  The paper discusses the problem of stability of a two-component plasma and
proposes a consistent consideration of quantum and long-range effects to
calculate the thermodynamic properties of such a plasma. We restrict ourselves
by the case of a non-degenerate plasma to avoid the fermionic sign problem and
consider the weakly coupled regime. Long-range interaction effects are taken
into account using the angular-averaged Ewald potential (AAEP). To calculate
thermodynamic properties, we apply both classical Monte Carlo (CMC) and path
integral Monte Carlo (PIMC) methods. A special method is developed to correctly
calculate potential energy in PIMC simulations with long-range interaction
effects. Our theoretical estimations show that the probability of a bound state
formation is very low at a coupling parameter $\Gamma~\le~0.01$, so both
classical and quantum simulations give the same energy at $\Gamma~\leq~0.01$,
and the thermodynamic limit coincides with the Debye--H\"uckel theory. At
higher $\Gamma$, the $N$-convergence is lost due to the formation of bound
states.
