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The dust
grain charge
is computed from the capacitance of the dust
particles,
![\begin{displaymath}
Q_d = 4\pi \epsilon_0 a U.
\end{displaymath}](img39.png) |
(4) |
Assume that the dust is composed
of 1 micron diameter solid spherical silica particles with a mass density
of 1500 kg/m
. The mass of an individual particle will be
kg. The balance of the charging equations
![\begin{displaymath}I_e =
I_I +I_\nu
\end{displaymath}](img42.png) |
(5) |
under the constraint that the total charge in the plasma is
conserved
![\begin{displaymath}
en_i = en_e + Q_d n_d
\end{displaymath}](img43.png) |
(6) |
allows an estimate of the average charge on the dust grains to be made.
This calculation is made using plasma parameters for a hydrogen plasma
generated by a spacecraft that is located at D = 1 AU, temperatures,
eV, and
(dust temperature)
eV,
densities,
, and dust densities in the
magnetic balloon of
. Under these assumptions, the
dust grain charge will be negative,
or
electronic charges. The total mass of dust
contained in a 20 km diameter magnetic balloon is
kg. Finally, this gives a mass loading for the sail and a 500 kg
payload (as computed from the ratio of total mass to projected circular
surface area of a spherical magnetic balloon) of 0.0026 gm/m
.
Figure 3 shows the total dust mass and dust grain charge as a
function of the dust density. Note that decreasing the dust grain charge
has the effect of increasing the gyro-orbit of the dust particles about
the magnetic field, thereby reducing their confinement.
Next: Advanced Dusty Sail Concepts
Up: ``Sticky'' Dusty Plasma Theory
Previous: Charge per Grain
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Robert Sheldon
2001-09-18