Widely known expressions for the ion and electron Debye length. However, for dense dusty plasma is important as dust Debye radius. I found only https://arxiv.org/pdf/1010.4435.pdf evaluation the particular case. Are there known estimations for common case?
What exactly do you mean by "the common case" - estimations for strongly ionized plasma?
Basically you should get a good estimation if you treat the charged dust particles like very heavy electrons (the net charge on a dust grain is usually negative due to the higher mobility of the electrons).
So, you can fix their position in space and let the positive ions oscillate around them - just like in the derivation of the electron Debye length you will have to solve the oscillator equation with the electric field originating from the dust particles as restoring force.
If you want to get even more fancy, you can also treat the contribution of free electrons as a disturbance.
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