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> | ||
Revision as of 20:13, 13 April 2015
Plasma performance is often expressed in terms of beta (), defined as: [1]
i.e., the ratio of the plasma pressure to the magnetic pressure. Here, is the mean plasma pressure, and the mean total field strength. It is customary to introduce also the poloidal beta and the toroidal beta , in which is replaced by the poloidal and toroidal magnetic field component, respectively. One has:
Normalized beta
The normalized beta (or Troyon factor)[2] is an operational parameter indicating how close the plasma is to reaching the Greenwald limit or destabilizing major MHD activity. Its definition is (for tokamaks): [3]
where is the external magnetic field in T, is the minor radius in m, and is the plasma current in MA. Typically, the maximum value of before the onset of deleterious instability is 3.5, although significantly higher values have been achieved. [4]
See also
References
- ↑ J.P. Freidberg, Plasma physics and fusion energy, Cambridge University Press (2007) ISBN 0521851076
- ↑ F. Troyon, R. Gruber, H. Saurenmann, S. Semenzato and S. Succi, MHD-Limits to Plasma Confinement, Plasma Phys. Control. Fusion 26 (1984) 209
- ↑ K. Miyamoto, Plasma Physics and Controlled Nuclear Fusion, Springer-Verlag (2005) ISBN 3540242171
- ↑ S.A. Sabbagh et al, Resistive wall stabilized operation in rotating high beta NSTX plasmas, Nucl. Fusion 46 (2006) 635-644