(a) Show that the potential energy (19.59) can be transformed into the following form:

Here symbols without tildes represent quantities in the plasma region, and those with tildes are in the vacuum region; ξ_n is the component of the fluid displacement orthogonal to the vacuum-plasma interface.

(b) Explain the physical interpretation of each term in the expression for the potential energy in part (a). Notice that, although our original expression for the potential energy, W = −1/2∫_V ξ · F[ξ]dV, entails an integral only over the plasma region, it actually includes the vacuum region’s magnetic energy.

Transcribed Image Text:

W[s] = 12 hdv [-jxb.g+ dV + + 1² S₁v² dΣ· V 2 av B² 2μ40 b² - но - + SP P - Δρ P B² 2μ0, 2 + 1 - So 1|2 vacuum dV 6² но (19.60)