Compute the power spectrum of the magnetic field given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.
call SHMagPowerSpectrum (c, a, r, lmax, spectrum)
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.
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:
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 ].