Spectra of Magnetic Turbulence in a Relativistic Plasma

We present a phenomenological and numerical study of strong Alfvénic turbulence in a magnetically dominated collisionless relativistic plasma with a strong background magnetic field. In contrast with the nonrelativistic case, the energy in such turbulence is contained in magnetic and electric fluctuations. We argue that such turbulence is analogous to turbulence in a strongly magnetized nonrelativistic plasma in the regime of broken quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scaling k−3/2, while the difference between the magnetic and electric energies, the so-called residual energy, has the scaling k−2.4. The electric and magnetic fluctuations at scale ℓ exhibit dynamic alignment with the alignment angle scaling close to $\cos {\phi }_{{\ell }}\propto {{\ell }}^{1/4}$. At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfvén turbulence steepens to k−3.5.