In plasma physics, there is an approximation called cold plasma approximation according to which, the temperature of a plasma species in an electron-ion plasma, say ions ( $T_i$ ) is assumed to be zero. As far as I have understood this approximation is valid when the average temperature of electrons ($T_e$) is much larger than that of ions ( $T_e>>T_i$).
For any plasma species, one can define Coulomb coupling parameter($\Gamma$), $$\Gamma=\frac{q^2}{4\pi\epsilon_0ak_BT_i},$$ which is basically the ratio of average interparticle potential energy to average thermal energy, where $q,\;a\;\text{and} \;T_i$ denotes charge, average interparticle distance and average temperature of ions respectively.
So, if one assumes ions to be cold, he/she gets infinite coupling for ions ( as $T_i\to0$, $\Gamma\to\infty).$
I don't understand the physical meaning of infinte coupling. Is this result ( i.e, $\Gamma\to\infty$ as $T_i\to 0)$ correct physically ?