A cylindrical pinch has axial field at radius

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fluid and magnetohydrodynamic description · Fluid and magnetohydrodynamic description

Plasma Physics, Ch Whether it stays held: the energy principle, interchange, kink and tearing

Problem

A cylindrical pinch has axial field Bz=3.0 TB_z = 3.0\,\mathrm T at radius r=0.30 mr = 0.30\,\mathrm m, magnetic shear s≡rq′/q=0.50s \equiv rq'/q = 0.50 there, and pressure gradient dp/dr=−5.0×105 Pa m−1\mathrm dp/\mathrm dr = -5.0\times10^5\,\mathrm{Pa\,m^{-1}}. The quoted Suydam criterion for stability against localised interchanges is rBz28μ0(q′q)2+dpdr>0.\frac{rB_z^2}{8\mu_0}\left(\frac{q'}{q}\right)^2 + \frac{\mathrm dp}{\mathrm dr} > 0. ((a)) Evaluate the shear (stabilising) term at r=0.30 mr = 0.30\,\mathrm m. ((b)) Decide whether the profile is Suydam-stable at this radius, and by how much the criterion is satisfied or violated.

Browse the problem library