{ "cells": [ { "cell_type": "markdown", "id": "coordinate-balance", "metadata": {}, "source": [ "# Particle motion in electromagnetic fields\n", "\n", "[A. Petrenko](https://www.inp.nsk.su/~petrenko/) (Novosibirsk, 2021)" ] }, { "cell_type": "markdown", "id": "advisory-relations", "metadata": {}, "source": [ "The equations of particle motion under the Lorentz force (in SI units)\n", "\n", "\\begin{equation}\n", "\\frac{d \\mathbf{p}}{dt} = q \\mathbf{E} + q[\\mathbf{v} \\times \\mathbf{B}],\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "\\frac{d \\mathbf{r}}{dt} = \\mathbf{v},\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "\\mathbf{p} = \\gamma m \\mathbf{v}.\n", "\\end{equation}\n", "\n", "Particle velocity $\\mathbf{v}$ can be derived from the momentum $\\mathbf{p}$ using the definition of relativistic factor $\\gamma = \\left(1 - \\frac{v^2}{c^2}\\right)^{-1/2} = \\sqrt{1 + \\left(\\frac{p}{mc}\\right)^2}$." ] }, { "cell_type": "markdown", "id": "english-algeria", "metadata": {}, "source": [ "Therefore the equations of motion\n", "\n", "\\begin{equation}\n", "\\frac{ d\\mathbf{r} }{dt} = \\frac{\\mathbf{p}}{\\gamma m},\\\\\n", "\\frac{d\\mathbf{p}}{dt} = q \\mathbf{E} + q\\left[\\frac{\\mathbf{p}}{\\gamma m} \\times \\mathbf{B}\\right].\n", "\\end{equation}\n", "\n", "And the final 6d vector equation to solve $d\\mathbf{Y}/dt = \\mathbf{F}(t,\\mathbf{Y})$:" ] }, { "cell_type": "markdown", "id": "finnish-coverage", "metadata": {}, "source": [ "\\begin{equation}\n", "\\frac{d}{dt}\n", "\\left(\n", "\\begin{array}{c}\n", "x \\\\\n", "y \\\\\n", "z \\\\\n", "p_x \\\\\n", "p_y \\\\\n", "p_z\n", "\\end{array}\n", "\\right) =\n", "\\left(\n", "\\begin{array}{c}\n", "p_x/\\gamma m \\\\\n", "p_y/\\gamma m \\\\\n", "p_z/\\gamma m \\\\\n", "qE_x + q(p_y B_z - p_z B_y)/\\gamma m \\\\\n", "qE_y - q(p_x B_z - p_z B_x)/\\gamma m \\\\\n", "qE_z + q(p_x B_y - p_y B_x)/\\gamma m\n", "\\end{array}\n", "\\right).\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 1, "id": "constitutional-medium", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp" ] }, { "cell_type": "markdown", "id": "happy-overall", "metadata": {}, "source": [ "Define external fields:" ] }, { "cell_type": "code", "execution_count": 2, "id": "premium-swedish", "metadata": {}, "outputs": [], "source": [ "def E(x,y,z,t): # V/m\n", " Ex = 0; Ey = 0; Ez = 0\n", " return Ex, Ey, Ez" ] }, { "cell_type": "code", "execution_count": 3, "id": "genuine-tanzania", "metadata": {}, "outputs": [], "source": [ "def B(x,y,z,t): # T\n", " Bx = 0; By = 0; Bz = 1.0 # T\n", " return Bx, By, Bz" ] }, { "cell_type": "markdown", "id": "three-politics", "metadata": {}, "source": [ "Define some constants:" ] }, { "cell_type": "code", "execution_count": 4, "id": "junior-minneapolis", "metadata": {}, "outputs": [], "source": [ "c = 299792458 # m/sec\n", "e = 1.602176634e-19 # C\n", "eV = e # J\n", "keV = 1e3*eV; MeV = 1e6*eV; GeV = 1e9*eV\n", "\n", "sec = 1; ns = 1e-9*sec\n", "\n", "# electron:\n", "q = -e\n", "mc2 = 511*keV # J\n", "\n", "mc = mc2/c # kg*m/sec\n", "m = mc/c # kg" ] }, { "cell_type": "code", "execution_count": 5, "id": "indian-output", "metadata": {}, "outputs": [], "source": [ "def F(t,Y):\n", " x = Y[0]; y = Y[1]; z = Y[2]\n", " px = Y[3]; py = Y[4]; pz = Y[5]\n", " gamma = np.sqrt(1 + (px*px + py*py + pz*pz)/(mc*mc))\n", " Ex, Ey, Ez = E(x,y,z,t) # V/m\n", " Bx, By, Bz = B(x,y,z,t) # T\n", " return np.array([\n", " px/(gamma*m),\n", " py/(gamma*m),\n", " pz/(gamma*m),\n", " q*Ex + q*(py*Bz-pz*By)/(gamma*m),\n", " q*Ey - q*(px*Bz-pz*Bx)/(gamma*m),\n", " q*Ez + q*(px*By-py*Bx)/(gamma*m)\n", " ])" ] }, { "cell_type": "markdown", "id": "interpreted-crash", "metadata": {}, "source": [ "Set the initial particle coordinates" ] }, { "cell_type": "code", "execution_count": 6, "id": "maritime-right", "metadata": {}, "outputs": [], "source": [ "x = 0; y = 0; z = 0\n", "px = 0.5*GeV/c; py = 0; pz = 0.1*GeV/c\n", "\n", "Y0 = np.array([x,y,z,px,py,pz])" ] }, { "cell_type": "code", "execution_count": 7, "id": "bibliographic-radiation", "metadata": {}, "outputs": [], "source": [ "t_span = (0, 200*ns) # sec\n", "\n", "t_eval = np.linspace(t_span[0], t_span[1], 500) # points of output" ] }, { "cell_type": "code", "execution_count": 8, "id": "combined-badge", "metadata": {}, "outputs": [], "source": [ "#help(solve_ivp)" ] }, { "cell_type": "code", "execution_count": 9, "id": "spread-renaissance", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 20 ms, sys: 4 ms, total: 24 ms\n", "Wall time: 25.5 ms\n" ] } ], "source": [ "%%time\n", "sol = solve_ivp(F, t_span, Y0, t_eval=t_eval, max_step=5*ns) # rtol=1e-4" ] }, { "cell_type": "markdown", "id": "detected-juvenile", "metadata": {}, "source": [ "## Plot the results" ] }, { "cell_type": "code", "execution_count": 10, "id": "separate-sector", "metadata": {}, "outputs": [], "source": [ "import plotly.io as pio\n", "import plotly.graph_objects as go" ] }, { "cell_type": "code", "execution_count": 11, "id": "coastal-salad", "metadata": {}, "outputs": [], "source": [ "pio.templates.default = pio.templates[\"simple_white\"]" ] }, { "cell_type": "code", "execution_count": 12, "id": "protecting-arnold", "metadata": {}, "outputs": [], "source": [ "x, y, z, px, py, pz = sol.y" ] }, { "cell_type": "code", "execution_count": 13, "id": "blind-louisiana", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "line": { "color": "blue", "width": 3 }, "mode": "lines", "type": "scatter", "x": [ 0, 0.40080160320641284, 0.8016032064128257, 1.2024048096192386, 1.6032064128256514, 2.0040080160320644, 2.404809619238477, 2.80561122244489, 3.2064128256513027, 3.6072144288577155, 4.008016032064129, 4.408817635270542, 4.809619238476954, 5.2104208416833675, 5.61122244488978, 6.012024048096193, 6.412825651302605, 6.813627254509019, 7.214428857715431, 7.615230460921845, 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", 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