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<ref>[http://link.aip.org/link/?PHPAEN/8/4096/1 F. Jenko et al, ''Critical gradient formula for toroidal electron temperature gradient modes'', Phys. Plasmas '''8''' (2001) 4096]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/8/4096/1 F. Jenko et al, ''Critical gradient formula for toroidal electron temperature gradient modes'', Phys. Plasmas '''8''' (2001) 4096]</ref> | ||
== Observations (tokamaks) == | == Observations ([[Tokamak|tokamaks]]) == | ||
* TFTR <ref>[http://dx.doi.org/10.1088/0029-5515/26/7/002 E.D. Fredrickson, J.D. Callen, et al., ''Heat pulse propagation studies in TFTR'', Nucl. Fusion '''26''' (1986) 849]</ref> | * TFTR <ref>[http://dx.doi.org/10.1088/0029-5515/26/7/002 E.D. Fredrickson, J.D. Callen, et al., ''Heat pulse propagation studies in TFTR'', Nucl. Fusion '''26''' (1986) 849]</ref> | ||
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* Various devices <ref>[http://dx.doi.org/10.1088/0741-3335/35/10/002 F. Wagner and U. Stroth, ''Transport in toroidal devices-the experimentalist's view'', Plasma Phys. Control. Fusion '''35''' (1993) 1321]</ref><ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter, C. Angioni, et al., ''Experimental studies of electron transport'', Plasma Phys. Control. Fusion '''43''' (2001) A323]</ref> | * Various devices <ref>[http://dx.doi.org/10.1088/0741-3335/35/10/002 F. Wagner and U. Stroth, ''Transport in toroidal devices-the experimentalist's view'', Plasma Phys. Control. Fusion '''35''' (1993) 1321]</ref><ref>[http://dx.doi.org/10.1088/0741-3335/43/12A/325 F. Ryter, C. Angioni, et al., ''Experimental studies of electron transport'', Plasma Phys. Control. Fusion '''43''' (2001) A323]</ref> | ||
== Observations (stellarators) == | == Observations ([[Stellarator|stellarators]]) == | ||
* W7-AS <ref>[http://dx.doi.org/10.1088/0741-3335/40/1/002 U. Stroth, ''A comparative study of transport in stellarators and tokamaks'', Plasma Phys. Control. Fusion '''40''' (1998) 9]</ref> | * W7-AS <ref>[http://dx.doi.org/10.1088/0741-3335/40/1/002 U. Stroth, ''A comparative study of transport in stellarators and tokamaks'', Plasma Phys. Control. Fusion '''40''' (1998) 9]</ref> | ||
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== Quantification methods == | == Quantification methods == | ||
It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify 'criticality' somehow | It is customary to introduce an ad-hoc transport model with a critical gradient (sharply enhanced transport above a critical value of the local gradient) to attempt to quantify 'criticality' somehow: | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/43/11/306 F. Imbeaux, F. Ryter, and X. Garbet, ''Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model'', Plasma Phys. Control. Fusion '''43''' (2001) 1503]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/43/11/306 F. Imbeaux, F. Ryter, and X. Garbet, ''Modelling of ECH modulation experiments in ASDEX Upgrade with an empirical critical temperature gradient length transport model'', Plasma Phys. Control. Fusion '''43''' (2001) 1503]</ref> | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/46/9/002 X. Garbet, P. Mantica, F. Ryter, et al., ''Profile stiffness and global confinement'', Plasma Phys. Control. Fusion '''46''' (2004) 1351]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/46/9/002 X. Garbet, P. Mantica, F. Ryter, et al., ''Profile stiffness and global confinement'', Plasma Phys. Control. Fusion '''46''' (2004) 1351]</ref> | ||
:<math>\chi = \chi_0 + \chi_1 \xi \left ( \frac{R}{L_T}-\frac{R}{L_{T,crit}}\right )^\alpha H_c</math> | |||
Here, ''H<sub>c</sub>'' is a step function (to activate supercritical transport), ''L<sub>T</sub>'' is the temperature gradient scale length, and χ is the heat transport coefficient. | |||
However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model.<ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, ''Quantifying profile stiffness'', Plasma and Fusion Research, '''3''' (2008) S1070]</ref> | However, it is possible to devise methods for the objective quantification of profile stiffness that do not depend so much on the introduction of any ad-hoc model.<ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, ''Quantifying profile stiffness'', Plasma and Fusion Research, '''3''' (2008) S1070]</ref> | ||
== References == | == References == | ||
<references /> | <references /> | ||