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MakeMagGridDH
Create 2D cylindrical maps on a flattened ellipsoid of all three vector components of the magnetic field, the magnitude of the magnetic field, and the magnetic potential.
Usage
rad
, theta
, phi
, total
= MakeMagGridDH (cilm
, r0
, [lmax
, a
, f
, sampling
, lmaxcalc
])
Returns
rad
: float, dimension(2*lmax
+2,sampling
*(2*lmax
+2))- A 2D equally sampled (
n
byn
) or equally spaced (n
by 2n
) grid of the radial component of the magnetic field corresponding to the input spherical harmonic coefficientscilm
. The first latitudinal band corresponds to 90 N, the latitudinal band for 90 S is not included, and the latitudinal sampling interval is 180/n
degrees. The first longitudinal band is 0 E, the longitudinal band for 360 E is not included, and the longitudinal sampling interval is 360/n
for an equally sampled and 180/n
for an equally spaced grid, respectively. theta
: float, dimension(2*lmax
+2,sampling
*(2*lmax
+2))- A 2D equally sampled or equally spaced grid of the theta component of the magnetic field.
phi
: float, dimension(2*lmax
+2,sampling
*(2*lmax
+2))- A 2D equally sampled or equally spaced grid of the phi component of the magnetic field.
total
: float, dimension(2*lmax
+2,sampling
*(2*lmax
+2))- A 2D equally sampled or equally spaced grid of the total magnetic field strength.
Parameters
cilm
: float, dimension (2,lmaxin
+1,lmaxin
+1)- The real Schmidt semi-normalized spherical harmonic coefficients to be expanded in the space domain. The coefficients
C1lm
andC2lm
refer to the cosine (Clm
) and sine (Slm
) coefficients, respectively, withClm=cilm[0,l,m]
andSlm=cilm[1,l,m]
. Alternatively,C1lm
andC2lm
correspond to the positive and negative order coefficients, respectively. r0
: float- The reference radius of the spherical harmonic coefficients.
lmax
: optional, integer, default =lamxin
- The maximum spherical harmonic degree of the coefficients
cilm
. This determines the number of samples of the output grids,n=2*lmax+2
, and the latitudinal sampling interval,90/(lmax+1)
. a
: optional, float, default =r0
- The semi-major axis of the flattened ellipsoid on which the field is computed.
f
: optional, float, default = 0- The flattening of the reference ellipsoid: i.e.,
F=(R_equator-R_pole)/R_equator
. sampling
: optional, integer, default = 2- If 1 the output grids are equally sampled (
n
byn
). If 2, the grids are equally spaced (n
by 2n
). lmaxcalc
: optional, integer, default =lmax
- The maximum spherical harmonic degree used in evaluating the functions. This must be less than or equal to
lmax
.
Description
MakeMagGridDH
will create 2-dimensional cylindrical maps from the spherical harmonic coefficients cilm
of all three components of the magnetic field, the total field strength, and the magnetic potential. The magnetic potential is given by
V = R0 Sum_{l=1}^LMAX (R0/r)^{l+1} Sum_{m=-l}^l C_{lm} Y_{lm}
and the magnetic field is
B = - Grad V
.
The coefficients are referenced to a radius r0
, and the function is computed on a flattened ellipsoid with semi-major axis a
(i.e., the mean equatorial radius) and flattening f
.
The default is to calculate grids for use in the Driscoll and Healy routines that are equally sampled (n
by n
), but this can be changed to calculate equally spaced grids (n
by 2n
) by setting the optional argument sampling
to 2. The input value of lmax
determines the number of samples, n=2lmax+2
, and the latitudinal sampling interval, 90/(lmax+1)
. The first latitudinal band of the grid corresponds to 90 N, the latitudinal band for 90 S is not calculated, and the latitudinal sampling interval is 180/n
degrees. The first longitudinal band is 0 E, the longitudinal band for 360 E is not calculated, and the longitudinal sampling interval is 360/n
for equally sampled and 180/n
for equally spaced grids, respectively.
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