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Beta: Difference between revisions
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Plasma performance is often expressed in terms of beta ( | Plasma performance is often expressed in terms of beta (<math>\beta</math>), defined as: | ||
<ref>J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref> | <ref>J.P. Freidberg, ''Plasma physics and fusion energy'', Cambridge University Press (2007) ISBN 0521851076</ref> | ||
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i.e., the ratio of the plasma pressure to the magnetic pressure. | i.e., the ratio of the plasma pressure to the magnetic pressure. | ||
Here, < | Here, <math>\left \langle p \right \rangle </math> is the mean plasma pressure, and <math>B</math> the mean total field strength. | ||
It is customary to introduce also the ''poloidal'' | It is customary to introduce also the ''poloidal'' beta <math>\beta_p</math> and the ''toroidal'' beta <math>\beta_t</math>, in which <math>B</math> is replaced by the poloidal and toroidal magnetic field component, respectively. One has: | ||
:<math>\frac{1}{\beta} = \frac{1}{\beta_p} + \frac{1}{\beta_t}</math> | :<math>\frac{1}{\beta} = \frac{1}{\beta_p} + \frac{1}{\beta_t}</math> | ||
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<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 = \ | :<math>\beta_N = \beta_t \frac{a B_0}{I_p}</math> | ||
where | where <math>B_0</math> is the external magnetic field in T, <math>a</math> is the minor radius in m, and <math>I_p</math> is the plasma current in MA. | ||
Typically, the maximum value of | Typically, the maximum value of <math>\beta_N</math> before the onset of deleterious instability is 3.5, although significantly higher values have been achieved. | ||
<ref>[http://dx.doi.org/10.1088/0029-5515/46/5/014 S.A. Sabbagh et al, ''Resistive wall stabilized operation in rotating high beta NSTX plasmas'', Nucl. Fusion '''46''' (2006) 635-644]</ref> | <ref>[http://dx.doi.org/10.1088/0029-5515/46/5/014 S.A. Sabbagh et al, ''Resistive wall stabilized operation in rotating high beta NSTX plasmas'', Nucl. Fusion '''46''' (2006) 635-644]</ref> | ||