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| author | Prefetch | 2026-09-14 18:11:38 +0200 |
|---|---|---|
| committer | Prefetch | 2026-09-14 18:11:38 +0200 |
| commit | cc391ce3b9867d88d124e147931d33be34e756fc (patch) | |
| tree | d719cf6ad60f559fcc0c2042907a2c4d8cd62977 /source/know/concept/grad-shafranov-equation/index.md | |
| parent | 5cacf4ffaf3a9621ab536195f6469f98a420f054 (diff) | |
Improve knowledge base
Diffstat (limited to 'source/know/concept/grad-shafranov-equation/index.md')
| -rw-r--r-- | source/know/concept/grad-shafranov-equation/index.md | 13 |
1 files changed, 7 insertions, 6 deletions
diff --git a/source/know/concept/grad-shafranov-equation/index.md b/source/know/concept/grad-shafranov-equation/index.md index b86c032..c9104d2 100644 --- a/source/know/concept/grad-shafranov-equation/index.md +++ b/source/know/concept/grad-shafranov-equation/index.md @@ -36,9 +36,9 @@ $$\begin{aligned} = 0 \end{aligned}$$ -Notice that $$\vb{E} = 0$$ is a result of the ideal generalized Ohm's law. -Under these assumptions, the relevant MHD equations to be solved are -Gauss' law for magnetism, Ampère's law, and the MHD momentum equation, respectively: +Notice that $$\vb{E} = 0$$ is a result of ideal MHD's generalized Ohm's law. +Under these assumptions, the relevant equations to be solved are +Gauss' law for magnetism, Ampère's law, and the momentum equation of MHD, respectively: $$\begin{aligned} 0 @@ -51,11 +51,12 @@ $$\begin{aligned} = \vb{J} \cross \vb{B} \end{aligned}$$ -The goal is to analyze them in this order, +The idea is to analyze them in this order, exploiting toroidal symmetry along the way, to arrive at a general equilibrium condition. -[Cylindrical polar coordinates](/know/concept/cylindrical-polar-coordinates/) $$(r, \theta, z)$$ -are a natural choice, with the $$z$$-axis running through the middle of the torus. +[Cylindrical polar coordinates](/know/concept/cylindrical-polar-coordinates/) +$$(r, \theta, z)$$ are a natural choice, +with the $$z$$-axis running through the middle of the torus. As preparation, it is a good idea to write $$\vb{B}$$ as the curl of a magnetic vector potential $$\vb{A}$$, |
