{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "_A Jupyter Notebook from my scipython blog at https://scipython.com/blog/exb-drift-for-constant-crossed-electric-and-magnetic-fields/_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# E x B drift for constant crossed electric and magnetic fields\n", "\n", "Consider a particle of charge $q$ and mass $m$ moving in a constant magnetic field, $\\boldsymbol{B} = (0, 0, B_z)$ perpendicular to a constant electric field, $\\boldsymbol{E} = (0, E_y, 0)$. The equation of motion is given by the Lorentz equation,\n", "$$\n", "m\\ddot{\\boldsymbol{r}} = q(\\boldsymbol{E} + \\dot{\\boldsymbol{r}} \\times \\boldsymbol{B}).\n", "$$\n", "In component form, with the definition $\\Omega = qB_z/m$, we have\n", "$$\n", "\\begin{align}\n", "\\ddot{x} &= \\Omega\\dot{y},\\\\\n", "\\ddot{y} &= \\frac{eE_y}{m} - \\Omega\\dot{x},\\\\\n", "\\ddot{z} &= 0.\n", "\\end{align}\n", "$$\n", "If the particle's initial velocity is perpendicular to the magnetic field, $\\boldsymbol{v} = (v_\\perp, 0, 0)$, these can be integrated by standard methods to yield:\n", "$$\n", "\\begin{align}\n", "\\dot{x} &= \\left( v_\\perp - \\frac{E_y}{B_z}\\right)\\cos \\Omega t + \\frac{E_y}{B_z},\\\\\n", "\\dot{y} &= \\left( v_\\perp - \\frac{E_y}{B_z}\\right)\\sin \\Omega t,\\\\\n", "\\dot{z} &= 0.\n", "\\end{align}\n", "$$\n", "and\n", "$$\n", "\\begin{align}\n", "x &= \\frac{1}{\\Omega}\\left( v_\\perp - \\frac{E_y}{B_z}\\right)\\sin \\Omega t + \\frac{E_y}{B_z}t,\\\\\n", "y &= \\frac{1}{\\Omega}\\left( v_\\perp - \\frac{E_y}{B_z}\\right)\\left(1 - \\cos \\Omega t \\right),\\\\\n", "z &= 0.\n", "\\end{align}\n", "$$\n", "\n", "There is therefore a drift along the $x$-axis of speed $E_y/B_z$. More generally, this drift velocity is equal to $(\\boldsymbol{E}\\times\\boldsymbol{B})/B^2$ and is known as the $\\boldsymbol{E}\\times\\boldsymbol{B}$ drift." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Setup a time grid on which to treat the particle's motion.\n", "dt = 0.001\n", "N = 1000\n", "tmax = N*dt\n", "t = np.linspace(0,tmax,N)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# particle mass, charge and charge/mass ratio.\n", "m, q = 0.01, 1\n", "qom = q / m\n", "\n", "# The magnetic and electric fields are (0,0,Bz) and (0,Ey,0)\n", "Bz = 0.4\n", "Ey = 0.7\n", "\n", "# The particle starts at (0,0) with initial velocity perpendicular to the\n", "# magnetic field, vy0\n", "vy0 = 7.5" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# The gyrofrequency, qB/m.\n", "Omega = qom * Bz\n", "\n", "x = (vy0 - Ey/Bz) / Omega * np.sin(Omega * t) + Ey/Bz * t\n", "y = (vy0 - Ey/Bz) / Omega * (1 - np.cos(Omega * t))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def add_field_annotations(ax):\n", " \"\"\"Indicate the electric field with a single arrow.\"\"\"\n", " \n", " xmin, xmax = ax.get_xlim()\n", " ymin, ymax = ax.get_ylim()\n", " Dx, Dy = xmax - xmin, ymax - ymin\n", " xpf, ypf = 0.05, 0.07\n", " axmin = xmin + xpf*Dx\n", " aymin, aymax = ymin + ypf*Dy, ymax - ypf*Dy\n", " adx, ady = 0, aymax-aymin\n", " ax.arrow(axmin, aymin, adx, ady, head_width=Dx*0.03, head_length=Dy*0.07,\n", " length_includes_head=True, facecolor='k', lw=3)\n", " # Add labels for the electric and magnetic fields.\n", " ax.text(s='E', x=axmin+xpf*Dx*0.5, y=aymax-ypf*Dy, fontsize=18, fontweight='bold',\n", " fontstyle='italic')\n", " ax.text(s='B', x=xmax-0.05*Dx, y=aymax-0.05*Dy, fontsize=18, fontweight='bold',\n", " fontstyle='italic', color='gray')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jwZG+EaxpqJiyc9+mTZtyThBRqrvMbsHV7mp0BfTJAAC5Nb/TO4KNnnrceuut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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "width, height, DPI = 600, 400, 72\n", "fig = plt.figure(figsize=(width/DPI, height/DPI))\n", "ax = fig.add_subplot(111)\n", "ax.plot(x, y)\n", "\n", "xmin, xmax = ax.get_xlim()\n", "ymin, ymax = ax.get_ylim()\n", "cX, cY = np.linspace(xmin,xmax,10), np.linspace(ymin,ymax,10)\n", "cX, cY = np.meshgrid(cX, cY)\n", "# Draw markers representing the magnetic field coming out of the plane of the plot.\n", "ax.scatter(cX, cY, marker='o', edgecolors='gray', s=200, c='white')\n", "ax.scatter(cX, cY, marker='.', c='gray')\n", "# Add an arrow representing the electric field.\n", "add_field_annotations(ax)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:py35]", "language": "python", "name": "conda-env-py35-py" }, "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": 1 }