Space weather is described as the variability of solar wind plasma that can disturb satellites and systems and affect human space exploration. Accurate prediction requires information of the heliosphere inside the orbit of the Earth. However, for predictions using remote sensing, one needs not only plane-of-sky position but also range information — the third spatial dimension — to show the distance to the plasma disturbances and thus when they might propagate or co-rotate to create disturbances at the orbit of the Earth. Appropriately processed radio signals from spacecraft having communications lines-of-sight passing through the inner heliosphere can be used for this spacetime localization of plasma disturbances.
The solar plasma has an electron density- and radio-wavelength-dependent index of refraction. An approximately monochromatic wave propagating through a thin layer of plasma turbulence causes a geometrical-optics phase shift proportional to the electron density at the point of passage, the radio wavelength, and the thickness of the layer. This phase shift is the same for a wave propagating either “up” or “down” through the layer at the point of passage. This attribute can be used for space-time localization of plasma irregularities.
The transfer function of plasma irregularities to the observed time series depends on the Doppler tracking “mode.” When spacecraft observations are in the two-way mode (downlink radio signal phase-locked to an uplink radio transmission), plasma fluctuations have a “two-pulse” response in the Doppler. In the two-way mode, the Doppler time series y2(t) is the difference between the frequency of the downlink signal received and the frequency of a ground reference oscillator. A plasma blob localized at a distance x along the line of sight perturbs the phase on both the up and down link, giving rise to two events in the two-way tracking time series separated by a time lag depending the blob’s distance from the Earth: T2 – 2x/c, where T2 is the two-way time-of-flight of radio waves to/from the spacecraft and c is the speed of light.
In some tracking situations, more information is available. For example, with the 5-link Cassini radio system, the plasma contribution to the up and down links, γup(t) and γdn(t), can be computed separately. The times series γup(t) and γdn(t) respond to a localized plasma blob with one event in each time series. These events are also separated in time by T2 – 2x/c. By cross-correlating the up and down link Doppler time series, the time separation of the plasma events can be measured and hence the plasma blob’s distance from the Earth determined. Since the plane-of-sky position is known, this technique allows localization of plasma events in time and three space dimensions.