import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import os
os.chdir('..')
import proppy as pp

Simulation setup

Parameters

sim = pp.Simulation()

# source
nr_particles = 5
source_pos = np.array([0.0, 0.0, 0.0], dtype=np.float32)
energy = 10**15 # eV
phi = 0
pitch_angle = 2*np.pi * 54.74/360
source = pp.PointSourceOriented(energy, source_pos, nr_particles, pitch_angle, phi)
sim.add_source(source)

# propagator
nr_steps = 4*10**4
step_size = 0.5*10**10 # [m]
mfp = np.array([2.13*10**12/2.0, 2.13*10**12/2.0, 2.1078*10**12], dtype=np.float32)  # [m]
rms = 1 # [Gaus]
magnetic_field = pp.OrderedBackgroundField(rms, [0,0,1]).magnetic_field
propagator = pp.AnisotropicPropagator(magnetic_field, mfp, nr_steps, step_size)
sim.add_propagator(propagator)

# observer
substeps = [True, True, True] # observe only steps (no substeps)
observer = pp.ObserverAllSteps(substeps)

sim.add_observer(observer)

start simulation
Propagator initialized
Observer initialized

%time sim.run_simulation()
sim.save_data('data/data_tut_3')

CPU times: user 4.34 s, sys: 90.4 ms, total: 4.43 s
Wall time: 4.43 s
saved data file data/data_tut_3.pkl

Analyze trajectories

Even though individual trajectories of particles performing a random walk have no physical meaning, their visualization is helpful in many respects:

• 1. The visualization of the substeps clarifies whether the implementation works as desired
• 1. The initial ballistic character of the propagation becomes visible
• 1. The diffusive character becomes visible on large time scales

First load simulated data file and create a trajectory object. As we simulated a 3d trajectory, we choose 3 dimensions and initialize the object with the dataframe. We also want to get a list of ids of our particles.

df = pd.read_pickle("data/data_tut_3.pkl")
df_time_evolution_observer = df.loc[df['radius'] == -1.0]
tra = pp.Trajectory(df_time_evolution_observer)
particle_ids = tra.get_particle_ids()

init trajectory plotting class

1. Substeps

The visualization of the substeps clarifies whether the implementation works as desired. We choose only a few steps of a single particle to have a good resolution.

substep_0 = 0 # positions after 1. substep
substep_1 = 2 # positions after 3. substep -> final position after each step for 3d
nr_steps = 10
file_name = None # where to save figure (None doesn't save a figure)
tra.plot_trjectory_substeps(substep_0, substep_1, particle_ids[0], nr_steps, file_name)

2. Ballistic movement

The initial ballistic character of the propagation becomes visible when plotting only a few steps.

nr_steps = 2*10**2
tra.plot_trajectory('x', 'y', 'd', particle_ids[0], nr_steps, None)
tra.plot_trajectory('d', 'z', 'd', particle_ids[0], nr_steps, None)

3. Diffusive behaviour

The diffusive character becomes visible on large time scales.

nr_steps = -1
tra.plot_trajectory('x', 'y', 'd', particle_ids[:10], nr_steps, None)

df

	id	i	d	x	y	z	phi	pitch_angle	radius	sub_step
0	0.0	1.0	0.000000e+00	-2.163573e+08	2.878789e+09	0.000000e+00	0.150029	0.955393	-1.0	0.0
1	0.0	1.0	0.000000e+00	-3.070836e+09	2.447292e+09	0.000000e+00	0.150029	0.955393	-1.0	1.0
2	0.0	1.0	5.000000e+09	-3.070836e+09	2.447292e+09	-2.886438e+09	0.150029	0.955393	-1.0	2.0
3	0.0	2.0	5.000000e+09	-3.715045e+09	5.261405e+09	-2.886438e+09	0.300058	0.955393	-1.0	0.0
4	0.0	2.0	5.000000e+09	-6.472964e+09	4.408106e+09	-2.886438e+09	0.300058	0.955393	-1.0	1.0
...	...	...	...	...	...	...	...	...	...	...
599995	4.0	39999.0	1.999900e+14	-3.317307e+11	-1.267863e+11	-4.635639e+12	717.871826	0.955393	-1.0	1.0
599996	4.0	39999.0	1.999950e+14	-3.317307e+11	-1.267863e+11	-4.638525e+12	717.871826	0.955393	-1.0	2.0
599997	4.0	40000.0	1.999950e+14	-3.288486e+11	-1.269511e+11	-4.638525e+12	717.721802	0.955393	-1.0	0.0
599998	4.0	40000.0	1.999950e+14	-3.292289e+11	-1.298129e+11	-4.638525e+12	717.721802	0.955393	-1.0	1.0
599999	4.0	40000.0	2.000000e+14	-3.292289e+11	-1.298129e+11	-4.641412e+12	717.721802	0.955393	-1.0	2.0

600000 rows × 10 columns