  An error field (EF) detection technique using the amplitude modulation of a
naturally rotating tearing mode (TM) is developed and validated in the EXTRAP
T2R reversed field pinch. The technique was used to identify intrinsic EFs of
$m/n = 1/-12$, where $m$ and $n$ are the poloidal and toroidal mode numbers.
The effect of the EF and of a resonant magnetic perturbation (RMP) on the TM,
in particular on amplitude modulation, is modeled with a first-order solution
of the Modified Rutherford Equation. In the experiment, the TM amplitude is
measured as a function of the toroidal angle as the TM rotates rapidly in the
presence of an unknown EF and a known, deliberately applied RMP. The RMP
amplitude is fixed while the toroidal phase is varied from one discharge to the
other, completing a full toroidal scan. Using three such scans with different
RMP amplitudes, the EF amplitude and phase are inferred from the phases at
which the TM amplitude maximizes. The estimated EF amplitude is consistent with
other estimates (e.g. based on the best EF-cancelling RMP, resulting in the
fastest TM rotation). A passive variant of this technique is also presented,
where no RMPs are applied, and the EF phase is deduced.
