Viscous Relaxation and the Transition between the Kinematic and Nonlinear Galactic Dynamos

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Abstract
This paper primarily treats the different stages in the buildup of small-scale magnetic energy in a turbulent Galactic dynamo and does not directly address the growth of a coherent Galactic-scale magnetic field. If the Galaxy is born with a very weak magnetic field, turbulence in the ISM causes the magnetic energy to grow rapidly on scales much smaller than the scale of the smallest turbulent eddy (Kulsrud & Anderson). In the early stages of growth, ambipolar diffusion (the relative motion between ions and neutrals) damps magnetic energy at the smallest scales and causes the characteristic length scale of the magnetic field to become larger as the total magnetic energy increases (Kulsrud & Anderson). When the total magnetic energy becomes as large as the kinetic energy in the smallest turbulent eddies, small, the length scale of the magnetic field becomes large enough that viscosity cannot freeze the neutrals in place in the presence of magnetic forces and ion-neutral collisions. When this happens, a new form of damping of magnetic energy termed "viscous relaxation" is shown to occur in which neutrals and ions move together to smooth out field lines. The rate of damping of magnetic energy in this regime is shown to increase over the ambipolar-diffusion damping rate. Viscous relaxation prevents the magnetic energy on scales smaller than the smallest turbulent eddy from becoming much larger than small. Numerically, small ~ kin R−1/2, where kin is the total turbulent kinetic energy and R is the ordinary Reynolds number of the interstellar turbulence. After the magnetic energy has saturated on scales smaller than the smallest turbulent eddy, the magnetic energy continues to grow on the scales of the turbulent eddies where viscous relaxation is ineffective. When the magnetic energy on the scale of the smallest turbulent eddy becomes comparable with small, strong MHD turbulence develops and the transition from the kinematic dynamo to the nonlinear dynamo is complete.