Progress on Coronal, Interplanetary, Foreshock, and Outer Heliospheric Radio Emissions
Iver H. Cairns , P. A. Robinson , and G. P. Zank, PASA, 17 (1), 22.
Next Section: TYPE II SOLAR RADIO
Title/Abstract Page: Progress on Coronal, Interplanetary,
Previous Section: TYPE III SOLAR RADIO
Contents Page: Volume 17, Number 1

EARTH'S FORESHOCK

Earth's foreshock (Figure 1) is the region upstream from the bow shock that is downstream of the 3-D bundle of magnetic field lines tangent to the shock. The foreshock plasma includes convected solar wind plasma as well as electrons and ions reflected by or leaking through the bow shock. The reflected particles are energised by shock-drift acceleration at the shock or by Fermi acceleration. In general a convection electric field ${\bf E} = - {\bf v}_{sw} \times{\bf B}_{sw}$ exists in the solar wind, due to the magnetic field ${\bf B}_{sw}$ not being aligned with the solar wind velocity ${\bf v}_{sw}$. All particles therefore suffer an ${\bf E} \times {\bf B}$ drift downstream into the foreshock (but perpendicular to the magnetic field), equal in magnitude to the solar wind speed perpendicular to ${\bf B}_{sw}$, which restricts particles leaving the shock to lie downstream of the tangent field lines. The gyrocenters of particles in the foreshock move with constant velocity ${\bf v}_{\parallel}$ parallel to ${\bf B}_{sw}$ and the common ${\bf E} \times {\bf B}$ drift perpendicular to to ${\bf B}_{sw}$. Electron beams are therefore formed naturally in the foreshock due to the spatial variations in ${\bf v}_{\parallel}$ required to reach a given location (Filbert & Kellogg 1979, Cairns 1987a), sometimes referred to a ``time-of-flight'' effects. Defining D_f as the distance along ${\bf v}_{sw}$ from the tangent field line (Figure 1), with D_f > 0 and < 0 in the foreshock and solar wind, respectively, the beam speed (i.e., the minimum parallel speed) required to reach a location increases as D_f > 0 decreases. Faster beams are therefore expected close to the foreshock boundary.

These electron beams are observed to obey the predicted variations in ${\bf v}_{\parallel}$ with location D_f (Fitzenreiter, Klimas & Scudder 1984, 1990). These beams drive bursty, irregular Langmuir waves (Filbert & Kellogg 1979, Anderson et al. 1981, Cairns et al. 1997), which persist much further from the bow shock than predicted by standard instability theory and quasilinear theory (Cairns 1987b). Radiation near 2f_p is also observed approximately 50% of the time (Hoang et al. 1981). It is difficult to routinely distinguish f_p radiation from thermal noise at f_p, but f_p radiation has been observed (Cairns 1986b, Burgess et al. 1987) and is presumed to be present as often as the 2f_p radiation.

Figure 7 (Cairns et al. 1997, Cairns & Robinson 1999) shows how the Langmuir wave fields varied with the coordinate D_f during a period when ${\bf B}_{sw}$, the other solar wind parameters, and the locations of the bow shock and global foreshock were either observed or predicted to be unusually slowly varying and constant, thereby allowing temporal and spatial variations in the wave fields to be reliably distinguished.

Figure 7: Bursty Langmuir wave fields observed as a function of position in the solar wind (D_f < 0) and in Earth's foreshock (D_f > 0) during the period 0820 - 0955 UT on 1 December 1977 (Cairns et al. 1997, 2000, Cairns & Robinson 1997, 1999).

(In general, time variations in ${\bf B}_{sw}$ lead to the foreshock sweeping back and forth across a spacecraft, thereby confusing spatial and temporal variations in the wave parameters.) The figure shows weak, thermal Langmuir waves in the solar wind (D_f < 0), and then widely varying fields in the foreshock which first increase and then decrease with increasing D_f > 0 . The estimated error in D_f is only $\pm 0.2\ R_{E}$. Accordingly, the wide scatter in the wave fields at constant D_f in the foreshock is direct evidence for intrinsic variability and burstiness of the wave fields at a given location. This provides a prima facie argument that SGT may well be relevant, rather than relying on weaker arguments based upon the analogies between type III bursts and the foreshock waves and the success of SGT at explaining type III bursts. Cairns & Robinson (1999) performed a strong test of SGT over a large fraction of the foreshock using Figure 7's data. Restricting attention to the region with D_f > 0.6 R_E, in which the envelope of wave fields falls off smoothly, they extracted trends in the quantities $\mu(D_{f})$ and $\sigma(D_{f})$ and then tested SGT using the normalised field variable

$$X = \frac{\log E - \mu(D_{f})}{\sigma(D_{f})} \ ,$$ (2)

for which Eq. (1) takes the simple form

$$P(X) = \frac{1}{\sqrt{2\pi}} e^{- X^{2} / 2} \ .$$ (3)

That is, with these trends extracted, simple SGT predicts that the distribution P(X) should be a Gaussian in X with zero mean, unit standard deviation, and no free parameters. Cairns & Robinson (1999) found that the quantities $E_{\mu}(D_{f}) = 10^{\mu(D_{f})}$ (the logarithmically-averaged field E) and $\sigma(D_{f})$ were both double power-law functions of D_f with a common breakpoint. They then fitted Eq. (3) to Figure 7's data by minimising $\chi^{2}$ with the double power-law functions for E_av(D_f) and $\sigma(D_{f})$ as free parameters. Figure 8 shows the SGT prediction Eq. (3) (solid line) and the distribution P(X) calculated from the data and the fitted power-law functions.

Figure 8: Comparison between observation (symbols with error bars) and the SGT prediction (solid line) for the distribution P(X) of wave fields given by Eq. (3), as described in detail in the text and by Cairns & Robinson (1999).

The figure provides very strong evidence for SGT. This evidence is strongly statistically significant according to the standard $\chi^{2}$ and Kolmogorov-Smirnov tests (Cairns & Robinson 1999). Furthermore, the power-law fits for $E_{\mu}(D_{f})$ and $\sigma(D_{f})$ given by the $\chi^{2}$-minimisation procedure lie within the uncertainty limits given by direct least-squares fits to the data. Thus, simple SGT explains the detailed characteristics of the Langmuir waves in a large fraction of the foreshock. Very recently Cairns et al. (2000) applied the predictions of SGT for purely thermal waves and for thermal waves subject to both net linear growth and stochastic growth effects (Robinson 1995) to Figure 7's Langmuir waves in the solar wind and the edge of the foreshock. This work therefore studied the approach to the pure SGT state demonstrated in Figure 8. Cairns et al. (2000) found that the observed $P(\log E)$ distribution in the solar wind agreed well with the SGT prediction for purely thermal waves, while the $P(\log E)$ distribution observed in the region 0 < D_f < 0.6 R_E agreed very well with the SGT prediction for thermal waves subject to net linear growth and stochastic growth effects. Accordingly, the results of Cairns & Robinson (1999) and Cairns et al. (2000) demonstrate that SGT can explain the detailed properties of the Langmuir waves from the solar wind to the deep foreshock, both in the absence of an electron beam and as an electron beam develops and evolves as a function of position in the foreshock.

It is not known what processes produce f_p and 2f_p radiation in Earth's foreshock. On the one hand, the Langmuir wave decay and the f_p and 2f_p emission processes in the SGT theory for type III bursts have long been hypothesised to produce the foreshock radiation (e.g., Cairns 1988). On the other hand, density turbulence can mode-convert Langmuir waves into f_p radiation and also reflect Langmuir waves so that they can then undergo the standard coalescence $L + L' \rightarrow T(2f_{p})$ to produce 2f_p radiation (Bale et al. 1998, Yin et al. 1998, Kellogg et al. 1999). SGT can incorporate linear mode conversion and/or the nonlinear processes as the generation mechanisms for the radiation. Further research is required to determine whether the mode conversion/reflection mechanisms provide a viable quantitative alternative to the nonlinear processes in Section 3, both in Earth's foreshock or in type III sources. In the current absence of definitive data, the success of the SGT theory for type III bursts suggests that the Langmuir wave decay and associated f_p and 2f_p emission processes should be favoured at the present time.

Next Section: TYPE II SOLAR RADIO
Title/Abstract Page: Progress on Coronal, Interplanetary,
Previous Section: TYPE III SOLAR RADIO
Contents Page: Volume 17, Number 1