A lithography method and system have means for determining a convergence value dc from a relation of beam current to beam position drift (or beam dimension drift) produced in the past; means for finding a beam current i(t) as a function of the convergence value dc of beam position drift (or beam dimension drift), a measured value dm of beam position drift (or beam dimension drift), a gain constant g, and a convergence value c of beam position drift (or beam dimension drift) per unit beam current and using an equation given by i(t)={(1+g)·dc−g·dm(t)}/c; means for making a check regarding dm and dc as to whether dm approaches dc and, thus, a relationship given by |dm−dc| 0.