Beta: Difference between revisions

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== Beta limit ==
== Beta limit ==


The upper limit of <math>\beta_N</math> has been determined empirically by Troyon to 0.028. Often <math>\beta</math> is expressed in percent, in which case <math>\beta_N = 2.8</math>. This limit results from many different numerical studies determined to find the overall <math>\beta</math> limit out of many different MHD instabilities, such as [[external kink modes]], [[ballooning kink modes]], [[internal modes]], [[localized modes]], etc. <ref name="freidberg"></ref>
The upper limit of <math>\beta_N</math> has been determined numerically by Troyon to 0.028. Often <math>\beta</math> is expressed in percent, in which case <math>\beta_N = 2.8</math>. This limit results from many different numerical studies determined to find the overall <math>\beta</math> limit out of many different MHD instabilities, such as [[external kink modes]], [[ballooning kink modes]], [[internal modes]], [[localized modes]], etc. <ref name="freidberg"></ref>


Empirical evaluation from the data of different tokamaks raises this value slightly to <math>\beta_N = 3.5</math>, although significantly higher values have been achieved.
Empirical evaluation from the data of different tokamaks raises this value slightly to <math>\beta_N = 3.5</math>, although significantly higher values have been achieved.