Jenifer Haselgrove
Encyclopedia
Jenifer Haselgrove (born 1930) 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 as Haselgrove's Equations.
and Hamilton's principle
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
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
, 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 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
. 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. Other publications applying Haselgrove's equations have recently appeared.
and published several highly cited, technical articles with him (e.g.). They are also credited for first solving the 6×10 Pentomino
. 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 resides in England.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
. She is most noted for her formulation of ray tracing
Ray tracing (physics)
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces,...
equations in a cold magneto-plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
, now widely known in the radio
Radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
science community as Haselgrove's Equations.
Haselgrove's Equations
Haselgrove developed her equations at Cambridge University in the 1950s, as a student under Kenneth Budden, by re-applying the earlier work of William Rowan HamiltonWilliam Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
and Hamilton's principle
Hamilton's principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action...
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
Eikonal equation
The eikonal equation is a non-linear partial differential equation encountered in problems of wave propagation, when the wave equation is approximated using the WKB theory...
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
EDSAC
Electronic Delay Storage Automatic Calculator was an early British computer. The machine, having been inspired by John von Neumann's seminal First Draft of a Report on the EDVAC, was constructed by Maurice Wilkes and his team at the University of Cambridge Mathematical Laboratory in England...
, 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 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
Ionosphere
The ionosphere is a part of the upper atmosphere, comprising portions of the mesosphere, thermosphere and exosphere, distinguished because it is ionized by solar radiation. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere...
. Here they have also been used to represent the radio propagation element of practical systems providing high frequency
High frequency
High frequency radio frequencies are between 3 and 30 MHz. Also known as the decameter band or decameter wave as the wavelengths range from one to ten decameters . Frequencies immediately below HF are denoted Medium-frequency , and the next higher frequencies are known as Very high frequency...
communication, direction finding
Direction finding
Direction finding refers to the establishment of the direction from which a received signal was transmitted. This can refer to radio or other forms of wireless communication...
and over-the-horizon radar
Over-the-horizon radar
Over-the-horizon radar, or OTH , is a design concept for radar systems to allow them to detect targets at very long ranges, typically up to thousands of kilometers...
. For a recent broad disccusion 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 HaselgroveC. Brian Haselgrove
Colin Brian Haselgrove was an English mathematician who is best known for his disproof of the Pólya conjecture in 1958....
and published several highly cited, technical articles with him (e.g.). They are also credited for first solving the 6×10 Pentomino
Pentomino
A pentomino is a polyomino composed of five congruent squares, connected along their edges ....
. Brian Haselgrove died in 1964, and Jenifer remarried to another British mathematician, John Leech
John Leech (mathematician)
John Leech was a British mathematician working in number theory, geometry and combinatorial group theory. He is best known for his discovery of the Leech lattice in 1965. He also discovered Ta in 1957...
, and took his surname. She worked at the University of Glasgow until 1982. She resides in England.