The thermal instabilities that develop in a conductor during nonlinear diffusion of a magnetic field were treated in a linear approximation by solving an eigenvalue/eigenfunction problem and an initial value problem. The limiting increment of thermal instabilities has been determined for the principal mode (for the wave number tending to infinity) as γ m ∼ ∂δ/∂T (j max) 2, where ∂δ/∂T is the temperature derivative of resistivity and j max is the maximum current density. It has been shown that as a nonlinear diffusion wave propagates through a conductor, the long-wave modes whose wavelengths are of the order of the conductor thickness are stable and the short-wave modes are localized near the diffusion wave front. As the diffusion wave arrives at the inner surface of the conductor, the instability increments of all modes with any wave number reach maxima.
ASJC Scopus subject areas
- Condensed Matter Physics