Two approaches to the stability problem for plasma equilibrium in a cylinder

✍ Scribed by K.V. Brushlinskii

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 439 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00026-0

✦ Synopsis

Using the example of the problem of the equilibrium of a plasma cylinder in a helical magnetic field, two approaches to the problem of its stability are proposed. The first approach uses the symmetry of the equilibrium configuration. Its model is constructed in terms of a boundary-value problem with the Grad-Shafranov equation. The equilibrium is said to be "diffusionally stable" if the solution of the problem can be obtained by iterative methods of the relaxation type. The stability is determined by the spectral property of the differential operator of the linearized equation. The other approach is the traditional linear theory o[ the MHDstability of equilibrium configurations. After its schematic description, as it applies to a cylinder, it is shown that for both of the approaches considered the eigenvalues of the eigenvalue problems for helical harmonies of any small perturbation vanish simultaneously. This indicates that the stability boundaries in the range of the parameters of the problem are identical in both cases.