PPPL-4161 is available in <a href="PPPL-4161.pdf">pdf</a> format (664 KB).

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<b>Finite Element Implementation of Braginskii's Gyroviscous Stress with Application to the Gravitational Instability</b>
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<b>Authors:</b> N.M. Ferraro and S.C. Jardin
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<b>Date of PPPL Report:</b> May 2006
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<b>Submitted to:</b> Physics of Plasmas</p>


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We present a general, coordinate-independent expression for Braginskii's form of the ion gyroviscosity in the two-dimensional potential field representation, and implement this force in a full two-dimensional, two-fluid extended magnetohydrodynamic (MHD) numerical model. Our expression for the gyroviscous force requires no field to be differentiated more than twice, and thus is appropriate for finite elements with first derivatives continuous across element boundaries (C<sup>1</sup> finite elements). We derive from our model, including the full gyroviscous stress, linear dispersion relations of a homogeneous equilibrium and of an inverted-density profile in the presence of gravity. Our treatment of the gravitational instability substantially extends previous work on the subject. Linear and nonlinear simulations of the gravitational instability are presented. The <q>gyroviscous cancellation</q> effect is demonstrated, and some limitations of the omega-star approximation are discussed.







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