= Algebraic alpha quenching
{title2=$\alpha(B)=\alpha_0-p|B|^2$}
= Alpha quenching
{synonym}
Algebraic alpha quenching prescribes a field-dependent <alpha effect> as a closure for nonlinear <mean-field dynamo> feedback. The polynomial law $\alpha=\alpha_0-p|B|^2$ with $p>0$ decreases alpha, so it can saturate positive alpha but makes negative alpha more negative. It therefore differs importantly from the sign-preserving rational law $\alpha_0/(1+|B|^2/B_*^2)$. Its solutions must satisfy nonnegative squared-amplitude conditions; an assertion based only on large $|\alpha_0|$ need not hold for both signs.
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