Obituary of John Morgan Greene

John Morgan Greene, an unusually creative, world-renowned physicist and applied mathematician, died on October 22, 2007 in San Diego, CA due to complications from Parkinson’s disease. His work on magnetohydrodynamics set the gold standard in fusion plasma physics and his co-discovery of the soliton inverse scattering transform is among the greatest of applied mathematics. Markedly accomplished, yet gentle and generous, John had a kind and humble spirit that drew the best from his fortunate collaborators.

Born on September 22, 1928 in Pittsburgh, PA, the bulk of John’s formative years were spent in Manhattan, KS, where his father was head of the Chemical Engineering Department at Kansas State College and his mother (a trained chemist) taught mathematics. John consistently placed first in the Kansas state mathematics competition and earned a scholarship from the Pepsi Cola Corporation to attend the California Institute of Technology. He graduated from Manhattan High School in 1946, Caltech in 1950, and the University of Rochester in 1956 with a Ph.D. in physics. While researching nuclear theory at Rochester he learned about inverse scattering in quantum mechanics, a fortuitous event of subsequent importance.

In 1955 John joined Project Matterhorn at Princeton University, the predecessor to the Plasma Physics Laboratory, where Lyman Spitzer was using his stellarator to confine plasma magnetically for controlled fusion. Simplified magnetohydrodynamic (MHD) equations were used in early theory to determine stellarator equilibrium and stability properties. Over several decades John and collaborators tackled evermore-realistic MHD calculations for toroidal devices. Greene, John Johnson, and Katherine Weimer co-authored classic papers on toroidal stellarator and tokamak equilibrium, ideal kink and interchange instabilities and, in collaboration with others including Bruno Coppi and Alan Glasser, developed a major treatment of dissipative instabilities. John had a lifelong interest in computation and early on he explored the limits of computer simulation. He, Ray Grimm, and Johnson developed the Princeton Equilibrium and Stability in Tokamaks code (PEST), an important tool used to design and interpret fusion experiments worldwide.

With Ira Bernstein and Martin Kruskal, John investigated both nonlinearity and inhomogeneity in the Vlasov equation. In a famous 1957 paper they constructed exact BGK modes, nonlinear periodic and pulse-like traveling wave solutions, by means of an inverse problem for obtaining trapped particles. This was a harbinger of the soliton solutions that were later obtained by inverse scattering.

The history of the KdV soliton has been widely recounted because of its broad importance in physics and mathematics. John’s unique contribution was to the inverse scattering transform, for which he, Clifford Gardner, Kruskal, and Robert Miura received the 2006 Steele Prize given by the American Mathematical Society. One day as Kruskal and Muira were working on the blackboard, John walked by to get coffee and quipped, “You are trying to solve the inverse scattering problem,” which he recalled from his days at Rochester. John was most pleased with his inverse scattering work; his wife recalls his triumphal announcement, “It unfolded like a lily!”

John’s interest in Hamiltonian dynamics arose from the area-preserving maps that describe magnetic field lines in stellarators. After many years of work, in 1968 he published numerical techniques for obtaining and describing periodic orbits, a precursor to his famous 1979 paper that described “Greene’s residue criterion”. This criterion, which provides a method for calculating, to very high accuracy, the parameter value for the destruction of the last (golden mean) torus, is deeply significant. This work was placed in a renormalization group setting in the 1980’s with his student Robert MacKay, and generalized to nontwist maps with Diego del-Castillo-Negrete and Phil Morrison in 1996. In 1979, Morrison interested him in viewing MHD as an infinite-dimensional Hamiltonian system, resulting in an influential 1980 paper on noncanonical Poisson brackets.

In 1982 John joined the theory group at General Atomics in La Jolla, CA and was an adjunct professor of physics at UCSD. In 1992 came his important paper about the significance of magnetic field nulls for reconnection. He continued to work productively with and inspire many colleagues until and after his retirement in 1995. In 1992 he received the distinguished Maxwell Prize given by American Physical Society for his many discoveries.

John, an Eagle Scout, avid hiker, camper, and bird watcher, was active in conservation projects and the Sierra Club. He is survived by his wife, Alice (Andrews) Greene, a biochemist who taught at Rutgers University and finished her research career at UCSD, his daughter Emily Greene, a physicist at Raytheon, two grandchildren, and his sister Priscilla Robinson, a retired environmental advocate and consultant.