Synchrotron radiation
Polarization
If the velocity vectors of the electrons gyrating around the magnetized plasma are isotropically distributed than the intrinsic degree of polarization of synchrotron radiation from plasma in a uniform magnetic field is given by,[১]
<math>\lVert p \rVert = \frac{3\gamma+3}{3\gamma+7}</math>
where <math>\gamma</math> is the spectral index of the energy distribution of the relativistic electrons,
<math>n_e(E) dE = AE^{-\gamma} dE</math>
Total electron density,
<math>n_e = \int_{E_0}^\infty n_e(E) dE</math>
where <math>E_0</math> is a cutoff energy that is required for the integral to converge.
From observations of Crab nebula it was determined that the <math>\gamma \approx 5/3</math>[২]. It implies that the internal polarized fraction of this radiation should be around <math>67%</math> independent of frequency. But radio observations show a much less degree of polarization and also it decreases steeply for higher frequencies.