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Scaling law: Difference between revisions
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== Dimensionless parameters == | == Dimensionless parameters == | ||
In the magnetic confinement context, and assuming quasi-neutrality, the relevant scaling laws (mainly, for the [[Energy confinement time|energy confinement time]]) can be cast into dimensionless forms that involve only three plasma parameters (apart from geometrical factors): | |||
<ref name="ITER"/> | <ref name="ITER"/> | ||
<ref>B.B. Kadomtsev, Sov. J. Plasma Phys. '''1''' (1975) 295</ref> | <ref>B.B. Kadomtsev, Sov. J. Plasma Phys. '''1''' (1975) 295</ref> | ||
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Here, ρ<sub>i</sub> is the ion Larmor radius and ν<sub>ii</sub> the ion-ion collision frequency. Also see [[Beta|beta]]. | Here, ρ<sub>i</sub> is the ion Larmor radius and ν<sub>ii</sub> the ion-ion collision frequency. Also see [[Beta|beta]]. | ||
In dimensionless form, the diffusivities can be written as: | |||
:<math>D = c_s \rho_s (\rho^*)^\alpha F(\nu^*,\beta,q, ...)\,</math> | |||
When α = 0, the scaling is said to be of the Bohm type, and when α = 1, of the gyro-Bohm type. | |||
== Confinement time scaling == | == Confinement time scaling == | ||
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=== Size scaling === | === Size scaling === | ||
The ELMy [[H-mode]] scaling is of the gyro-Bohm type (α = 1). | |||
The ELMy [[H-mode]] scaling is of the gyro-Bohm type. | |||
Gyro-Bohm scaling is what one would expect for diffusive transport based on a diffusive scale length proportional to ρ<sub>i</sub> (the ion gyroradius). | Gyro-Bohm scaling is what one would expect for diffusive transport based on a diffusive scale length proportional to ρ<sub>i</sub> (the ion gyroradius). | ||
By contrast, the L-mode scaling is of the Bohm type, which suggests that transport may [[Non-diffusive transport|not be diffusive]] and not characterized by a typical scale length, i.e., it is dominated by the scale length corresponding to the machine size (non-locality). | By contrast, the L-mode scaling is of the Bohm type (α = 0), which suggests that transport may [[Non-diffusive transport|not be diffusive]] and not characterized by a typical scale length, i.e., it is dominated by the scale length corresponding to the machine size (non-locality). | ||
<ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref> | <ref>A. Dinklage, ''Plasma physics: confinement, transport and collective effects'', Vol. 670 of Lecture notes in physics, Springer (2005) ISBN 3540252746</ref> | ||
One possible explanation of this behaviour is [[Self-Organised Criticality]], i.e., the self-regulation of transport by turbulence, triggered when a critical value of the gradient is exceeded. As a corollary, this mechanism might also explain the phenomenon of [[Profile consistency|profile consistency]]. | One possible explanation of this behaviour is [[Self-Organised Criticality]], i.e., the self-regulation of transport by turbulence, triggered when a critical value of the gradient is exceeded. As a corollary, this mechanism might also explain the phenomenon of [[Profile consistency|profile consistency]]. | ||