Working with Don DuBois, they derived a correction to Landau's relation for the damping excitations of unmagnetized plasma.

Through a fellowship from the Radcliffe Institute for Advanced Study, Kivelson was able to conduct scientific research in a university setting at Harvard and MIT.

[2] Motivated by her experiences in academia through the Radcliffe Institute, Kivelson joined UCLA in 1967 as an assistant research geophysicist.

From 1977 to 1983 Kivelson served on the board of overseers at Harvard College as well as NASA's advisory council from 1987 to 1993, the National Research Council's Committee on Solar-Terrestrial Research from 1989 to 1992, and co-chaired the UCLA Academic Faculty Senate's Committee on Gender Equality issues from 1998 to 2000.

[1] Some of her accomplishments are discovering an internal magnetic field at Ganymede,[6] providing compelling evidence for a sub-surface ocean at Europa,[7] and elucidating some of the processes explaining the behavior of ultralow frequency waves in the terrestrial magnetosphere,[8] the discovery of cavity mode oscillations in the magnetosphere,[9] developed new ways of describing wave-particle interactions in magnetohydrodynamic waves,[10] and provided insight into the mechanism of interchange diffusion in rotating plasmas.

[12] Some of Kivelson's recollections about establishing a career as a woman scientist have been documented in an interview by the American Astronomical Society and piece in the Annual Review of Earth and Planetary Sciences.

In 1954, she gave birth to her first child, Steven Kivelson, now a professor of physics at Stanford, and afterwards she often faced criticism for continuing to work despite being a mother.

A few months after receiving her PhD in 1957, she gave birth to her second child, Valerie Kivelson, now a professor of history at the University of Michigan.