  The omnipresence of dust particulates in space and astrophysical plasmas has
been attracting numerous researchers to study the collective excitation and
propagation dynamics of different eigen-mode structures in diversifed
astrocosmic circumstances for years. It includes planetary rings,
interplanetary space, cometary tails, asteroid zones, planetary atmospheres,
etc. The ubiquitous charged dust particulates possess collective degrees of
dynamic freedom resulting in the excitation of relatively low-frequency modes,
such as dust-ion-acoustic waves (DIAWs), dust-acoustic waves (DAWs),
dust-Coulomb waves (DCWs), and so forth. An interesting prevalency of dusty
plasma stability research lies in the Jovian magnetosphere (i.e., Jovian
plasmas), embedded inside the supersonic solar wind. A brief review of the
updated research works on dust-acoustic waves and related collective
instability dynamics in the presence of trapped plasma particles is presented
herein. The key aim of the proposed explorative meta-analysis is rooted in
outlining concisely the main up-to-date investigations on such collective
instability processes chronologically. An especial attention is given primarily
to the thermostatistical distribution laws of the constitutive lighter
electrons and ions against the heavier positively charged dust grains
(microspheres). The trapping mechanism of both the lighter species
(electrons+ions) is another additive feature revisited here properly. Finally,
we clearly extrapolate a number of futuristic directions in light of sensible
novelties with a wider scope, both horizontally as well as vertically.
