Profile consistency: Difference between revisions
→Ad-hoc transport models
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:<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> | :<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'' 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'). | Here, ''H'' is a [[:Wikipedia:Heaviside_step_function|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 in response 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. | ||