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2. SATURN'S PLASMA ENVIRONMENT

The electrostatic potential of a dust particle not only depends on the physical properties of the particle, but also on the plasma environment, such as the plasma number density, temperature (energy), velocity distribution of the plasma particles, intergrain distance, and the relative motion between the dust particles and the plasma [4].

Inside of Saturn's plasmasphere, the plasma density increases towards the planet from ~ 1 electron cm-3 at Saturn radius 10 Rs to ~ 100 electrons cm-3 at 3 Rs, and the electron energy kTe decreases from ~ 100 eV to ~ 10 eV.

To characterize Saturn's plasma, we utilized plasma data from M. Horanyi. This plasma data is a four component plasma (hydrogen, oxygen, hot electrons, and cold electrons) fit to the Voyager data described in [5]. The Debye screening length is the distance that the Coulomb field of an arbitrary charge of the plasma is shielded. We can calculate the charge for an isolated grain if we have only one grain within a sphere of radius Debye length. Figures 1 and 2 show the energy, density our plasma data, and we state, in Table 2, some representative plasma values for our plasma data.

Saturn Plasma Energies

Saturn Plasma Energies

Saturn Radii (r/Rs )

Figure 1. Saturn plasma energies of our four component plasma: hot electrons, cold electrons, oxygen ions, and hydrogen ions.

3. CHARGING PROCESS

We calculate the time-varying charge due to currents acting on a dust particle in a planetary magnetosphere using the following expression:

k where is the current of the fc-th charging processes [4], We consider 3 charging currents. The first charging current is: /¡,e,moving; which is the collection of ions and electrons onto the dust particle from the ambient plasma. The second current: Isec, the secondary electron current, occurs when a high energy electron impacts the dust particle, some of the dust material is ionized, and electrons are ejected from the particle. The third current, Iv, photoelectron emission current, occurs when a UV photon impacts the dust particle and photoelectrons are released. For a more complete treatment, one should add reflected electrons from the secondary electron emission [6] and the small particle effect [7].

The secondary electron current is dependent on the dust particle material. If one wants to characterize different dust material properties, then one applies the secondary electron emission maximum yield ¿m and the primary energy Em at which the maximum yield occurs, acquired from laboratory measurements. The yield is the ratio of the secondary current to the primary current, given the energy of the impacting electron or ion. Example yield and energy values for relevant solar system material is shown in Table 3.

4. CHARGING RESULTS

We choose, as our canonical example, a hybrid dust particle with material properties similar to a conducting graphite particle ¿m=1.5, Em = 250 eV, but with photoelectron

Saturn Plasma Densities

Saturn Plasma Densities

Saturn Radii (r/Rs )

Figure 2. Saturn plasma densities of our four component plasma: hot electrons, cold electrons, oxygen ions, and hydrogen ions. The highest energy and density components are the oxygen ions and hot electrons.

yield properties similar to a dielectric particle (in Horanyi et al.'s, modeling work, the photoelectron yield is denoted \ and ranges from 1-0 for conducting magnetite dust particles to x=0.1 f°r dielectric olivine particles). These properties were chosen in order to compare with charging results we have obtained for a dust particle in Earth's magnetosphere.

For our canonical dust particle, we calculated the equilibrium potential ('equipotential'), the charging time, and examined the dominant currents for a particle at Saturn radii locations of 3 Rs to 10 Rs. Equilibrium potential for the dust particle is reached when the sum of the charging currents is zero. The charging time is the time for a particle's potential to reach an equilibrium. The currents that we examined are the electron and ion collection currents, the photoelectron current and the secondary electron current. Figures

Table 3

Examples of dust particle material properties.

Table 3

Examples of dust particle material properties.

Material

density (g cm3)

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