OBSERVATIONS OF THE FINE STRUCTURE OF ION DISTRIBUTION FUNCTION AT THE BOW SHOCK
V.N.Smirnov1, O.L.Vaisberg1, L.A.Avanov1, A.A.Petrukovich1, A.A.Skalsky1, J.L.Burch2, J.H.Waite, Jr. 2
1 Space Research Institute, 84/32 Profsoyuznaya str.,
117810 Moscow, Russia, E-mail: email@example.com
2 Southwest Research Institute, San Antonio, USA
The fast ion spectrometer SCA-1 on Interball Tail Probe measures 3-D ion distribution in the energy range 0.05-5.0 keV/Q in less than 10 sec. With new data we are testing the hypothesis, proposed on the basis of measurements on Prognoz-8 and Prognoz-10, that the thermalization of ion core on the strong Q-perpendicular shock front is provided by non-stationarity of the shock front. One supercritical Q-perpendicular bow shock crossing is analyzed. The downstream transmitted beam consists of multiple beams with thermal width of about upstream solar wind thermal width. This supports previous suggestion that the heated core of the downstream ion velocity distribution is formed of beamlets originating at patchy and oscillating structure of the shock front.
Reflected beams are a main source of free energy at supercritical (magnetoacoustic Mach number > 2-3) quasi-perpendicular shock. The beams are accelerated in the upstream solar wind and then cross the shock front, forming the downstream bi-modal distribution Leroy et al.(1982), Gosling et al. (1985) that subsequently relaxes. It is thought that all downstream thermalization is a result of relaxation of this bi-modal ion distribution Sckopke et al. (1983).
Fast ion measurements on Prognoz-8 and Prognoz-10 showed, however, that the transmitted ion beam (the ion core) is already heated just behind the shock front, and that the relaxation of bi-modal distribution leads to additional heating of the ion core Vaisberg et al. (1984). The downstream ion core itself has a multi-beam structure Vaisberg et al. (1986). Maxwellian fits to these peaks showed that distribution of "temperature" values of these spectral peaks has a maximum at a value that is quite close to the value of proton temperature in the upstream solar wind Vaisberg et al. (1989).
The closeness of the "temperature" of the beams in the downstream ion core to the ion temperature of the solar wind, and very short scale (~ 10 km) within magnetic ramp where solar wind beam transforms to downstream distribution Greenstadt et al. (1980), (Smirnov and Vaisberg, 1987) led Vaisberg et al. (1989) suggests that thermalisation of ion core in quasi-perpendicular shock may occur as a result of non-stationary structure of quasi-perpendicular shock front, similar to ballistic processes discussed by (Tidman and Krall, 1971). Fluctuations of either electrostatic potential jump, or magnetic ramp magnitude, or local normal direction, or any combination of above will lead to fluctuations of direction and energy of transmitted beam. A downstream observer situated relatively close to the shock front will see the core of ion distribution consisting of multiple "cold" ion beams (Figure 1). This nonstationary ramp structure may also affect the density of reflected beam leading to observed gyrophase bunched beams as observed by Gurgiolo et al. (1981).
Figure 1. Cartoon showing possible mechanism of ion core formation on the front of strong quasi-perpendicular shock. Fluctuations of electrostatic potential jump, magnetic ramp magnitude, and local normal direction lead to fluctuations of direction and energy of transmitted beam. Downstream observer situated close to the shock front will see core of ion distribution consisting of multiple "cold" ion beams.
The SCA-1 ion spectrometer on Interball-1 satellite, although inferior to MONITOR ion spectrometer in speed, provides better sampling of velocity space. We discuss one shock crossing observed on Interball-1 and analyze downstream ion velocity distribution.
The complex plasma spectrometer SCA-1 Vaisberg et al. (1995)
is part of payload of the Interball Tail Probe (Interball-1) launched on
August 3, 1995 from Plesetsk Cosmodrome on highly-elliptic orbit. The satellite
is spin-stabilized around nearly-Sun-directed axis with period of revolution
of 120 sec.
The main features of SCA-1 are its fast 3-D capability and absence of averaging in velocity space. 3-D capabilities of the ion E/Q spectrometer are provided by combination of 16 narrow-angle electrostatic analyzers and electrostatic angular scanning. The energy range of 0.05-5.0 E/Q is scanned over 15 nearly logarithmically spaced energy intervals. Altogether 64 directions are scanned within less than 10 sec.
We analyze here shock crossing observed at ~ 16:11 UT on August 17,
1995. During this crossing the satellite was at coordinates X = 4.95 RE
, Y = -19.2 RE , Z = 1.17 RE. Parameters of
the bow shock were obtained as following. As SCA-1 was designed for measurements
of magnetospheric plasma, the measurements in solar wind in its direction
are saturated. The solar wind parameters were calculated from measurements
of 8 analyzers looking at
= 17o from sun-directed axis of satellite. The calculated solar
wind velocity was 377 ± 20 km/s, and
proton temperature was 12.2 ± 3.7 eV.
The magnetic field value in the upstream solar wind was 5.85 nT (values
of components: -3.7, 1.0, -4.4). With this magnetic field and model shock
normal we estimated
Bn ~ 75o. With allowance for all uncertainties, we estimated magnetosonic Mach number Mms = 4.0 ± 0.6. The magnetic field profile, sharpness of the shock, and registration of narrow reflected beam all support identification of this shock as supercritical quasi-perpendicular shock.
From ion spectra observed by SCA-1 analyzers at different viewing angles in the time interval between 16:11 UT and 16:17 UT we have selected 60 spectra that show distinctive beams. Individual beams in the energy range below upstream solar wind energy but higher than 150 eV (in order to avoid most of reflected and transmitted beam particles) were then approximated by convected Maxwellian distribution in assumption that that all ions are protons. Examples of this fitting are shown on Figures 2. These examples show that in spite of complexity of ion spectra there are spectral components, traced through 4-5 successive energy steps, that can be nicely approximated by convected Maxwellian distribution. This supports a hypothesis of ballistic heating of the ion core.
Figure 2. Examples of E/Q spectra in magneto-sheath the time interval. Maxwellian fits of some observed by individual analyzers are shown. Time is indicated above respective spectrum
Figure 3. Histogram of calculated "temperatures" (eV), "number densities" (cm-3), and "velocities" (km/s) of beams.
Histograms of "number densities" n, "velocities" V, and "temperatures" T, calculated by approximate Maxwellian fits to individual beams, are shown on Figure 3. It should be kept in mind that the use of narrow-angle analyzerís data and isotropic Maxwellian fit give quite crude estimation of "number densities" and "temperatures". Median values of calculated parameters of ion beams are: n = 0.1 cm -3, V = 300 km/s, and T = 12 eV. This preliminary analysis shows that median value of calculated "temperatures" of ion beams in magnetosheath behind shock front is close to the estimated temperatures of solar wind protons. This result is analogous to one obtained at other shock crossing with another plasma spectrometer (Vaisberg et al., 1989), and it supports the hypothesis that thermalization of ion core at the supercritical quasi-perpendicular shock may occur due to instability of the shock front.
We can estimate parameters of fluctuations of the shock front. Fluctuations
of electrostatic potential jump can be assessed from the energy fluctuation
of the beams. Calculated velocities of the beams (Fig. 3) give rms fluctuations
of energies of beans relative to the average one of about 145 eV. We may
consider this as an estimation of electrostatic potential jump at the shock
The size of the shock front element with given electrostatic potential jump and the frequency of fluctuations of shock front structure are influencing the density of beamlets observed behind shock front. Let us assume that the linear scale of respective element of the shock front is , and that time scale is 2 /f, where f is characteristic frequency of shock front fluctuations. Then the number of ions passed through individual element is:
n 2 V 2/f (1)
with 2 being the surface of element, V 2/f is the length of plasma parcel passed, n is the solar wind number density, and V is the solar wind velocity. If observer is situated at the distance L behind the shock front, the size of plasma parcel will increase due to final temperature of the solar wind ions. The new volume occupied by the same plasma parcel will be:
(V 2 /f + V L/V)( + 2 V L/V) (2)
where V is the solar wind thermal velocity. The factor by which phase volume increases is:
(1+ V L f/2 V2 )(1+ 2 V L/V) (3)
We should use some evidences of what may be characteristic linear scale and characteristic frequency. ELF turbulence in the foot has characteristic frequency of about 5 HZ, and characteristic linear scale of about 10 km (Smirnov and Vaisberg, 1995). These waves have propagation velocities less than solar wind velocity, so they are brought by the solar wind flow from the foot to the shock front. Let us assume that turbulent structures hit the front and cause modulation of it. Taking these values as f and , and taking V = 300 km/s, V/V = 0.1, L = 100 km, we will obtain from (3) that phase space volume increased by factor of 15. This is a factor that approximately corresponds to ratio of solar wind density to observed densities of beamlets (see Fig. 3b).
Preliminary analysis SCA-1 Interball-1 data on the structure of the transmitted beam at the front of (one) supercritical quasi-perpendicular shock shows that it consists of multiple beams (beamlets) with median "temperature" that is close to upstream solar wind temperature.
This result support the hypothesis that formation of wide ion core at the supercritical quasi-perpendicular shock may occur due to patchy, non-stationary structure of the shock front.
Subsequent analysis of more shock crossings is required.
Work at IKI was supported by RSF 94-02-04232 grant, ISF MQ8300 grant, and INTAS-93-2031 grant. Authors are grateful to E.B.Ivanova for the help in data visualization.
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