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Astron. Astrophys. 335, 746-756 (1998)

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1. Introduction to pick-up ion behaviour in velocity space

The phenomenon and existence of pick-up ions were already predicted in very early years (Semar (1970), Fahr (1971), Holzer (1972), Fahr (1973)), long before their later detection. It was already clear at these times that interstellar atoms when ionized in the interplanetary medium shall immediately be picked up by local electric induction forces and shall essentially be convected outwards with the solar wind, but it was fairly unclear at these times how these newly generated ions while comoving with the solar wind behave in velocity space.

Meanwhile, since already quite a long time now, such interplanetary pick-up ions also have been detected by space probes. The first detection of such suprathermal ion species succeeded in the years 1984/85 with the plasma analyzer SULEICA onboard the earth-bound satellite AMPTE (see Möbius et al., (1985)). In the years after 1984 many more identifications of cometary, lunar, planetary and interplanetary pick-up ions came up which need not be mentioned here in detail. Perhaps best suited for the study of the velocity-space behaviour of these ions were the recent measurements by the SWICS instrument onboard of the ULYSSES space probe (see Gloeckler et al., (1993), Geiss et al., (1994)). Arising from more recent interpretations of measurements of the SULEICA instrument (Möbius et al., (1996), (1997)) and of the SWICS instrument (Gloeckler et al., (1995), Fisk et al., (1997)) the theoretical discussion on the pick-up ion behaviour in velocity space was again restarted which began with papers by Wu & Davidson (1972), Wu et al. (1973), Hartle & Wu (1973), Wu & Hartle (1974).

These latter papers were studying the instability of the initial pick-up ion distribution against wave excitation and could show that due to the identified instabilities with respect to electrostatic or electromagnetic wave excitations the initial toroidal ring distribution of pick-up ions in the solar wind reference frame may decay into a broadened distribution with reduced values of pick-up ion velocities [FORMULA] parallel and [FORMULA] perpendicular to the solar wind magnetic field [FORMULA] within time periods of the order of [FORMULA] sec ([FORMULA]) and [FORMULA] sec ([FORMULA]), respectively. How much this decay in fact affects the intensity of pick-up ion resonance emissions in the extreme ultraviolet was analysed earlier by Paresce et al. (1983) and presently in more detail by Fahr et al. (1998) and Gruntman & Fahr (1998).

From the studies by Wu & Davidson (1972), Wu et al. (1973), and Hartle & Wu (1973) it could not be concluded into which specific forms the initial toroidal pick-up ion distribution will actually develop. It was only later tacitly assumed that most probably the toroidal will first develop into a spherical shell distribution under strong energy-conserving pitch-angle scattering processes and then will suffer from an adiabatic cooling effect operating in the expanding solar wind. The combined effect of both processes on the pick-up ion distribution function was first described by Vasyliunas & Siscoe (1976). In the period following this publication it had more or less generally been accepted that pick-up ion distributions first undergo a fast pitch angle scattering towards an isotropic function caused by resonant ion interactions with ambient hydromagnetic wave fields (Isenberg, (1987), Lee & Ip, (1987), Fahr & Ziemkiewicz, (1988), Bogdan et al., (1991). On the basis of this expectation also the energy diffusion of pick-up ions by Fermi-2 scattering processes were described in papers by Isenberg (1987), Bogdan et al. (1991), Chalov et al. (1995, 1997), Chalov & Fahr (1996) and it was demonstrated that pick-up ions experience substantial acceleration while being convected outwards with the solar wind.

Nevertheless, it was already recognized by Lee & Ip (1987) that the growth rates [FORMULA] for linear wave excitations by thermally broadened, toroidal pick-up ion functions very much depend on the initial injection conditions (i.e the initial velocities [FORMULA] and [FORMULA] of newly picked-up ions) since leading to an expression


where [FORMULA] and [FORMULA] are the plasma frequency and the thermal velocity spread of the pick-up ions, and where [FORMULA] and [FORMULA] are the local Alfvén speed and the proton gyrofrequency. The above expression shows that the growth rates become vanishingly small for vanishing velocities [FORMULA], meaning that a toroidal function around pitch angle cosines [FORMULA] and [FORMULA] are marginally stable. This may be interpreted as saying that whenever pitch angle scattering brings ions from [FORMULA] towards [FORMULA] then it may become inefficient. It also may point to the fact that pitch angle scattering is not likely to produce complete shell distributions. The evolutionary tendencies of noncomplete shell distributions have been explicitly studied by Freund & Wu (1988) were it has been demonstrated that shell distributions are the less unstable the more complete they are, meaning that completion of the shell and establishment of an isotropic distribution function may be a very time-consuming asymptotic process.

In view of both these theoretical results and most recent pick-up ion flux observations Gloeckler et al. (1995), Isenberg (1997), Möbius et al. (1996, 1997) and Fisk et al. (1997) have restarted the discussion on incomplete and anisotropic pick-up ion distributions. Möbius et al. (1997) have registered pick-up ion flux reductions over periods when the magnetic tilt angle with respect to the solar wind velocity is small (radial field). They ascribe this phenomenon to the fact that at these events when pick-up ions are exclusively injected into the sunward hemisphere of the velocity space substantially anisotropic distribution functions may prevail so that the SULEICA plasma analyzer then may miss essential fractions of the pick-up ions passing over the detector. Fisk et al. (1997) have also analysed these events of reduced fluxes in terms of hemispherical pick-up ion populations underlying differential exchange processes by pitch angle scatterings and can show that the flux reductions seen with SWICS can be explained with effective scattering mean free paths eventually increasing to values of about 1 AU meaning that pitch angle scattering at some periods may be fairly inefficient. Under these auspices we have considered it highly worthwhile to more thoroughly study the evolution of pick-up ion distribution functions taking into account all forms of diffusion processes in configuration and velocity space. In the present work we shall present the first results of these studies demonstrating the effect of general phase space diffusion processes of pick-up protons which are locally injected at one specific event of time.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998