Let $\kappa$ and $\lambda$ infinite cardinals such that $\kappa\leq\lambda$. We say that two sets $A,B\in\mathcal{P}(\lambda)$ are $\kappa$-$\lambda$-ad iff $|A\cap B|<\kappa$. A family $\mathcal{A}\subseteq[\mathcal{P}(\lambda)]^\kappa$ is $\kappa$-$\lambda$-ad iff for any $A,B\in\mathcal{A}$ with $A\neq B$ we have that $|A\cap B|<\kappa$ and, it is called $\kappa$-$\lambda$-mad if it is $\subseteq$-maximal.
Define the cardinal $$\mathfrak{a}(\kappa,\lambda):=\min\{|\mathcal{A}|:\mathcal{A} \text{ is } \kappa\text{-}\lambda\text{-mad}\}$$
Somebody knows if this cardinal it had been defined before? If it is. Can please give me the reference to study it?
Thanks!