Example of GT in the Magnetosphere
---------


Consider the task of the calculation of the cut-off rigidity of antiprotons at altitude of 400 km, null meridian,
and 40 degrees northern latitude in a vertical direction. These coordinates correspond to :math:`\vec{r} = (0.8139, 0, 0.6829)`
radius of earth, and the velocity along :math:`-\vec{r}`. Calculations are done in IGRF13 field. These initial parameters correspond to

.. code-block:: python

    Bfield = Gauss(model = "IGRF", model_type = core, version = 13)
    InitialFlux = Flux(Spectrum = Monolines(energy = np.linspace(4.30, 6.00, 171) * Units.GeV),
                       Distribution = SphereSurf(Center = np.array([0.8139, 0, 0.6829]) * Units.RE, V0 = np.array([-0.8139, 0, -0.6829]), Radius=0)
                       Names = "apr",
                       Nevents = 171)


Overall the codes looks like:

.. code-block:: python

    import os
    import numpy as np
    from datetime import datetime

    from gtsimulation.Global import Regions, Units
    from gtsimulation.Algos import BunemanBorisSimulator

    Region = Regions.Magnetosphere
    Bfield = Gauss(model = "IGRF", model_type = core, version = 13)
    Date = datetime(2006, 6, 15)

    Medium = None
        
    InitialFlux = Flux(Spectrum = Monolines(energy = np.linspace(4.30, 6.00, 171) * Units.GeV),
                       Distribution = SphereSurf(Center = np.array([0.8139, 0, 0.6829]) * Units.RE, V0 = np.array([-0.8139, 0, -0.6829]), Radius=0)
                       Names = "apr",
                       Nevents = 171)

    UseDecay = False
    NuclearInteraction = None

    Nfiles = 1
    Output = "IGRFSteps" + os.sep + "IGRF_Step5e-6"
    Save = [4, {"Bfield":True}]
    Verbose = True
    BreakConditions = {"Rmin": 1 * Units.RE, "Rmax": 10 * Units.RE, "MaxPath": 1000 * Units.RE}
    simulator = BunemanBorisSimulator(Date=Date,
                                      Region=Region,
                                      Bfield=Bfield,
                                      Particles=InitialFlux,
                                      Num=int(5e7),
                                      Step=5e-6,
                                      Save=Save,
                                      Nfiles=Nfiles,
                                      Output=Output,
                                      Verbose=Verbose,
                                      BreakCondition=BreakConditions,
                                      ForwardTrck=-1)
    simulator()

The methodology of calculation of cut-off is the following. We backtrace the particle, and see whether it falls onto the earth,
gets captured or leaves the magnetosphere. To turn on backtracking regime we pass in `BunemanBorisSimulator(ForwardTrack=-1)`.
These conditions are written in `BreakConditions` respectively.

.. code-block:: python

    BreakConditions = {"Rmin": 1 * Units.RE, "MaxPath": 1000 * Units.RE, "Rmax": 10 * Units.RE}

The particles that statisfy the first or the second condition, then these particles cannot be revered and the trajectories are forbidden.
On the plot they are showed in black. Otherwise, the particles and reach the altitude from outside the magnetosphere, hence those are
allowed trajectories (white lines on the plot).

.. image:: images/cut_off.jpg