irfpy.jupsci.ganymede_magfield

Models of ganymede magnetic field

A simple dipole is implemented in SimpleDipole.

A tilted dipole is implemented in TiltedDipole.

An MHD simulation provides more realisitic fields. It is indeed implemented in irfpy.mhddata.MagneticField1201.

class irfpy.jupsci.ganymede_magfield.SimpleDipole(dipole_moment=None)

Bases: object

A simplest dipole approximation.

Centered at the center, no tilt.

It is obviously not valid, but for the very first approximation.

The formulation of the dipole field is

\[\mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi}\frac{1}{r^3} (3(\mathbf{m}\cdot\hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{m})\]

The usage is:

>>> sd = SimpleDipole()
>>> pos = np.array([2631.0, 0.0, 0.0])  # Position at equator
>>> bfield_equator = sd.get_field(pos)
>>> print('%.1f, %.1f, %.1f' % (bfield_equator[0], bfield_equator[1], bfield_equator[2]))
0.0, 0.0, 719.3

>>> pos = np.array([0.0, -2631.0, 0.0])  # Also at equator.
>>> bfield_equator2 = sd.get_field(pos)
>>> print('%.1f, %.1f, %.1f' % (bfield_equator2[0], bfield_equator2[1], bfield_equator2[2]))   # The -0.0 will be a little bit ugly.
0.0, -0.0, 719.3

>>> pos = np.array([0.0, 0.0, 2631.0])  # At the pole.
>>> bfield_pole = sd.get_field(pos)
>>> print('%.1f, %.1f, %.1f' % (bfield_pole[0], bfield_pole[1], bfield_pole[2]))
-0.0, -0.0, -1438.6

The dipole_moment is set to the dipole_moment. The default value is np.array([0, 0, -1.31e20]) which produces ~719 nT at the equatorial surface. This value is verified by Kivelson et al., 2002.

mu0 = 1.2566370614359173e-06

dipole_moment

The magnetic dipole moment. Preset to -1.31e20 only z direction

get_field(position_km)

Get the field at the position.

Parameters

position_km (np.array with shape of (3,)) – Position vector in km (x, y, z).

Returns

Mangetic field vector in nT.

Return type

np.array with shape of (3,)

interpolate3d(x, y, z)

Interface to get the magnetic field.

To make the same interface with irfpy.pep.mhddata.MagneticField1201, this method is prepared.

Parameters

• x – X position in Rg

• y – Y position in Rg

• z – Z position in Rg

Returns

A numpy array of the B-field with shape of (3,)

Since the dipole field is analytical and contiuous, no interpolation is needed, but again ,this is prepared for the interface.

class irfpy.jupsci.ganymede_magfield.TiltedDipole

Bases: irfpy.jupsci.ganymede_magfield.SimpleDipole

A second simplest model of the Ganymede field.

The second simplest model is dipole tilted a certain angle. Indeed the implementation is quite the same to SimpleDipole.

According to Kivelson et al., 2002, “it is tilted by 176 degrees from the spin axis with the pole in the southern hemisphere rotated by 24 degrees from the Jupiter-facing meridian plane toward the trailing hemisphere.”

The coordinate system plays into this game, indeed. It is really annoying, but I will follow the SPICE for future consistency.

For SPICE, IAU_GANYMEDE coordinate system is defined. This looks as “x points to jupiter; y opposite to ganymede motion”. The definition is indeed deferent from Figure 2 in Kivelson et al., 2002.

Nevertheless, the Kivelson’s statement is quite complete. Tilt of 176 deg is, as stated, in the southern hemisphere. Rotate of 24 deg from Jupiter-facing meridian (=x-z plane in IAU) toward the trailing hemisphere (=minus y in IAU).

This means that the magnetic dipole moment vector is

\[\begin{split}m_x = m \sin(176.) * \cos(-24.) \\ m_y = m \sin(176.) * \sin(-24.) \\ m_z = m \cos(176.)\end{split}\]

irfpy.jupsci.ganymede_magfield.doctests()