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Internal inductance: Difference between revisions
→Normalized internal inductance
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In a [[tokamak]], the field produced by the plasma current is the ''poloidal'' magnetic field ''B<sub>θ<sub>'', so only this field component enters the definition. | In a [[tokamak]], the field produced by the plasma current is the ''poloidal'' magnetic field ''B<sub>θ<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{\left \langle B_\theta^2 \right \rangle_P}{B_\theta^2(a)} = \frac{2 \pi \ | :<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''), where angular brackets signify taking a mean value. | (for circular cross section plasmas with [[Toroidal coordinates|minor radius]] ''a''), where angular brackets signify taking a mean value. | ||