Plasma Processes : Minimum dissipative relaxed states in toroidal plasmas

[摘要] Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the 𝑚 = 0; 𝑛 = 0 (𝑚 and 𝑛 are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, 𝑞 (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue 𝜆 𝑟0. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of 𝜆 𝑟0, which is related directly to volt-sec in the experiment.

[学科分类] 物理（综合）

[关键词] Minimum dissipation;tokamak;reversed field pinch.