sequences and series - Evaluate the expression $sqrt{2}^{sqrt{2}^{sqrt{2}^{cdots}}}$

Is there a way to check whether the expression below converges to a specific number.
$$\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\cdots}}}$$
or in other words does the sequence defined by $x_0=\sqrt{2}$ and $x_n=\sqrt{2}^{x_{n-1}}$ converges?

Trying with a calculator to evaluate an eight-length $\sqrt{2}$ construct I got $1.9656648865173187$ but I couldn't yet confirm convergence.