What is the definition of a plasma? I understand that the conventional definition of a plasma is that the Debye length is much smaller than the size of the plasma, however I can't seem to find what the numerical value of this ratio should be. Is it something like $10^{-3}$ or something like $10^{-9}$ or smaller yet? Cheers
 A: There's no fixed value, and if you consider a few common examples of plasmas, the ratio $\lambda_D/L$ takes a pretty big spectrum of values. For instance,

*

*$\theta$ Pinch: $\lambda_D\approx 10^{-7}\,\mathrm{m},L\approx10^{-1}\,\mathrm{m}$.

*Tokamak: $\lambda_D\approx 10^{-4}\,\mathrm{m},L\approx10^{0}\,\mathrm{m}$.

*Glow discharge: $\lambda_D\approx 10^{-4}\,\mathrm{m},L\approx10^{-2}\,\mathrm{m}$.

Once the ratio becomes too large, you lose the notion of collective behavior and the approximations made become progressively bad.
In particular, computations of waves and drifts in plasmas often assume quasi-neutrality. Recall that $\lambda_D$ is indicative of the length scale of Debye shielding (i.e. it's an indicator of the distance beyond which the field of a charged body placed in the plasma is not felt by particles of the plasma). In the limit $\lambda_D\to L$, the field of a charged zone in one part of the plasma will be experienced by an increasing fraction of particles of the plasma, which invalidates in those regions all computations that assume quasi-neutrality.
A: A plasma originally had stricter definitions based upon things like the number of particles in a Debye sphere being statistically large and that it exhibit collective behavior governed by long-range forces.
In the solar wind, the Debye length typically falls in the range ~4.74-13.8 meters [Wilson et al., 2021] but as the other answer pointed out, lab plasmas tend to have micron-scale Debye lengths.  As I pointed out in my answer at https://physics.stackexchange.com/a/340276/59023, the distinction between a hot gas and a plasma can become very mirky.  For instance, a normal fire is sometimes considered a plasma and other times not.  The arguments in favor are that it behaves like a very dusty plasma dominated by binary collisions.  The argument against is usually that the ionization ratio is too low for it to exhibit collective behavior.
Unfortunately, there is no clear cut answer here because there is no line between gas and plasma.  It's a context-specific blur.
