A stream will stop being a stream when one can no longer recognize that a family of meteoroids are moving on similar orbits. There are two distinct possibilities here. Either individual meteoroids experience some catastrophic event so that they cease to be able to produce observable meteor trails, or the individual orbits have changed, so that, though the individual meteoroid still exists, the resulting meteor is no longer recognizable as being part of a known shower.
All the mechanisms discussed above lead to changes in the orbital parameters, but they lead to a dispersal of the stream only if they produce different changes to the orbital elements of different meteors. They are also different in their effect, the Poynting-Robertson effect may be quite efficient at changing the orbital parameters over a short time period, but it moves similar sized meteoroids by the same amount. Hence, all large (or visible) meteors say will be affected by the same amount which will be smaller than the changes experienced but radio meteors. Nevertheless, though the visible meteors may now be on a different orbit, they will be on a recognizable orbit and so have not merged into the sporadic background.
Gravitational perturbations depend on the exact distance of the meteoroid from each of the planets. Hence every meteoroid experiences a different perturbation and can in theory evolve differently. Unfortunately over many orbits, these perturbations average out and most experience the average perturbation with only a small variance about this. The stream may move and become wider but the meteoroids in general still appear to belong to a stream. Other effects must thus play their part in dispersing a stream.
The most obvious loss mechanism from a meteoroid stream is the production of a meteor shower. Every dust grain that is seen as a meteor has burnt up in the Earth's atmosphere and so has been lost from the stream. But this mechanism is simply a meteoroid removal mechanism which leaves the surviving stream unaffected. However, for every meteoroid that hits the Earth, many more have a near miss and they will be scattered by the gravitational field of the Earth. Those affected however represent only a fraction of the stream, a few Earth radii is a tiny part of the circumference of a typical stream.
Other mechanisms that have been proposed are inter-meteoroid collisions, in particular high velocity collisions as discussed by Williams et al. . Again unlikely to be important to the stream as a whole. Fragmentation following collisions with solar wind electrons, which leads to an increased efficiency of radiation forces also leads to meteoroid loss. A mechanism that has not received much attention is the sublimation of residual ices which again leads to fragmentation. A much less dramatic effect is the combined perturbation of the planets that slowly change the orbital parameters so that coherence is gradually lost and the stream appears to get weaker and weaker and of longer and longer duration. From the point of view of a stream none of these effects may appear dramatic, but they all do the same thing, they feed the inter-planetary dust complex with small grains. All streams do this and so the cumulative effect is significant.
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