Jenifer Leech (née Wheildon Brown; later Haselgrove; 3 August 1930 – 13 March 2015) was 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 Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...

science community as Haselgrove's Equations.J. M. Kelso : "Radio ray propagation in the ionosphere", McGraw-Hill, 1964, 408 pp

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Haselgrove's equations

Haselgrove developed her equations at

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

in the 1950s, as a student under Kenneth Budden, by re-applying the earlier work of

William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...

and

Hamilton's principle In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single funct ...

in geometrical optics to radio propagation in a plasma. 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 An eikonal equation (from Greek εἰκών, image) is a non-linear first-order partial differential equation that is encountered in problems of wave propagation. The classical eikonal equation in geometric optics is a differential equation of t ...

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, 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 The Electronic Delay Storage Automatic Calculator (EDSAC) was an early British computer. Inspired by John von Neumann's seminal ''First Draft of a Report on the EDVAC'', the machine was constructed by Maurice Wilkes and his team at the Universit ...

, to study ray propagation in the Earth's ionosphere in the late 1950s. Historically the best-known code applying Haselgrove's equations is the Jones-Stephenson code which was developed in the 1970s 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 The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays ...

. Here they have also been used to represent the radio propagation element of practical systems providing

high frequency High frequency (HF) is the ITU designation for the band of radio waves with frequency between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengths range from one to ten decameters (ten to one ...

communication,

direction finding Direction finding (DF), radio direction finding (RDF), or radiogoniometry is the use of radio waves to determine the direction to a radio source. The source may be a cooperating radio transmitter or may be an inadvertent source, a naturall ...

and

over-the-horizon radar Over-the-horizon radar (OTH), sometimes called beyond the horizon radar (BTH), is a type of radar system with the ability to detect targets at very long ranges, typically hundreds to thousands of kilometres, beyond the radar horizon, which is t ...

. For a recent broad discussion on ray tracing in the ionosphere see Bennett ''et al''. Other publications applying Haselgrove's equations have recently appeared.

Personal life

Haselgrove was married to British mathematician C. Brian Haselgrove and published several highly cited, technical articles with him. Example.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 6×10

Pentomino A pentomino (or 5-omino) is a polyomino of order 5; that is, a polygon in the Plane (geometry), plane made of 5 equal-sized squares connected edge to edge. The term is derived from the Greek word for '5' and "domino". When rotation symmetry, rota ...

. Brian Haselgrove died in 1964, and Jenifer remarried to another British mathematician, John Leech, and took his surname. She worked at the University of Glasgow until 1982. She resided in England until her death on 13 March 2015.

References

{{DEFAULTSORT:Haselgrove, Jenifer 2015 deaths 1930 births 20th-century British mathematicians 21st-century British mathematicians British women scientists