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, M., & Lanzerotti, L. J. (1974). Particle Diffusion in the Radiation Belts (Vol. 7). Springer-Verlag Berlin Heidelberg. Retrieved from http://www.springer.com/physics/book/978-3-642-65677-4

\[T( \alpha ) \approx T_0 - \frac{1}{2}(T_0 - T_1) \cdot \left( \sin( \alpha ) + \sin( \alpha)^1/2 \right)\]

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, M., & Lanzerotti, L. J. (1974). Particle Diffusion in the Radiation Belts (Vol. 7). Springer-Verlag Berlin Heidelberg. Retrieved from http://www.springer.com/physics/book/978-3-642-65677-4

\[Y( \alpha ) \approx 2(1 - \sin( \alpha ))T_0 + (T_0 - T_1) \cdot \left( \sin( \alpha ) \cdot \ln( \sin( \alpha ) ) + 2 \sin( \alpha ) - 2 \sqrt{ \sin( \alpha ) } \right)\]