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Beta: Difference between revisions
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Plasma performance is often expressed in terms of beta (<math>\beta</math>), defined as: | Plasma performance is often expressed in terms of beta (<math>\beta</math>), defined as: | ||
<ref name="freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref> | <ref name="freidberg">J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) {{ISBN|0521851076}}</ref> | ||
:<math>\beta = \frac{\left \langle p \right \rangle}{B^2/2\mu_0}</math> | :<math>\beta = \frac{\left \langle p \right \rangle}{B^2/2\mu_0}</math> | ||
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[[File:Troyon limit.png|200px|thumb|Troyon Limit<ref>ITER Physics Expert Group on Disruptions, Plasma Control, and MHD, ''ITER Physics Basis Chapter 3: MHD stability, operational limits and disruptions'', [[doi:10.1088/0029-5515/39/12/303|Nucl. Fusion '''39 ''' (1999) 2251-2389]]</ref>]] | [[File:Troyon limit.png|200px|thumb|Troyon Limit<ref>ITER Physics Expert Group on Disruptions, Plasma Control, and MHD, ''ITER Physics Basis Chapter 3: MHD stability, operational limits and disruptions'', [[doi:10.1088/0029-5515/39/12/303|Nucl. Fusion '''39 ''' (1999) 2251-2389]]</ref>]] | ||
<math>\beta</math> is often expressed in terms of the normalized beta (or Troyon factor)<ref>F. Troyon, R. Gruber, H. Saurenmann, S. Semenzato and S. Succi, ''MHD-Limits to Plasma Confinement'', [[doi:10.1088/0741-3335/26/1A/319|Plasma Phys. Control. Fusion '''26''' (1984) 209]]</ref>, an operational parameter indicating how close the plasma is to reaching the [[Greenwald limit]] or a destabilising major MHD activity. Its definition is (for tokamaks): | <math>\beta</math> is often expressed in terms of the normalized beta (or Troyon factor)<ref>F. Troyon, R. Gruber, H. Saurenmann, S. Semenzato and S. Succi, ''MHD-Limits to Plasma Confinement'', [[doi:10.1088/0741-3335/26/1A/319|Plasma Phys. Control. Fusion '''26''' (1984) 209]]</ref>, an operational parameter indicating how close the plasma is to reaching the [[Greenwald limit]] or a destabilising major MHD activity. Its definition is (for tokamaks): | ||
<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref> | <ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN|3540242171}}</ref> | ||
:<math>\beta_N = \beta \frac{a B_T}{I_p}</math> | :<math>\beta_N = \beta \frac{a B_T}{I_p}</math> | ||