{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Motion of charged particle in E and B fields\n", "\n", "Start of by importing numpty and pyplot. The line magic function (indicated by %) ensures plots appear in the notebook." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Basic idea: use Euler method to look at motion of particle in electric and magnetic fields.\n", "Define proton mass and charge, B field, E field, initial position and velocity." ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mP = 1.67E-27 # kg\n", "qP = 1.6E-19 # C\n", "c = 3.0E8 # m/s\n", "Bvec = np.zeros(3)\n", "Bvec[0] = 0\n", "Bvec[1] = 0\n", "Bvec[2] = 2 # T\n", "Evec = np.zeros(3)\n", "Evec[0] = 0\n", "Evec[1] = 3000E3 # V/m\n", "Evec[2] = 0\n", "rVec = np.zeros(3)\n", "rVec[0] = 0\n", "rVec[1] = 0\n", "rVec[2] = 0\n", "vVec = np.zeros(3)\n", "vVec[0] = c/10\n", "vVec[1] = 0\n", "vVec[2] = c/20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Force given by $\\vec{F} = q \\vec{E} + q \\vec{v} \\times \\vec{B}$. Algorithm used for numerical solution is:\n", "$$\n", "\\begin{align}\n", "d\\vec{v}_i &= \\frac{dt}{m}\\left( q \\vec{E}_i + q \\vec{v}_i \\times \\vec{B} \\right), \\\\\n", "\\vec{r}_{i+1} &= \\vec{r}_i + dt\\vec{v}_i, \\\\\n", "\\vec{v}_{i+1} &= \\vec{v}_i + d\\vec{v}_i.\n", "\\end{align}\n", "$$\n", "Set up number of iterations, time step, arrays for storing position and velocity as a function of time. Then loop to determine position and velocity in small time steps and plot the result." ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial position [ 5.36 -0.03 55.5 ]\n", "Initial velocity [ 24521215.7 37349360.44 15000000. ]\n", "Time step 1e-12 s and total time 1e-07 s.\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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tvbe2un37ra6qffjh2k0UqvR0v8cX0ckef/1VL5zef1+7Vh94QKcIMP5ZwmJM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\nLvREZAmLKXNEdJrpevXgzDPDXD15yxbYutV3FMY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nIter = 100000\n", "dt = 1E-12 # secs\n", "rX = np.zeros(nIter)\n", "dvVec = np.zeros(3)\n", "#\n", "rX = np.zeros(nIter)\n", "rY = np.zeros(nIter)\n", "rZ = np.zeros(nIter)\n", "#\n", "vX = np.zeros(nIter)\n", "vY = np.zeros(nIter)\n", "vZ = np.zeros(nIter)\n", "#\n", "print(\"Initial position \",np.array_str(rVec,precision=2,suppress_small=True))\n", "print(\"Initial velocity \",np.array_str(vVec,precision=2,suppress_small=True))\n", "print(\"Time step {:0.2} s and total time {:0.2} s.\".format(dt,nIter*dt))\n", "#\n", "for i in range(0,nIter):\n", " rX[i] = rVec[0]\n", " rY[i] = rVec[1]\n", " rZ[i] = rVec[2]\n", "#\n", " vX[i] = vVec[0]\n", " vY[i] = vVec[1]\n", " vZ[i] = vVec[2]\n", "#\n", " dvVec = (qP*Evec + qP*np.cross(vVec,Bvec))*dt/mP\n", " rVec = rVec + dt*vVec\n", " vVec = vVec + dvVec\n", "#\n", "plt.plot(rX,rY,\"b--\")\n", "# plt.xlim([-0.6,0.6])\n", "# plt.ylim([-0.6,0.3])\n", "ax = plt.gca()\n", "ax.set_title(\"Path of charged particle\", size = 14, weight = \"bold\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot position in 3D." ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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wFRdckMURR6g49FAVDQ1ej7Z8ynGlMte8uY+unaXFr/h5bIUwX/+xGHDyyQpO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\n++03ZGdn4+rVq4iPj8epU6fw3nvvAVC5L4wYMYLbftiwYahTpw5iY2Nx/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ax.plot(rX,rY,rZ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot velocity." ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vx41HRKSrXXGF3yFZ2k8JhRQ1YADsvTeMHg3XXx87GhERqWa6l4cUNWgQPPBA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\nChERESmbEgoREREp2/8Hbt27IwNrLiYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(vX,vY,\"b--\")\n", "# plt.xlim([-0.6,0.6])\n", "# plt.ylim([-0.6,0.3])\n", "ax = plt.gca()\n", "ax.set_title(\"Velocity of charged particle\", size = 14, weight = \"bold\")\n", "ax.set_xlabel(\"v_x\")\n", "ax.set_ylabel(\"v_y\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot velocity in 3D." ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oWiKtUChAlmVNpLW3tw9KpBUpR8sostaskTQmonO5HMrlMuU9tTBeFDW0OiIVGHhJrfuq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\nD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fdd2HUYzrYR/iCMPIZTlFaqibM/9W96jabduHEDEyZMwJ49e7Bs2TL89a9/rfbnPaEq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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ax.plot(vX,vY,vZ)" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }