What is the origin of the dust near the sun? note: Solar Probe+ is now officially Parker Solar Probe

In https://space.stackexchange.com/q/17498/12102 I asked about the Solar Probe Plus mission. Reading a 2008 report I saw that there is an elevated exposure to high velocity dust near the sun. I understand the high velocity, anything in orbit that close will be moving fast, but I don't understand why there is dust there.
Simply put - wouldn't the gravity pull it in or the solar wind blow it away?
What is the origin of the refractory carbon and silicates? Is this orbiting leftover material from the formation of the solar system, or is it falling in from farther out, or is it left-over carbon and silicon that fell into the early forming sun and is now being blown back out?

4.3.5 Micrometeoroid and Dust. Solar Probe+ will encounter dust particles ranging in diameter from submicron up to several hundred microns and consisting of highly refractory carbon and silicate species with a typical bulk density of ~2.5 g/cm2. The particles will be traveling at relative speeds as high as 350 km/s. To define the shielding requirements for Solar Probe+, a dust model was developed based primarily on the work of Mann et al. (2004). The model employs the following assumptions...


above: screen shot from SolarProbePlus2008

above: screen shot from NASA's Solar Probe Plus Fact Sheet

above: illustration of NASA's Solar Probe Plus from http://solarprobe.jhuapl.edu/spacecraft/ Sun is up - to state the obvious!
There are two primary dust populations near 1 AU, interplanetary dust (IPD) and interstellar dust (ISD) [Mann, 2010].  I also discussed dust observations in detail at https://physics.stackexchange.com/a/160627/59023.

Interplanetary Dust

IPD of ~1 $\mu$m size drift sunward due to Poynting-Robertson drag while following roughly Keplerian orbits [e.g., Malaspina et al., 2014].  Closer to the sun, these particles break up due to collisions, sublimation/ablation, and/or sputtering.

Dust grains of ~0.1 $\mu$m size are the so-called "$\beta$ meteorites", which travel away from the sun due to the imbalance of radiation pressure over gravity [Mann, 2010].

The smallest dust grains with $\ll$ 0.1 $\mu$m size, the so-called nanograins or nanodust, act like large pickup ions, which are carried anti-sunward by the frame-dependent convective electric field (i.e., just the Lorentz force) produced when the dust grain moves relative to the solar wind flow (i.e., $\mathbf{E}_{conv} = - \mathbf{V}_{sw} \times \mathbf{B}_{sw}$, where the subscript $conv$($sw$) stands for convective(solar wind), and $\mathbf{V}$ and $\mathbf{B}$ are the bulk flow velocity and quasi-static magnetic field).  These particles can reach speeds in excess of 100 km/s relative to the sun [Meyer-Vernet et al., 2009].

Interstellar Dust

ISD was first discovered by the Ulysses spacecraft, which is ~1 $\mu$m size and moves at ~26 km/s relative to the solar system barycenter.  More recent work [Malaspina et al., 2014] has found a relationship between dust impact count rates and ecliptic longitude.

The reason can be seen from the following.  The Earth's transverse speed about the sun is ~29 km/s.  Thus, when the Earth moves anti-parallel(parallel) to the ISD flow direction the relative dust-spacecraft speed is ~55(~3) km/s, which produced an enhanced(depressed) dust count rate.  This occurs because there is a threshold impact speed necessary to produce a large enough plasma cloud (i.e., $\gtrsim$5-10 km/s depending on dust size) [Meyer-Vernet et al., 2009; 2014].


  What is the origin of the dust near the sun?


The primary sources of ~1 $\mu$m size near 1 AU are cometary debris trails, asteroids, planets, moons, and ISD [Mann, 2010; Zaslavsky, 2015].  


  Simply put - wouldn't the gravity pull it in or the solar wind blow it away?


Some are attracted by a combination of gravity and Poynting-Robertson drag while the smaller grains are either "pushed" out by radiation pressure (i.e., $\beta$ meteorites) or "picked-up" by the solar wind Lorentz force (i.e., nanodust).

References


D.M. Malaspina et al., "Interplanetary and interstellar dust observed by the Wind/WAVES electric field instrument," Geophys. Res. Lett. 41, pp. 266-272, doi:10.1002/2013GL058786, 2014.
Mann, I. "Interstellar Dust in the Solar System," Annual Review of Astronomy and Astrophysics 48, pp. 173-203, doi:10.1146/annurev-astro-081309-130846, 2010.
Meyer-Vernet, N., et al. "Dust detection by the Wave instrument on STEREO: Nanoparticles picked up by the solar wind?," Sol. Phys. 256, pp. 463-474, doi:10.1007/s11207-009-9349-2, 2009.
Meyer-Vernet, N., et al. "The importance of monopole antennas for dust observations: Why Wind/WAVES does not detect nanodust," Geophys. Res. Lett. 41, pp. 2716-2720, doi:10.1002/2014GL059988, 2014.
Zaslavsky, A. "Floating potential perturbations due to micrometeoroid impacts: Theory and application to S/WAVES data," J. Geophys. Res. 120, pp. 855-867, doi:10.1002/2014JA020635, 2015.