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 $< sim 4times 10^{-9}$ 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.
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