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We modeled the radio non-detection of two Type Ia supernovae (SNe) 2011fe and2014J considering synchrotron emission from the interaction between SN ejectaand the circumstellar medium. For an ejecta with the outer part having a powerlaw density structure we compare synchrotron emission with radio observations.Assuming that 20$\%$ of the bulk shock energy is being shared equally betweenelectrons and magnetic fields we found a very low density medium around boththe 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 magneticfield amplification is less than that presumed for energy equipartition. Thisconclusion also holds if the progenitor of SN 2014J was a rigidly rotatingwhite dwarf (WD) with a main sequence (MS) or red giant companion. For a Hestar companion, or a MS for SN 2014J, with 10$\%$ and 1$\%$ of bulk kineticenergy in magnetic fields, we obtain a mass loss rate $< 10^{-9}$ and $< \sim4\times 10^{-9}$ M$_{\odot}$yr$^{-1}$ for a wind velocity of 100 km/s. Theformer requires a mass accretion efficiency $>$ 99$\%$ onto the WD, but is lessrestricted for the latter case. However, if the tenuous medium is due to arecurrent nova it is difficult from our model to predict synchrotronluminosities. Although the formation channels of SNe 2011fe and 2014J are notclear, the null detection in radio wavelengths could point toward a lowamplification efficiency for magnetic fields in SN shocks.

Constraining magnetic field amplification in SN shocks using radio observations of SNe 2011fe and 2014J