  Mkn 421 is a nearby active galactic nucleus dominated at all wavelengths by a
very broad non-thermal continuum thought to arise from a relativistic jet seen
at a small angle to the line of sight. Its spectral energy distribution peaks
in the X-ray and TeV gamma-ray bands, where the energy output is dominated by
cooling of high-energy electrons in the jet. In order to study the electron
distribution and its evolution, we carried out a dedicated multi-wavelength
campaign, including extensive observations by the recently launched highly
sensitive hard X-ray telescope NuSTAR, between December 2012 and May 2013. Here
we present some initial results based on NuSTAR data from January through March
2013, as well as calibration observations conducted in 2012. Although the
observations cover some of the faintest hard X-ray flux states ever observed
for Mkn 421, the sensitivity is high enough to resolve intra-day spectral
variability. We find that in this low state the dominant flux variations are
smooth on timescales of hours, with typical intra-hour variations of less than
5%. We do not find evidence for either a cutoff in the hard X-ray spectrum, or
a rise towards a high-energy component, but rather that at low flux the
spectrum assumes a power law shape with a photon index of approximately 3. The
spectrum is found to harden with increasing brightness.
