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 Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral), a green translucent silica mineral * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood pla ...

, now widely known in the

radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...

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 , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

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

William Rowan Hamilton Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the ...

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 function ...

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 ...

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 Universi ...

, 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 an ...

. 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 range of radio frequency electromagnetic waves (radio waves) 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 ...

communication,

direction finding Direction finding (DF), or radio direction finding (RDF), isin accordance with International Telecommunication Union (ITU)defined as radio location that uses the reception of radio waves to determine the direction in which a radio station ...

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 ...

. 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 Colin Brian Haselgrove (26 September 1926 – 27 May 1964) was an England, English mathematician who is best known for his disproof of the Pólya conjecture in 1958. Haselgrove was educated at Blundell's School and from there won a scholar ...

and published several highly cited, technical articles with him (e.g.,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 Derived from the Greek word for ' 5', and "domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to ...

. 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