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Where do the particles come from? Some of them are obviously from the spacecraft. For example, the image on Jan 14, 1998 shows tracks that seem to emanate from a point. We believe that something must have hit the spacecraft and we see a shower of particles from the impact. But most of the images just show one or possibly 2 tracks. We believe that these are the interplanetary dust particles.
The LASCO coronagraphs are very sensitive to dust particles that pass through the field of view. This is similar to the effect of a sunbeam shining through a window and scattering from the minute dust particles suspended in the air. Similarly, very small particles, at small angles from the Sun, get illuminated by the bright sun and are easily seen. Usually the space environment is very clean, but sometimes a streak is observed. Even more rare are images with multiple streaks, indicating more than one particle.
The width of the streaks vary because the particles are at varying distances from the instrument. Since the instrument is focused for infinity the particles appear out of focus and thus broad. This can be used to determine how far away the particle is, assuming that the particle is otherwise very small.
The length of the streak depends upon how fast the particle is moving, and how far it is from the instrument. For a given speed, the closer the particle is, the longer the track.