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 On the other hand, the energy contained in the magnetic field produced by the loop is
 :<math>W = \int{\frac{B^2}{2\mu_0} d\vec r}</math>
-It can be shown that<ref>P.M. Bellan, ''Fundamentals of Plasma Physics'', Cambridge University Press (2006) ISBN 0521821169</ref><ref>[[:Wikipedia:Inductance]]</ref>
+It can be shown that<ref>P.M. Bellan, ''Fundamentals of Plasma Physics'', Cambridge University Press (2006) {{ISBN|0521821169}}</ref><ref>[[:Wikipedia:Inductance]]</ref>
 :<math>W = \frac12 L I^2</math>
-The internal inductance is defined as the part of the inductance obtained by integrating over the plasma volume ''P'' <ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref>:
+== Internal inductance of a plasma ==
+The ''internal'' inductance is defined as the part of the inductance obtained by integrating over the plasma volume ''P'' <ref name="Freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) {{ISBN|0521851076}}</ref>:
 :<math>\frac12 L_i I^2 = \int_P{\frac{B^2}{2\mu_0} d\vec r}</math>
 Its complement is the external inductance (''L = L<sub>i</sub> + L<sub>e</sub>'').
+== Normalized internal inductance ==
 In a [[tokamak]], the field produced by the plasma current is the ''poloidal'' magnetic field ''B<sub>&theta;<sub>'', so only this field component enters the definition.
-In this context, it is common to use the ''normalized'' internal inductance<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>
+In this context, it is common to use the ''normalized'' internal inductance<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN|3540242171}}</ref>
-:<math>l_i = \frac{2 \pi \int_P{B_\theta^2(\rho) \rho d\rho}}{\pi a^2 B_\theta^2(a)} </math>
+:<math>l_i = \frac{\left \langle B_\theta^2 \right \rangle_P}{B_\theta^2(a)} = \frac{2 \pi \int_0^a{B_\theta^2(\rho) \rho d\rho}}{\pi a^2 B_\theta^2(a)}</math>
-(for circular cross section plasmas with [[Toroidal coordinates|minor radius]] ''a'').
+(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.
-This differs from the preceding definition according to <math>l_i' = l_i/(2\pi R_0)</math>.
-The value of the normalized internal inductance depends on the current density profile in the toroidal plasma.
+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>
+:<math>l_i(3) = \frac{2 V \left \langle B_\theta^2 \right \rangle}{\mu_0^2I^2 R_0}</math>
+which is equal to <math>l_i</math> assuming the plasma has a perfect toroidal shape, <math>V = \pi a^2 \cdot 2 \pi R_0</math>.<ref>[[Effective plasma radius]]</ref>
+== Relation to current profile ==
+The value of the normalized internal inductance depends on the current density profile in the toroidal plasma (as it produces the <math>B_\theta(\rho)</math> profile): a small value of <math>l_i</math> corresponds to a broad current profile.
 == References ==
 <references />