A simple solution is assuming a viscosity much larger than the magnetic diffusivity in the disk.
2.
In the Sweet-Parker model, the common assumption is that the magnetic diffusivity is constant.
3.
Where L is the typical length scale of the system, \ eta is the magnetic diffusivity and v _ A is the Alfv�n velocity of the plasma.
4.
However, numerical simulations, and theoretical models, show that the viscosity and magnetic diffusivity have almost the same order of magnitude in magneto-rotationally turbulent disks.
5.
Nevertheless, if the drift velocity of electrons exceeds the thermal velocity of plasma, a steady state cannot be achieved and magnetic diffusivity should be much larger than what is given in the above.
6.
It is also common to write \ eta instead of \ rho which can be confusing since it is the same notation used for the magnetic diffusivity defined as \ eta = 1 / \ mu _ 0 \ sigma.
7.
Here, \ eta = 1 / \ mu _ 0 \ sigma is the magnetic diffusivity ( in the literature, the electrical resistivity, defined as 1 / \ sigma, is often identified with the magnetic diffusivity ).
8.
Here, \ eta = 1 / \ mu _ 0 \ sigma is the magnetic diffusivity ( in the literature, the electrical resistivity, defined as 1 / \ sigma, is often identified with the magnetic diffusivity ).
9.
Where \ \ mu _ 0 is the magnetic permeability, \ \ rho is the density of the fluid, \ \ nu is the kinematic viscosity, and \ \ lambda is the magnetic diffusivity . \ B _ 0 and \ d are a characteristic magnetic field and a length scale of the system respectively.
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