Zero Field Eigenvalues of Force Free Plasma in Sharp Edge Compact Tokamaks (CT's)

Khalil, Sh. M.; Altuijri, R. A.
August 2011
International Review of Physics;Aug2011, Vol. 5 Issue 4, p145
Academic Journal
It is shown that the numerical method (Collocation Method) used here, works quite well, not only for curved cross-sections but also for cross sections with sharp edge in the boundary (e.g., tokamaks with rectangular or squared cross-sections). We calculated numerically, with high accuracy, the zero fields lowest eigenvalues μ of force free equation ∇̄ x B̄ = µ B̄ for tokamaks with various arbitrary tight aspect ratios α, where α = R / α → 1, R; α are the major and some sort of minor radii respectively). Furthermore, an excellent fulfillment of the zero field boundary condition B̄ ⋅ n̄ = 0 along the whole boundary for different sharp edged cross-section is achieved. Dependence of μ on the aspect ratio is also obtained. Several runs of the programme for various wave numbers k showed that μ is very insensitive to the choice of k . Besides, the magnetic field topologies inside the tokamak are represented. Shape of cross-sections and aspect ratio are found to affect strongly the physical picture of compact tori.


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