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Wave energy density

< PlasmaWiki(Link to this page as [[PlasmaWiki/Wave energy density]])

$W=\frac{1}{16 \pi} [B^* \cdot B+E^*\cdot \partial_{\omega}(\omega \epsilon_h) \cdot E ]$

From Stix p. 78

For waves in the electrostatic approximation using the dispersion relation $k\cdot \epsilon \cdot k = 0$
Kinetic flux (electrostatic):

$T=-\frac{\omega}{16 \pi} |\phi|^2 k\cdot \frac{\partial \epsilon_h}{\partial k} \cdot k$

Note that T is a vector.

Energy density (electrostatic):

$W \simeq \frac{\omega}{16 \pi} |\phi|^2 k\cdot \frac{\partial \epsilon_h}{\partial \omega} \cdot k$

And W is a scalar.

Now the Poynting flux P can be found from the following relationship (06 P2 Q5):
$\frac{P+T}{W}=v_g$