Magnetohydrodynamic stability of a toroidal plasma's separatrix

Area of Science:

• Plasma physics
• Fusion energy research
• Magnetohydrodynamics

Background:

• Large tokamaks, essential for fusion power, must mitigate edge localized modes (ELMs).
• ELMs are believed to be caused by ideal magnetohydrodynamic instabilities at the plasma's separatrix boundary.
• Previous analytical and numerical studies yielded conflicting stability results due to geometric approximations.

Purpose of the Study:

• To develop a generalized model for toroidal separatrix geometry to analyze ELM stability.
• To identify key parameters governing ELM stability in realistic tokamak configurations.
• To overcome analytical and numerical challenges posed by the plasma separatrix.

Main Methods:

• Generalizing a cylindrical model to toroidal separatrix geometry.
• Employing a generalized conformal transformation method to handle boundary conditions.
• Calculating the equilibrium vacuum field to analytically determine the stability parameter Delta'.

Main Results:

• Stability is determined by a single parameter, Delta'.
• The energy principle indicates instability as the boundary approximates a separatrix.
• The growth rate of instabilities asymptotes to zero as the boundary approaches a separatrix.

Conclusions:

• The developed toroidal model provides a more accurate assessment of ELM stability.
• The parameter Delta' is crucial for understanding and predicting ELM behavior.
• Instability is predicted, but with a vanishing growth rate near the separatrix, suggesting potential stabilization mechanisms.