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Profile consistency: Difference between revisions
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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' | 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 the 'criticality' of transport: | ||
<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> | ||
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:<math>\chi = \chi_0 + \chi_1 \xi \left ( \frac{R}{L_T}-\frac{R}{L_{T,crit}}\right )^\alpha H_c</math> | :<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. | 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 (χ<sub>0</sub> and χ<sub>1</sub> being the sub- and super-critical transport coefficients, and ξ the 'stiffness factor'). | ||
This sharply non-linear dependence of the transport coefficient on the relevant profile parameter (''L<sub>T</sub>'') makes the profiles 'stiff' in the sense that the gradients (''L<sub>T</sub>'') will change little to a large change in drive (the heat source) in the appropriate parameter range. | |||
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, simply by making this idea of stiffness explicit (i.e., by measuring the response of the gradient to a change in drive or heat source). | ||
<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 /> | ||