How does pressure balance work in the magnetosphere?

Thread starter ergospherical
Start date Jan 1, 2024
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Balance Magnetosphere Pressure

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Pressure balance in the magnetosphere involves understanding the relationship between kinetic energy and magnetic energy density. The equation ##\frac{1}{2} \dot{M} v^2 \sim## magnetic energy density suggests a balance between mass flow and magnetic forces. Properly setting up this balance is crucial for modeling magnetospheric dynamics. Energy equations play a significant role in determining how pressure varies in response to solar wind interactions. Understanding these principles is essential for studying the behavior of the magnetosphere.

Jan 1, 2024

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Homework Statement: How does the radius of the magnetosphere of a neutron star, accreting from a binary companion, scale with the surface magnetic field ##B##, the radius ##R## and the accretion rate ##\dot{M}##?

Relevant Equations: Spin down rate ##\dot{\Omega} = -B^2 R^6 \Omega^3 / (I \mu_0 c^3)##

I'm not sure how to set up the pressure balance at the magnetosphere? Maybe some energy equation relating ##\frac{1}{2} \dot{M} v^2 \sim## magnetic energy density?

Thread 'Product of two boosts and then two inverse boosts is rotation matrix'

So is there some elegant way to do this or am I just supposed to follow my nose and sub the Taylor expansions for terms in the two boost matrices under the assumption ##v,w\ll 1##, then do three ugly matrix multiplications and get some horrifying kludge for ##R## and show that the product of ##R## and its transpose is the identity matrix with det(R)=1? Without loss of generality I made ##\mathbf{v}## point along the x-axis and since ##\mathbf{v}\cdot\mathbf{w} = 0## I set ##w_1 = 0## to...

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