Internal inductance: Difference between revisions

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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>:

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 = Li + Le'').

== Normalized internal inductance ==

In a [[tokamak]], the field produced by the plasma current is the ''poloidal'' magnetic field ''Bθ'', so only this field component enters the definition.

@@ Line 7: / Line 7: @@
 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>:
+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.