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Scaling law: Difference between revisions
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* using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately) | * using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately) | ||
* guaranteeing the (linear) ''statistical independence'' of the independent variables (applying, e.g., [[:Wikipedia:Principal component analysis|Principal Component Analysis]]) | * guaranteeing the (linear) ''statistical independence'' of the independent variables (applying, e.g., [[:Wikipedia:Principal component analysis|Principal Component Analysis]]) | ||
== Dimensionless parameters == | |||
Assuming quasi-neutrality, the relevant scaling laws can be cast into dimensionless forms that involve only three plasma parameters (apart from geometrical factors): | |||
<ref name="ITER"/> | |||
<ref>B.B. Kadomtsev, Sov. J. Plasma Phys. '''1''' (1975) 295</ref> | |||
:<math>\rho* = \frac{\rho_i}{a}</math> | |||
:<math>\beta = \frac{\left \langle p \right \rangle}{B^2/2\mu_0}</math> | |||
:<math>\nu* \propto \nu_{ii}</math> | |||
Here, ρ<sub>i</sub> is the ion Larmor radius and ν<sub>ii</sub> the ion-ion collision frequency. Also see [[Beta|beta]]. | |||
== Confinement time scaling == | == Confinement time scaling == | ||
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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). Bohm scaling, however, suggests that transport may not be diffusive and may not characterized by a typical scale length. | 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). Bohm scaling, however, suggests that transport may not be diffusive and may not characterized by a typical scale length. | ||
(''More detail needed'') | (''More detail needed'') | ||
== References == | == References == | ||
<references /> | <references /> | ||