Profile consistency: Difference between revisions

Profile consistency (view source)

28 bytes added , 21 March 2011

Anonymous user

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 <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_{crit}</math>
+:<math>\chi = \chi_0 + \chi_1 \xi \left ( \frac{R}{L_T}-\frac{R}{L_{T,crit}}\right )^\alpha H\left ( \frac{R}{L_T}-\frac{R}{L_{T,crit}}\right )</math>
-Here, ''H<sub>crit</sub>'' is a step function (to activate supercritical transport), ''L<sub>T</sub> = T/&nabla; T'' is the temperature gradient scale length, and &chi; is the heat transport coefficient (&chi;<sub>0</sub> and &chi;<sub>1</sub> being the sub- and super-critical transport coefficients, and &xi; the 'stiffness factor').
+Here, ''H'' is a step function (to activate supercritical transport), ''L<sub>T</sub> = T/&nabla; T'' is the temperature gradient scale length, and &chi; is the heat transport coefficient (&chi;<sub>0</sub> and &chi;<sub>1</sub> being the sub- and super-critical transport coefficients, and &xi; 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 in response to a large change in drive (the heat source) in the appropriate parameter range.