From 544b63d5082d51d0f700ce906f3a7159b16a915d Mon Sep 17 00:00:00 2001 From: Samuel Lazerson Date: Thu, 23 Jan 2025 11:20:49 +0100 Subject: [PATCH] Added deffinition of CURPOL for Bnorm. --- BNORM.md | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) diff --git a/BNORM.md b/BNORM.md index 0823fe49..d2725d8a 100644 --- a/BNORM.md +++ b/BNORM.md @@ -32,6 +32,24 @@ called to handle contribution to the vector potential by the point x. The curl of this vector potential then provides the normal component of the magnetic field on the VMEC surface. +The code utlizes a normalization for total poloidal current CURPOL which +is + +\$$ I_{pol}=\frac{2\pi B_v\left(0,0\right)}{N_{per}}. $$ + +This normalization arrises from the deffinition of a wire and the +vector identities. The field of a wire is: + +\$$ B_{wire}=\frac{\mu_0 I_{pol}}{2\pi R} $$ + +and the deffinition of the toroidla field is: + +\$$ B_\phi = RB^v = R \frac{B_v}{R^2} = \frac{B_v}{R} $$ + +Combining these deffinitions gives: + +\$$ I_{pol} = \frac{2\pi B_v}{\mu_0} = \frac{CURPOL N_{per}}{\mu_0} $$ + ------------------------------------------------------------------------ ### Compilation