Plasma scintillation noise

4.2 Plasma scintillation noise

The radio waves of the Doppler system pass through three irregular media: the troposphere, the ionosphere, and the solar wind⁴ . Irregularities in the solar wind and ionospheric plasmas cause irregularities in the refractive index. The refractive index fluctuations $δn$ for a cold unmagnetized plasma are $− λ2reδne ∕(2π)$ and the phase perturbation is $− ∫ λreδne dz$ , where $λ$ is the wavelength, $re$ is the classical electron radius, and $δn e$ is the electron density fluctuation along the line of sight $z$ . These phase perturbations mimic time-varying distance changes (thus velocity errors) and so are a noise source in precision Doppler experiments. The transfer function of plasma phase scintillation to two-way Doppler is shown schematically in Figure 7

. A solar wind plasma blob at a distance x from the earth (producing a one-way fractional frequency fluctuation time series y^sw) and an ionospheric plasma blob at negligible light time from the ground station (with one-way time series y^ion) produce two-way time series $sw y (t) ∗ [δ(t) + δ(t − T2 + 2x ∕c)]$ and $ion y ∗ [δ(t) + δ(t − T2)]$ , respectively.

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Figure 9:

Doppler time series for DSS 25 Cassini track on 2003 DOY 324. Upper panel: time series of the two-way X-band, showing two discrete events at about 10:20 and 10:40 ground received time, echoed about a two way light time, T₂, later. Middle panel: time series of X-(880/3344) Ka1, which isolates the downlink plasma (and cancels nondispersive noises and signals: FTS, troposphere, antenna mechanical noise, and GWs). This shows that the events observed in the upper panel are due to plasma scintillation. Lower panel: acf of the two-way Doppler time series. The arrow marks the two-way light time. The lower right panel is a blow-up of the acf near the two-way light time (indicated by the vertical line). The acf peaks at lags slightly smaller than T₂ $≃$ 8021.5 s, indicating that the features observed in the upper panels are caused by near-earth plasma.Update

Plasma scintillation is mostly a statistical contribution to variability in the two-way Doppler time series. As such it can be seen in the autocorrelation function (acf) of the Doppler time series. Examples of S-band correlation functions which peak at $τ$ = T₂ (presumably ionospheric scintillation) and $τ <$ T₂ (localized solar wind scintillation) are shown in [9 ]. Occasionally, however, large time-localized plasma events can be seen in the raw time series. Figure 9 shows an example in Cassini data taken at DSS 25 on 2003 DOY 324. The top panel shows the time series of the two-way X-band, with two discrete events observed near 10:20 and 10:40 ground received time, echoed with positive correlation at about the two way light time. The middle panel is the time series of X-(880/3344) Ka1Update , which isolates the downlink plasma (and cancels nondispersive processes such as FTS noise, tropospheric noise, antenna mechanical noise, and gravitational waves; see Section 4.6). This indicates that the large events observed in the upper panel are due to plasma scintillation. The lower panel shows the acf of the two-way Doppler time series, $⟨y (t) y (t + τ)⟩ 2 2$ . The arrow marks the two-way light time. The acf peaks slightly earlier than T₂, indicating that the features observed in the other panels are caused by near-earth plasma.

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Figure 10:

Summary of propagation and antenna mechanical noises as functions of sun-earth-spacecraft angle (updated from [22

], reproduced by permission of the American Geophysical Union; see also [124

, 21

, 62

, 9

, 10

, 11

, 114

, 113

]). Left axis: spectral density of fractional frequency fluctuations at f = 0.001 Hz. Right axis: fractional frequency fluctuation (Allan deviation $σy$ ) at $τ$ = 1000 s. S-band $≃$ 2.3 GHz; X-band $≃$ 8.4 GHz; Ka-band $≃$ 32 GHz. Red curves are for plasma scintillation at the indicated radio frequencies (circles are S-band, more precisely: S-(3/11)X differential frequency fluctuations, data from Viking [124

, 21

]); crosses are X-band (more precisely X-(880/3344) Ka1 differential frequency fluctuations, from Cassini [114

, 11

, 19

, 30

, 113

]). Blue region shows typical uncalibrated tropospheric scintillation levels at a moderate-altitude dry site such as Goldstone, CA, or the National Radio Astronomy Observatory’s Very Large Array [20

, 71

, 72

]. Green arrows show upper (for antennas in the DSN “high efficiency” sub-network, operated under operational but benign conditions) and lower (for DSS 25, near solar opposition) limits to antenna mechanical noise [9

, 19

, 22

Figure 10 summarizes the magnitude of the effect of plasma scintillation, tropospheric scintillation, and antenna mechanical noise (the last two discussed below) on the stability of a Doppler tracking system [43 , 9 , 10 , 11 , 12 , 22 ]. Shown in red are data and model curves for plasma phase scintillation: Circles are S-band (frequency $≃$ 2.3 GHz) observations taken in the ecliptic using the Viking orbiters spacecraft taken over a wide range of sun-earth-spacecraft (SEP) angles [124 , 21 ]; crosses are X-band (frequency $≃$ 8.4 GHz) taken near the antisolar direction using the Cassini spacecraft [19 , 22 ]. Clearly plasma scintillation minimizes for observations near the antisolar direction. The model curves drawn through the data are described in [21 ]. (Ionospheric phase scintillation is, of course, included in the data presented in Figure 10 . Based on very limited multiple-station observations [21 ] and on transfer function studies [9 ], high-elevation-angle plasma noise appears dominated by solar wind rather than ionospheric phase scintillation. In any case, the effect of any plasma scintillation effect can be made small by observing at high enough radio frequencies [121 , 43 , 21 ] or by using multi-link observations [62 , 38 , 28 , 114 , 113 , 30 ] to solve-for and remove the plasma scintillation effect.)