Analytic theory of the nonlinear M = 1 tearing mode
Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate.
- Research Organization:
- Texas Univ., Austin (USA). Inst. for Fusion Studies
- DOE Contract Number:
- FG05-80ET53088
- OSTI ID:
- 5111743
- Report Number(s):
- DOE/ET/53088-205; IFSR-205; ON: DE86001783
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
TEARING INSTABILITY
INSTABILITY GROWTH RATES
TOKAMAK DEVICES
ELECTRIC FIELDS
G VALUE
NONLINEAR PROBLEMS
CLOSED PLASMA DEVICES
INSTABILITY
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
THERMONUCLEAR DEVICES
700107* - Fusion Energy- Plasma Research- Instabilities