Compute the power of the magnetic field for a single degree l given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.
Usage
power = SHMagPowerL (cilm, a, r, l)
Parameters
power: output, real(dp)- The power at degree
l cilm: input, real(dp), dimension (2, l+1, l+1)- The Schmidt seminormalized spherical harmonic coefficients of the magnetic potential.
a: input, real(dp)- The reference radius of the magnetic potential spherical harmonic coefficients.
r: input, real(dp)- The radius to evaluate the magnetic field.
l: input, integer(int32)- The spherical harmonic degree for which the power will be calculated.
Description
SHMagPowerL will calculate the power of the magnetic field at radius r for a single degree l given the magnetic potential Schmidt seminormalized spherical harmonic coefficients c evaluated at radius a. This is explicitly calculated as:
S(l) = (l+1) (a/r)**(2l+4) Sum_{m=0}^l [ cilm(1, l+1, m+1)**2 + cilm(2, l+1, m+1)**2 ].