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CRPropa / CRPropa3

CRPropa is a public astrophysical simulation framework for propagating extraterrestrial ultra-high energy particles. https://crpropa.github.io/CRPropa3/
https://crpropa.desy.de
GNU General Public License v3.0
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Signature of sIndex in TurbulenceSpectrum #370

Closed saikatxdas closed 2 years ago

saikatxdas commented 2 years ago

Hi, I have a usage question. Does "alpha" in initTurbulence has the same signature as "sIndex" in SimpleTurbulenceSpectrum? I am trying to set the value of "alpha" in <B^2(k)> ~ k^alpha to obtain a Kolmogorov spectrum. So should I put +11/3 or -11/3 for "sIndex" in SimpleTurbulenceSpectrum?

adundovi commented 2 years ago

Hi, @saikatxdas. No, sIndex is the slope of the omnidirectional energy spectrum: E(k) ~ k^(-s) e.g., s = 5/3 for Kolmogorov's, or s = 3/2 for Kraichnan's spectrum. While "alpha" is -(sIndex + 2), e.g., alpha = -(5/3 + 2) = -11/3 for Kolmogorov's. See:

https://github.com/CRPropa/CRPropa3/blob/d93e9aab152dda143b6eba8ffee72ba083b1b757/src/magneticField/turbulentField/SimpleGridTurbulence.cpp#L15

The reason for this change in the signature is that "s" is more widespread in the literature than "alpha", especially in plasma physics. Most of people know what 5/3 is, while, -11/3 could be seen as a "derived" quantity.