The dynamics of nanometer-sized grains (nanodust) is strongly affected by electromagnetic forces. High-velocity nanodust was proposed as an explanation for the voltage bursts observed by STEREO. A study of nanodust dynamics based on a simple time-stationary model has shown that in the vicinity of the Sun the nanodust is trapped or, outside the trapped region, accelerated to high velocities.

We investigate the nanodust dynamics for a time-dependent solar wind and magnetic field configuration in order to find out what happens to nanodust during a coronal mass ejection (CME).

The plasma flow and the magnetic field during a CME are obtained by numerical simulations using a 3-D magnetohydrodynamic (MHD) code. The equations of motion for the nanodust particles are solved numerically, assuming that the particles are produced from larger bodies moving in near-circular Keplerian orbits within the circumsolar dust cloud. The charge-to-mass ratios for the nanodust particles are taken to be constant in time. The simulation is restricted to the region within 0.14 AU from the Sun.

We find that about 35 %
of nanodust particles escape
from the computational domain during the CME,
reaching very high speeds (up to 1000 km s

The vicinity of the Sun is a possible source region of nanometer-sized
dust grains (nanodust) produced by collisional fragmentation of
larger dust grains or released from comets

High-velocity submicron dust streams were discovered by Ulysses
within 1–2 AU from Jupiter

The results from STEREO/WAVES imply that the
flux of nanodust near the orbit of the Earth is variable in time by a
high factor, showing intermittent behavior.

Recently,

In the present work, we study the effect of
a CME on nanodust dynamics in the vicinity of the Sun by numerical simulation.
In connection
with recent STEREO observations

As a model of
a CME we use the numerical solution of the MHD equations obtained
using the same method and parameters as in

We assume that the nanodust particles originate from the fragmentation of
larger bodies in the circumsolar dust cloud. The initial positions and
velocities of nanodust particles we take to correspond to circular
Keplerian orbits of different radii and inclinations situated within
the circumsolar dust disk or inside the spherical halo region

We found that, in the model CME, a fraction of

For comparison, we also made calculations using the time-stationary
MHD solution (the initial or final configurations without the model CME).
In this case, only very few (fraction of

In our particle simulations we included also the
“time-extended” plasma and magnetic field configurations. These consist
of the MHD model of the CME (with a time extent of 1.6 days) and
the subsequent time-stationary configuration (the final time frame of
the MHD model) assumed to continue without change for a longer
time period. In these time-extended models, we found that the
nanodust particles continue to escape from the computational
domain after the CME has left the computational volume.
The fraction of these “slowly escaping” particles reaches 13 %

Perspective rendering of our model's magnetic field and flow
configuration.

We also identified a subpopulation of particles moving in orbits similar to
the trapped orbits obtained in the simple model of

The paper is organized as follows. In Sect. 2 (and in the Appendix) the
numerical MHD model of the CME is described. Section 3 is an
introduction to
our numerical simulations of particle motion. Section 4 briefly presents
the simplified 2-D (heliocentric distance

We solve the equations of motion for the nanodust particles subject to a
solar wind plasma flow

Rather than using the full energy equation, we simply assume that pressure

The fluid variables are initialized at

Within the inner radial boundary layer, quantities

This system is then self-consistently evolved until a sufficiently stationary
state is reached at

CMEs are complex dynamical structures that come in a wide variety of morphologies
and exhibit an equally wide range of physical parameters. Despite the wealth of observational
data that have been accumulated and the modeling effort invested by the space-weather
community, key questions about their origin and the physical mechanisms that govern their
eruption and propagation remain unanswered to this day. Details on CME modeling may be
found in reviews by

In the present context, our aim is merely to obtain a first assessment of how influential
the passage of a CME can be on a nanodust population near the Sun and an
indication of the type and expected magnitude of its effects. This justifies the use
of a rather simple density-driven CME model

The CME departs from a circular patch of radius

The respective MHD configurations of the quiet Sun and during CME passage
are illustrated in the panels of Fig.

For numerical convenience, the plasma configuration

Plasma radial velocity profiles in the model
along the direction

Our calculations are similar to those in

The electric charge of nanodust cannot be reliably estimated, so we
have to use an extrapolation from the results for the larger grains

As in

The equation of motion for a nanodust particle with mass

In some calculations we also included

Equation (

The initial conditions for

Most of our particle simulations stay within the time limits of the
MHD model for the CME (time from

The initial and (maximum) final times for particle motion are taken to be
the same for all particles in the sample. All simulations
presented here (also including the time-extended calculations)
start from the same initial time equal to

Nanodust creation rate as a function of the heliocentric distance assumed in our calculations (Czechowski and Mann, 2010).

To calculate the averages over the ensemble of the initial conditions, we
have to assign probability weights to the initial points. For any quantity

For comparison, we also repeated the calculations with a different
approximate expression for the sum over the initial states
used by

We use the same nanodust creation rates as

The dust–dust collision
and fragmentation model used for calculating the rates is described in

We present the results of simulations for different cases listed in
Table

In Table

Escape fractions

Distribution of the final velocity for
non-escaping and escaping particle populations obtained
in the CME model for a sample of 4800 nanodust
particles with

As Fig.

A significant fraction of particles (Table

The velocity distribution of this rapidly escaping population is different
from that of the remaining particles and extends to about 1000 km s

In heliographic longitude

The distribution of the final values of the colatitude

As Fig.

The distributions over final
values of solar colatitude

As Fig.

The loss of particles from the computational domain continues after the end
of the CME. The final velocity distribution obtained for the time-extended
model (CME

The distribution of the initial heliographic longitude

Distributions of

As Fig.

Cumulative fraction of particles escaping from the computational
domain as a function of time for a time-extended (33 days long) simulation
including the ion drag. Rapidly escaping particles (39 %) are not
included in the figure. The result implies that only

The fraction of particles remaining inside the calculation region as
a function of time for the CME time-extended models with and without the ion
drag. The vertical dotted line marks the end of the CME. The dashed lines
shows the two parameter (

The drag force increases the fraction of slowly escaping particles from 21 to
29 % (Table

Figure

We performed additional time-extended simulations to estimate the surviving
particle fraction after a longer time period. The results were the following: with drag
included, 6 % survived after 33 days (Fig.

Although the guiding center approximation is not used in our simulations,
it was found to be helpful in understanding the trapping mechanism
of nanodust in the vicinity of the Sun

The equations for the parallel component

In the study by

The sliding motion is determined by the force terms in Eq. (

A more detailed analysis

Equations (

In the solar system,

Trapped particle trajectories projected onto the (

Distance versus time plots for a sample of trajectories of the nanodust
particles (

Distribution of the difference

Effect of the (photon) Poynting–Robertson force
and the plasma drag force on a trapped particle
trajectory. While the Poynting–Robertson force leaves the
minimum and maximum

As explained in the previous subsection, the motion of a trapped particle in
the simple time-stationary model

Figure

The particles in the trapped class constitute the majority of particles
that remain inside the computational domain after the extended period of

Assuming that the nanodust particles are created continuously, the trapped
nanodust would accumulate in the vicinity of the Sun until some loss
mechanism balanced the creation rate. Our calculations suggest that the
main loss mechanism may be due to the plasma ion drag. The ion drag force
causes contraction of the orbits of trapped particles (Fig.

The result of the long-term (33 days) simulation (Fig.

The lifetime of small dust grains in the vicinity of the Sun, particularly
those belonging to the trapped class, can be limited by sublimation and
sputtering. An estimation (ignoring the effect of the ion drag) was made by

In this subsection we present the estimation of the sublimation loss fraction
based on our simulations, taking into account the effect of the drag force on
particle trajectories. According to

We present the results of numerical simulations of the motion of nanodust
particles released from circular Keplerian orbits between 0.005 and 0.14 AU
from the Sun with the solar wind flow and the magnetic field approximately
corresponding to the MHD model of the CME by

In part of our calculations we include the plasma ion drag
force, which was omitted in the earlier work on nanodust dynamics
near the Sun

In a simple time-stationary model of the solar wind with constant
radially directed velocity and the Parker spiral form of the magnetic field,
the nanodust released from low-inclination circular orbits within the region

About 35 % of the nanodust particles released during the CME form the
rapidly escaping population with a broad velocity distribution extending
to 1000 km s

The remaining particles, which belong to neither the rapidly escaping nor
the trapped class, escape from the region after the time span
(

The ion drag force differs from other forces (Lorentz, gravity, and
Poynting–Robertson) included in our calculations by its destructive effect on
trapped particle trajectories. The trapped orbits contract and ultimately
cross the inner boundary. The lifetime of trapped particles is consequently
limited by the ion drag force. From our simulations, we estimated the average
lifetime of nanodust to be

The effect of the ion drag on particle trajectories increases the nanodust
destruction rate due to sublimation. Assuming that the results of

Since our computational domain was restricted to

Calculated nanodust trajectories are available from Andrzej Czechowski (ace@cbk.waw.pl). MHD simulation results are available from Jens Kleimann (jk@tp4.rub.de).

The usual magnetic field of a point dipole, which reads

AC performed the nanodust simulations and analysis of the results. JK designed the MHD model of the CME.

The authors declare that they have no conflict of interest.

We thank the referee for the important suggestion to include the ion drag term in our calculations. We are grateful to Horst Fichtner for helpful comments, discussions, and support, as well as to Ralf Kissmann for valuable technical assistance with his CRONOS code. Furthermore, Jens Kleimann acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) via grant FI 706/8-2 and from the Ruhr Astroparticle and Plasma Physics (RAPP) Center, funded as MERCUR grant St-2014-040. The topical editor, Elias Roussos, thanks two anonymous referees for help in evaluating this paper.