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Exponential growth of nonlinear ballooning instability
P Zhu1, C C Hegna, C R Sovinec
1Center for Plasma Theory and Computation, University of Wisconsin-Madison, Madison, WI 53706, USA.
Physical Review Letters
|August 8, 2009
Summary
Recent theory and simulations confirm that plasma instabilities grow exponentially in the nonlinear phase. This occurs when ballooning nonlinearity reaches unity, maintaining the linear growth rate.
Area of Science:
- Plasma Physics
- Magnetohydrodynamics
- Instability Theory
Background:
- Ideal magnetohydrodynamics (MHD) theory describes plasma behavior.
- Linear ballooning instabilities are a key phenomenon in plasma physics.
- Understanding nonlinear evolution is crucial for plasma confinement.
Purpose of the Study:
- To verify the prediction of ideal MHD theory regarding nonlinear instability growth.
- To investigate the intermediate nonlinear phase of ballooning instabilities.
- To determine the conditions under which exponential growth persists.
Main Methods:
- Ideal magnetohydrodynamic (MHD) simulations were employed.
- Analysis focused on the evolution of perturbations from linear instabilities.
- Lagrangian compression was used as a measure of nonlinearity.
Main Results:
- Simulations confirmed the theoretical prediction of exponential growth in the nonlinear phase.
- Exponential growth was observed to continue at the linear rate.
- The intermediate nonlinear phase begins when Lagrangian compression approaches unity.
Conclusions:
- The intermediate nonlinear phase of ballooning instabilities exhibits sustained exponential growth.
- Plasma displacement and kinetic energy increase exponentially during this phase.
- Ideal MHD simulations validate theoretical predictions for nonlinear instability dynamics.
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