Space-based interferometric gravitational wave instruments such as the ESA/NASA Laser Interferometer Space Antenna (LISA) observe gravitational waves by measuring changes in the light travel time between widely-separated spacecraft. One potential noise source for these instruments is interaction with the solar wind, in particular the free electrons in the interplanetary plasma. Variations in the integrated column density of free electrons along the laser links will lead to time-of-flight delays which directly compete with signals produced by gravitational waves. In this paper we present a simplified model of the solar plasma relevant for this problem, anchor key parameters of our model using data from the NASA \emph{Wind}/SWE instrument, and derive estimates for the effect in the LISA measurement. We find that under normal solar conditions, the gravitational-wave sensitivity limit from the free-electron effect is smaller than other noise sources that are expected to limit LISA's sensitivity.
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