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SHMagPowerSpectrum
Compute the power spectrum of the magnetic field given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.
Usage
spectrum
= SHMagPowerSpectrum (c
, a
, [r
, lmax
])
Returns
spectrum
: float, dimension (lmax
+1)- The power spectrum of the magnetic field.
Parameters
c
: float, dimension (2,lmaxin
+1,lmaxin
+1)- The Schmidt seminormalized spherical harmonic coefficients of the magnetic potential.
a
: float- The reference radius of the magnetic potential spherical harmonic coefficients.
r
: float, default =a
- The radius to evaluate the magnetic field.
lmax
: optional, integer, default =lmaxin
- The maximum spherical harmonic degree to calculate the power spectrum.
Description
SHMagPowerSpectrum
will calculate the power spectrum of the magnetic field at radius r
given the magnetic potential Schmidt seminormalized spherical harmonic coefficients c
evaluated at radius a
. For a given degree l
, this is explicitly calculated as (Lowes 1966):
S(l) = (l+1) (a/r)**(2l+4) Sum_{m=0}^l [ c[0,l,m]**2 + c[1,l,m]**2 ].
Reference
Lowes, F. J., Mean-square values on sphere of spherical harmonic fields, J. Geophys. Res., 71(8), 2179, 1966.
See also
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