  We modeled the radio non-detection of two Type Ia supernovae (SNe) 2011fe and
2014J considering synchrotron emission from the interaction between SN ejecta
and the circumstellar medium. For an ejecta with the outer part having a power
law density structure we compare synchrotron emission with radio observations.
Assuming that 20$\%$ of the bulk shock energy is being shared equally between
electrons and magnetic fields we found a very low density medium around both
the SNe. A less tenuous medium with particle density $\sim$ 1 $\rm cm^{-3}$,
which could be expected around both SNe, can be estimated when the magnetic
field amplification is less than that presumed for energy equipartition. This
conclusion also holds if the progenitor of SN 2014J was a rigidly rotating
white dwarf (WD) with a main sequence (MS) or red giant companion. For a He
star companion, or a MS for SN 2014J, with 10$\%$ and 1$\%$ of bulk kinetic
energy in magnetic fields, we obtain a mass loss rate $< 10^{-9}$ and $< \sim
4\times 10^{-9}$ M$_{\odot}$yr$^{-1}$ for a wind velocity of 100 km/s. The
former requires a mass accretion efficiency $>$ 99$\%$ onto the WD, but is less
restricted for the latter case. However, if the tenuous medium is due to a
recurrent nova it is difficult from our model to predict synchrotron
luminosities. Although the formation channels of SNe 2011fe and 2014J are not
clear, the null detection in radio wavelengths could point toward a low
amplification efficiency for magnetic fields in SN shocks.
