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Can asteroid fields ever exist locally in a system, or do they tend to form belts exclusively?

And by asteroid field, I mean clusters of asteroids scattered around a planetary system.

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    $\begingroup$ "Ever" is pretty big. Are you happy with them existing only for a short period of time? (Consider: It is theorized that planetary rings formed due to breakup of one or more moons. At some point then the material must have gone from collected in a large ball of rock and ice, to a number of smaller balls of rock and ice.) $\endgroup$ – a CVn Jun 7 '16 at 12:55
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    $\begingroup$ Welcome to the site overburn. $\endgroup$ – James Jun 7 '16 at 13:28
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    $\begingroup$ This seems far more applicable to the astronomy of physics SE. $\endgroup$ – iAdjunct Jun 7 '16 at 13:47
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    $\begingroup$ Astro mod here: We would take this question if you want to migrate it. $\endgroup$ – called2voyage Jun 7 '16 at 21:29
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    $\begingroup$ Keep in mind that even in fields and belts, asteroids are usually hundreds of thousands of miles apart from each other (farther than the Earth and moon). Density of objects is very relative in the vast void of space. $\endgroup$ – ApproachingDarknessFish Jun 7 '16 at 22:57
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I contend that the Trojan, Greek, and Hilda groups associated with Jupiter in our own solar system constitute "fields" as opposed to "belts." The Hildas are perhaps more scattered, but they do not fit the word "belt" as I assume you mean it. Certainly, the green and orange dots in this image seem far less belt-like than the white dots (the main asteroid belt) do:

Simulated image of the solar system within Jupiter's orbit

image source: wikipedia

Each of these clusters is associated with one or more Lagrangian points of Jupiter, which more or less means these objects are locked in a gravitational dance with Jupiter, and orbit the sun in concert with Jupiter and each other.

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    $\begingroup$ I learned something new today. Thanks Mr Duck. $\endgroup$ – James Jun 7 '16 at 13:39
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    $\begingroup$ Now the question is, was he looking for a part of a belt, or Star wars style maze of asteroids $\endgroup$ – Ryan Jun 7 '16 at 15:56
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    $\begingroup$ I wish I could upvote your answer more than once. $\endgroup$ – Renan Jun 7 '16 at 16:40
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    $\begingroup$ Worth remembering the scale here though... the orbit around Jupiter's L4/L5 is wider than the Earth's around the sun! Still quite sparse. $\endgroup$ – Adam D. Ruppe Jun 7 '16 at 23:54
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Current theory is that planetary systems form via gravitational collapse of a cloud of material into a rotating disk, with resulting accretion and breakup of colliding masses within the disk. Zones where accretion forces did not produce a planet would end in a 'belt' of smaller objects. Gravitational resonance would shape the size and concentration of the belt, and would occasionally throw an object into an eccentric trajectory.

'Asteroids' will be found in belts aligned with the plane of the system. Concentrated fields will only be found in the vicinity of recently disintegrated large masses or in Lagrange points.

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