Dipole field model functions
The dip contains functions corresponding to the dipole field model.
Functions
- rbamlib.models.dip.B(r, mlat=0, planet='Earth')
The dipole model of magnetic field.
- Parameters:
r (float or ndarray) – The distance from the center of the planet, in planet’s radii.
mlat (float or ndarray, default = 0) – The magnetic latitude (MLAT), or geomagnetic latitude, is measured northwards from the equator in radians
planet (str, default = 'Earth') – The planet.
- Returns:
The magnetic field strength, in Gauss.
- Return type:
float or ndarray
- rbamlib.models.dip.B0(r, planet='Earth')
Magnetic field value at the magnetic equator.
Simplified calculation of the magnetic field at the magnetic equator.
- Parameters:
r (float or ndarray) – The distance from the center of the planet, in planet’s radii.
planet (str, default = 'Earth') – The planet.
- Returns:
The magnetic field strength, in Gauss.
- Return type:
float or ndarray
- rbamlib.models.dip.T(al)
Approximation of the integral function T related to the bounce period, derived in the dipole approximation.
- Parameters:
al (float or ndarray) – Equatorial pitch angle, in radians.
- Returns:
Value of T
- Return type:
float or ndarray
Notes
See Schulz & Lanzerotti (1974) [1].
\[T( \alpha ) \approx T_0 - \frac{1}{2}(T_0 - T_1) \cdot \left( \sin( \alpha ) + \sin( \alpha)^1/2 \right)\]Reference
- rbamlib.models.dip.Y(al)
Approximation of the integral function Y related to the second adiabatic invariant, derived in the dipole approximation.
- Parameters:
al (float or ndarray) – Equatorial pitch angle, in radians.
- Returns:
Value of Y
- Return type:
float or ndarray
Notes
See Schulz & Lanzerotti (1974) [2].
\[Y( \alpha ) \approx 2(1 - \sin( \alpha ))T_0 + (T_0 - T_1) \cdot \left( \sin( \alpha ) \cdot \ln( \sin( \alpha ) ) + 2 \sin( \alpha ) - 2 \sqrt{ \sin( \alpha ) } \right)\]References