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SHMagPowerSpectrum
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
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