Twisted Ray Paths in the Ionosphere, Proc. Phys. Soc. 75 No 3 (1 March 1960) 357-363.] They are also credited for first solving the 6X10 Pentomino. Brian Haselgrove died in 1964, and Jenifer remarried to another British mathematician, John Leech, ^{[http://www-groups.dcs.st-andrews.ac.uk/~history/Biographies/Leech.html]} and took his surname. She worked at the University of Glasgow until 1982. She resides in England.

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