Internal inductance: Difference between revisions

Internal inductance (view source)

114 bytes removed , 10 August 2012

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 (for circular cross section plasmas with [[Toroidal coordinates|minor radius]] ''a''), where angular brackets signify taking a mean value.
-Alternatively, sometimes the internal inductance per unit length is used, defined as<ref name="Freidberg"/>
+Using Ampère's Law (<math>2 \pi a B_\theta(a) = \mu_0 I</math>), one obtains <ref name="Freidberg"/>
-:<math>l_i' = \frac{L_i}{2\pi R_0}\frac{4\pi}{\mu_0} = \frac{2L_i}{\mu_0R_0}</math>
+:<math>l_i = \frac{L_i}{2\pi R_0}\frac{4\pi}{\mu_0} = \frac{2L_i}{\mu_0R_0}</math>
 where ''R<sub>0</sub>'' is the [[Toroidal coordinates|major radius]], and similar for the external inductance.
-Using Ampère's Law (<math>2 \pi a B_\theta(a) = \mu_0 I</math>), one finds <math>l_i = 2 \pi l_i'</math>.
 The [[ITER]] design uses the following approximate definition:<ref>[[doi:10.1088/0029-5515/48/12/125002|G.L. Jackson, T.A. Casper, T.C. Luce, et al., ''ITER startup studies in the DIII-D tokamak'', Nucl. Fusion '''48''', 12 (2008) 125002]]</ref>