astro-particle-physics-geom.../particle_tracking.ipynb
2024-12-10 13:11:49 +01:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.integrate as spi\n",
"\n",
"import spacepy.time as spt\n",
"import spacepy.coordinates as spc\n",
"import spacepy.irbempy as ib\n",
"\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# INTITIAL CONDITIONS\n",
"# we use the GEO coordinates: Earth-centered, and Earth-fixed\n",
"# Format: (X, Y, Z), where (0, 0, 0) is the center of the Earth\n",
"# We use meters for units\n",
"X_0 = [6.6e6, 0, 0]\n",
"# similarly for velocities\n",
"# we use m/s for units\n",
"V_0 = [-100000, 100000, 100]\n",
"\n",
"\"\"\"# Coordinate system: (lat, lon, alt) = (47.6205, -122.3493, 20000)\n",
"# Velocity system: (v_north, v_east, v_down) = (0, 0, 10)\n",
"X_0 = [3, 0, 0]\n",
"SPEED_OF_LIGHT = 299792458 # m/s\n",
"# X_0 = [47.6205, -122.3493, 20000]\n",
"V_0 = [0, 0, 10]\n",
"\"\"\"\n",
"\n",
"SPEED_OF_LIGHT = 3e8 # m/s\n",
"EARTH_RADIUS = 6.371e6\n",
"CHARGE = 15 # coulomb cancel out\n",
"M = 2\n",
"T = spt.Ticktock('2022-02-02T12:00:00', 'ISO')"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# EQUATIONS OF MOTION\n",
"# neglect gravity - only the lorentz force from the geomagnetic field is considered\n",
"def rel_lambda(v: np.ndarray) -> float:\n",
" return 1 / np.sqrt(1 - (np.linalg.norm(v) / SPEED_OF_LIGHT)**2)\n",
"\n",
"\n",
"def force(x: np.ndarray, v: np.ndarray) -> np.ndarray:\n",
" coords = spc.Coords(x, 'GEO', 'car')\n",
" field = ib.get_Bfield(T, coords)[\"Bvec\"]\n",
" # B = np.array([result.bx, result.by, result.bz])\n",
" F = rel_lambda(v) * CHARGE * np.cross(v, field)\n",
" return F.flatten()\n",
"\n",
"\n",
"# linearized equations of motion\n",
"def y_prime(y, t):\n",
" x = y[:3]\n",
" v = y[3:]\n",
" a = force(x, v) / M\n",
" return np.concatenate((v, a))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# setup of initial conditions\n",
"TIMESTEP = 2\n",
"N_STEPS = 300\n",
"t = np.linspace(0, TIMESTEP*N_STEPS, N_STEPS)\n",
"Y = np.zeros((N_STEPS, 6))\n",
"Y[0] = np.concatenate((X_0, V_0))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# integrate the equations of motion\n",
"Y = spi.odeint(y_prime, Y[0], t)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot the trajectory on a three-dimensional plot\n",
"plt.figure()\n",
"ax = plt.axes(projection='3d')\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('y')\n",
"ax.set_zlabel('z')\n",
"# ensure the aspect ratio is correct\n",
"ax.set_box_aspect([1,1,1])\n",
"\n",
"\n",
"\n",
"# starting point\n",
"ax.scatter3D(Y[0, 0], Y[0, 1], Y[0, 2], c='r')\n",
"# trajectory\n",
"ax.plot3D(Y[:, 0], Y[:, 1], Y[:, 2], 'gray')\n",
"# ending point\n",
"ax.scatter3D(Y[-1, 0], Y[-1, 1], Y[-1, 2], c='g')\n",
"\n",
"# Also plot the Earth\n",
"u = np.linspace(0, 2 * np.pi, 100)\n",
"v = np.linspace(0, np.pi, 100)\n",
"x = EARTH_RADIUS * np.outer(np.cos(u), np.sin(v))\n",
"y = EARTH_RADIUS * np.outer(np.sin(u), np.sin(v))\n",
"z = EARTH_RADIUS * np.outer(np.ones(np.size(u)), np.cos(v))\n",
"ax.plot_surface(x, y, z, color='b', alpha=0.1)\n",
"plt.show()"
]
}
],
"metadata": {
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