Compute the power spectrum of the magnetic field given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.

Usage

call SHMagPowerSpectrum (c, a, r, lmax, spectrum, exitstatus)

Parameters

c : input, real*8, dimension (2, lmax+1, lmax+1)
The Schmidt seminormalized spherical harmonic coefficients of the magnetic potential.
a : input, real*8
The reference radius of the magnetic potential spherical harmonic coefficients.
r : input, real*8
The radius to evaluate the magnetic field.
lmax : input, integer
The maximum spherical harmonic degree to calculate the power spectrum.
spectrum : output, real*8, dimension (lmax+1)
The power spectrum of the magnetic field.
exitstatus : output, optional, integer
If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

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(1, l+1, m+1)**2 + c(2, l+1, m+1)**2 ].

Reference

Lowes, F. J., Mean-square values on sphere of spherical harmonic fields, J. Geophys. Res., 71(8), 2179, 1966.

See also

shmagpowerl

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