 Asymptotic energy of a radial magnetohydrodynamic wind

ID: asymptotic-energy-of-a-radial-magnetohydrodynamic-wind

r^{2} ∣ B_{p} ∣ \to F

and

u_{p} \to u_{\infty}

along an open magnetic surface, then

B_{ϕ} \sim - \frac{ω F}{u _{\infty} r}, ∣ v_{A ϕ} ∣ \to ω \frac{F}{μ _{0} k u _{\infty}} .

When enthalpy and gravity vanish asymptotically, the Bernoulli invariant becomes

ϵ = \frac{1}{2} u_{\infty}^{2} + \frac{ω ^{2} F}{μ _{0} k u _{\infty}} .

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