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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