ag.algebraic geometry - generators of the ideal of an unipotent-generated algebraic group

Given any affine algebraic group $G$ over an algebraically closed field $mathbb{F}$ of characteristic $0$ with a faithfull representation in $GL_n(mathbb{F})$ . If one knows the generators of the corresponding ideal, what can be said about the generators of $G^u$. Here $G^u$ shall denote the group generated by all unipotent elements of $G$. (Unlike the case where $G$ is irreducible and solvable, this group is not necessarily unipotent).

I am particular interested in bounds on the degrees of the generators; also any reference, which deals with unipotent generated groups is welcome.