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Finite Larmor Radius Stabilization of Ideal Ballooning Modes in Three-Dimensional Geometry
| Author: | Hegna C. C. |
| Coauthor: | J. W. Wohlbier |
| Institution : | University of Wisconsin |
| Abstract text: | The stabilizing effect of finite Larmor radius (FLR) on ideal MHD ballooning modes has been known for some time. However, there are additional complications in three-dimensional geometry. Due to the prominent field line dependence of the leading order theory ballooning eigenvalues, it is anticipated that the corresponding global mode is highly localized on the magnetic surface. Hence, nonideal physics, such as FLR, may more easily stabilize these modes in 3-D systems relative to the corresponding axisymmetric systems. The standard analysis of the ideal MHD ballooning mode problem uses a WKB-like formalism that in leading order results in an ordinary differential equation (the ballooning equation) that determines local eigenvalues as functions of flux surface label, field line, and wavenumber. To next order, ray equations need to be solved that then lead to the identification of global eigenvalues after imposing the WKB quantization condition. Inclusion of FLR modifies the eigenvalue by a term proportional to the field line derivative of the ballooning mode eikonal. In axisymmetric systems, this quantity is a constant along ray trajectories and WKB quantization in the presence of FLR is trivial. However, in three-dimensional systems, since the local ballooning mode eigenvalue is field line dependent, the FLR correction (~ w*) is not constant along the ray trajectories of the corresponding ideal MHD system. The presence of FLR significantly modifies the structure of the WKB ray trajectories. In this work, we introduce a ‘toy’ 3-D equilibrium that models the behavior of ideal ballooning eigenvalues in 3-D systems and solve the corresponding ray equations. |
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