- #1
vibe3
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I am trying to understand the Grad Shafranov equation, and in particular its inputs and outputs.
I understand that the equation determines the conditions under which plasma may be in equilibrium. In particular, the MHD equations of equilibrium state:
[tex]\nabla p = J \times B[/tex]
and the solutions to the Grad Shafranov equation state the possible values of pressure p, current J and magnetic field B which will satisfy the above equation.
However, my question has to do with imposing an ambient magnetic field B_0 like you would, in say, a tokamak.
If you impose an ambient field B_0 and the plasma is able to reach an equilibrium, it will then create a diamagnetic current
[tex]J_{dia} = B \times \nabla p / B^2[/tex]
which has its own magnetic field B_dia. So the total field is then B_0 + B_dia.
So my question is, the Grad Shafranov equation seems to provide self-consistent pressure functions, currents and magnetic fields, but how do you incorporate a pre-existing ambient field B_0?
I haven't been able to find a discussion of this
I understand that the equation determines the conditions under which plasma may be in equilibrium. In particular, the MHD equations of equilibrium state:
[tex]\nabla p = J \times B[/tex]
and the solutions to the Grad Shafranov equation state the possible values of pressure p, current J and magnetic field B which will satisfy the above equation.
However, my question has to do with imposing an ambient magnetic field B_0 like you would, in say, a tokamak.
If you impose an ambient field B_0 and the plasma is able to reach an equilibrium, it will then create a diamagnetic current
[tex]J_{dia} = B \times \nabla p / B^2[/tex]
which has its own magnetic field B_dia. So the total field is then B_0 + B_dia.
So my question is, the Grad Shafranov equation seems to provide self-consistent pressure functions, currents and magnetic fields, but how do you incorporate a pre-existing ambient field B_0?
I haven't been able to find a discussion of this