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Profile consistency: Difference between revisions
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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 (χ<sub>0</sub> and χ<sub>1</sub> being the sub- and super-critical transport coefficients, and ξ the 'stiffness factor'). | Here, ''H<sub>c</sub>'' is a step function (to activate supercritical transport), ''L<sub>T</sub> = T/∇ T'' 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. | 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. | ||
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). | 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). | ||