
#1
Aug2109, 09:30 PM

P: 8

1. The problem statement, all variables and given/known data
An idealized thetapinch geometry is an infinitely long, cylindrically symmetric (dbyd theta = 0), translationallyinvariant (dbyd z = 0) plasma column with an externally applied axial magnetic field B_z_ext. This induced a large diamagnetic azimuthal current which produces its own magnetic field which opposes the external magnetic field. Assume the plasma column is in MHD equilibrium with velocity v = 0 and with mag field B_z(r) and gas pressure p(r). I'm stuck on the first part of the question which is find the differential relationwhich the field B_z and the gas pressure must satisfy. 2. Relevant equations gradp = j cross B maxwell's equations to replace the current with the curl of B 3. The attempt at a solution grad p = (del cross B_z zhat) cross B_z zhat del cros B_x zhat =  dbydr B_z thetahat grad p = dbydr p (1/mu_0)( dbydr B_z)thetahat cross B_z zhat = (1/mu_0)( dbydr B_z) = dbydr p Is that the correct answer? Do I need to go further? Next I need to integrate to find an expression for the externally applied mag field as a function of B_z and p and I just don't see how i can integrate the expression i found above. 


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