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Aims: The test-field method for computing turbulent transport coefficientsfrom simulations of hydromagnetic flows is extended to the regime with amagnetohydrodynamic (MHD) background. Methods: A generalized set of testequations is derived using both the induction equation and a modified momentumequation. By employing an additional set of auxiliary equations, we derivelinear equations describing the response of the system to a set of prescribedtest fields. Purely magnetic and MHD backgrounds are emulated by applying anelectromotive force in the induction equation analogously to the ponderomotiveforce in the momentum equation. Both forces are chosen to have Robertsflow-like geometry. Results: Examples with an MHD background are studied wherethe previously used quasi-kinematic test-field method breaks down. In caseswith homogeneous mean fields it is shown that the generalized test-field methodproduces the same results as the imposed-field method, where the field-alignedcomponent of the actual electromotive force from the simulation is used.Furthermore, results for the turbulent diffusivity tensor are given, which areinaccessible to the imposed-field method. For MHD backgrounds, new mean-fieldeffects are found that depend on the occurrence of cross-correlations betweenmagnetic and velocity fluctuations. For strong imposed fields, $\alpha$ isfound to be quenched proportional to the fourth power of the field strength,regardless of the type of background studied.

Test-field method for mean-field coefficients with MHD background