## Averaging Method for Studying Magnetohydrodynamic Equilibrium and Stability of Toroidal Helical Systems |

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applied helical field applied helical magnetic averaged equations averaged equilibrium averaging method axisymmetric axisymmetry ballooning boundary value Comp.Phys.Comm coordinate lines coordinate transformation curvilinear coordinate d*dr derive a set differential equation divB eigenvalue energy integral equation Bp equations in stellerator equilibrium and stability Equilibrium Equations ERATO stability externally applied helical field line form 8V formulae full three dimensional Grad-Shafranov equation helical magnetic field helical tori inverse aspect ratio J.L.Johnson Jacobian L.M.Kovrizhnykh and S.V.Shchepetov lines of force magnetic lines Magnetohydrodynamic MHD equilibrium Nagoya Nuclear Fusion 23 order term oscillating outermost magnetic surface Phys.Fluids 26 plasma boundary plasma current plasma displacement Plasma Physics poloidal recover the three residual field rotational transform S2 BP+ Section set of averaged stability code stellerator approximation stellerator configuration three dimensional magnetic three dimensional problem tokamak codes toroidal field toroidal helical devices toroidal helical systems toroidal mode number toroidal stellerators V.D.Shafranov V.E.Lynch V)v Vp vector written