  Methone and Anthe are two tiny moons (with diameter $<3$ km) in the inner
part of Saturn's E ring. Both moons are embedded in an arc of dust particles.
To understand the amount of micron-sized dust and their spatial distribution in
these arcs, we model the source, dynamical evolution, and sinks of these dust
in the arc. We assume hypervelocity impacts of micrometeoroids on the moons as
source of these dust (Hedman et al., 2009), the so called impact-ejecta process
(Krivov et al., 2003; Spahn et al., 2006). After ejecting and escaping from the
moons, these micron-sized particles are subject to several perturbing forces,
including gravitational perturbation from Mimas, oblateness of Saturn, Lorentz
force, solar radiation pressure, and plasma drag. Particles can be either
confined in the arcs due to corotational resonance with Mimas, as their source
moons (Spitale et al., 2006; Cooper et al., 2008; Hedman et al., 2009), or
pushed outward by plasma drag. Particle sinks are recollisions with the source
moon, collision with other moons, or migrate out of the radial zone of
interest. In addition to that, the upper limit of the particle lifetimes are
controlled by plasma sputtering, which decreases the particle size in a rate of
order 1$\mu$m radius every 100 years (Johnson et al., 2008). Our simulation
results show that ejecta from both moons can form the arcs of maximal optical
depths $\tau$ in the order of $10^{-8} - 10^{-6}$, although the absolute amount
of dust have uncertainties. We also find out the longitudinal extension of the
arcs in our simulation are consistent with observation and the theory. Smaller
particles are more likely to escape the arc because of the stronger influence
of plasma drag. On the other hand, large particles can stay in arcs for longer
time and therefore are more likely to collide with the source moon.
