{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Relativistic 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", "\n", "The relativistic motion of a charged particle in electric and magnetic fields is described by the equations:\n", "$$\n", "\\gamma \\frac{d}{{dt}}\\left[ {\\begin{array}{*{20}{c}}\n", "{\\gamma mc}\\\\\n", "{\\gamma m\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }\n", "\\end{array}} \\right] = q\\left[ {\\begin{array}{*{20}{c}}\n", "0&{ - \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} }}{c}}\\\\\n", "{\\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} }}{c}}&{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} }\n", "\\end{array}} \\right]\\left[ {\\begin{array}{*{20}{c}}\n", "{\\gamma c}\\\\\n", "{ - \\gamma \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }\n", "\\end{array}} \\right] = \\gamma \\left[ {\\begin{array}{*{20}{c}}\n", "{q\\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} }}{c} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }\\\\\n", "{q\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right)}\n", "\\end{array}} \\right].\n", "$$\n", "Rewriting, we have:\n", "$$\n", "\\begin{array}{c}\n", "\\frac{d}{{dt}}\\gamma m{c^2} = q\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\ {\\rm{ and}}\\\\\n", "\\frac{d}{{dt}}\\gamma m\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} = q\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right).\n", "\\end{array}\n", "$$\n", "The latter equations can be used to solve for the motion of the particle using Euler's method. Using the first equation to determine $ \\frac {d \\gamma}{dt}$ and the latter to find $ \\frac {d \\vec{v}}{dt} $ and recasting gives:\n", "$$\n", "\\begin{array}{c}\n", "\\frac{{d\\gamma }}{{dt}} = \\frac{q}{{m{c^2}}}\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\\\\n", "\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\frac{{d\\gamma }}{{dt}} + \\gamma \\frac{{d\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{dt}} = \\frac{q}{m}\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right)\\,\\\\\n", "\\gamma \\frac{{d\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{dt}} = \\frac{q}{m}\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right) - \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\frac{{d\\gamma }}{{dt}}\\,\\\\\n", "\\gamma \\frac{{d\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{dt}} = \\frac{q}{m}\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right)\\, - \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\frac{q}{{m{c^2}}}\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\\\\n", "d\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} = \\left( {\\frac{q}{{\\gamma m}}\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} + \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over B} } \\right) - \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{\\gamma }\\frac{q}{{m{c^2}}}\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over E} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} } \\right)\\,dt.\n", "\\end{array}\n", "$$\n", "Note that the relativistic formula must be used for the addition of the velocities:\n", "$$\n", "\\begin{array}{c}\n", "\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\oplus \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} = \\frac{1}{{1 + \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{{c^2}}}}}\\left[ {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} + \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{{\\gamma _u}}} + \\frac{1}{{{c^2}}}\\frac{{{\\gamma _u}}}{{1 + {\\gamma _u}}}\\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} } \\right)\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} } \\right]\\\\\n", " = \\frac{1}{{1 + \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{{c^2}}}}}\\left[ {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} + \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{{\\gamma _u}}} + \\frac{1}{{{c^2}}}\\frac{{{\\gamma _u}}}{{1 + {\\gamma _u}}}\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\times \\left( {\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\times \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} } \\right)} \\right].\n", "\\end{array}\n", "$$\n", "It might also be useful to note that ${\\gamma _u}{\\gamma _v} = \\left( {1 + \\frac{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over u} \\cdot \\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\rightharpoonup$}} \n", "\\over v} }}{{{c^2}}}} \\right)$.\n", "\n", "Try using this algorithm with the above static field configuration. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\green\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:32: RuntimeWarning: divide by zero encountered in double_scalars\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "E field (0.00e+00, 0.00e+00, 1.00e+06) V/m.\n", "B field (0.00e+00, 0.00e+00, 0.00e+00) T.\n", " \n", "Initial position (0.00e+00, 0.00e+00, 0.00e+00) m.\n", "Initial velocity (9.49e+07, 0.00e+00, 0.00e+00) m/s.\n", "Speed 9.49e+07 m/s and gamma factor 1.05e+00.\n", "Energy 9.90e+08 eV and momentum 3.13e+08 eV.\n", "Approximate RoC (dependent on orientations of B field and velocity!) inf m.\n", "Time step 1e-11 s and total time 1e-06 s.\n", " \n", "Final position (9.31e+01, 0.00e+00, 4.18e+01) m.\n", "Final velocity (8.97e+07, 0.00e+00, 8.11e+07) m/s.\n", "Speed 1.21e+08 m/s and gamma factor 1.09e+00.\n", "Energy 1.03e+09 eV and momentum 4.14e+08 eV.\n", "Expected energy gain 4.178e+07 and final energy 1.068230e+09.\n" ] }, { "data": { "image/png": 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LY7cBZkbEpMqmnpTSKxGxNPAd8hiPJ4DVgR8ADwCXlxCyJLWUgw6CTTeFzTcv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\nAElFTkSuQmCC\n", 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FkkrrqfuASJKk7YMBRJIktc4AIkmSWmcAkSRJrTOASJKk1hlAJElS6wwgklq3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\nOKpj2vFUoxwPUA19799l3R+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mP = 1.67E-27 # kg\n", "qP = 1.6E-19 # C\n", "c = 3.0E8 # m/s\n", "#\n", "Bvec = np.zeros(3)\n", "Bvec[0] = 0.0 # T\n", "Bvec[1] = 0.0 # T\n", "Bvec[2] = 0.0 # T\n", "Evec = np.zeros(3)\n", "#\n", "Evec[0] = 0.0E6 # V/m\n", "Evec[1] = 0.0E6 # V/m\n", "Evec[2] = 1.0E6 # V/m\n", "#\n", "#\n", "rVec0 = np.zeros(3)\n", "rVec0[0] = 0.0\n", "rVec0[1] = 0.0\n", "rVec0[2] = 0.0\n", "rVec = np.zeros(3)\n", "rVec = rVec0\n", "#\n", "vVec = np.zeros(3)\n", "vVec[0] = np.sqrt(0.1)*c\n", "vVec[1] = np.sqrt(0.0)*c\n", "vVec[2] = np.sqrt(0.0)*c\n", "vMag = np.sqrt(vVec[0]**2 + vVec[1]**2 + vVec[2]**2)\n", "vMa\n", "gamma = 1/np.sqrt(1 - (vVec[0]**2 + vVec[1]**2 + vVec[2]**2)/c**2)\n", "#\n", "Ep = gamma*mP*c**2/qP\n", "pp = gamma*mP*vMag*c/qP\n", "RoC = pp/(0.3*10**9*Bvec[2])\n", "#\n", "nIter = 100000\n", "dt = 1E-11 # 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(\"E field ({:0.2e}, {:0.2e}, {:0.2e}) V/m.\".format(Evec[0],Evec[1],Evec[2]))\n", "print(\"B field ({:0.2e}, {:0.2e}, {:0.2e}) T.\".format(Bvec[0],Bvec[1],Bvec[2]))\n", "print(\" \")\n", "print(\"Initial position ({:0.2e}, {:0.2e}, {:0.2e}) m.\".format(rVec[0],rVec[1],rVec[2]))\n", "print(\"Initial velocity ({:0.2e}, {:0.2e}, {:0.2e}) m/s.\".format(vVec[0],vVec[1],vVec[2]))\n", "print(\"Speed {:0.2e} m/s and gamma factor {:0.2e}.\".format(vMag,gamma))\n", "print(\"Energy {:0.2e} eV and momentum {:0.2e} eV.\".format(Ep,pp))\n", "print(\"Approximate RoC (assuming B field along z axis) {:0.2e} m.\".format(RoC))\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", " gamma = 1/np.sqrt(1 - (vVec[0]**2 + vVec[1]**2 + vVec[2]**2)/c**2)\n", " dgamma = qP/(mP*c**2)*np.dot(Evec,vVec)*dt\n", " dvVec = qP/(gamma*mP)*(Evec + np.cross(vVec,Bvec))*dt - vVec/gamma*dgamma\n", "#\n", " rVec = rVec + dt*vVec\n", "#\n", " F01 = 1/(1 + np.dot(vVec,dvVec)/c**2)\n", " F02 = vVec + dvVec/gamma\n", " F03 = 1/c**2*gamma/(1+gamma)*np.dot(vVec,dvVec)*vVec\n", " vVec = F01*(F02+F03)\n", "#\n", "vMag = np.sqrt(vVec[0]**2 + vVec[1]**2 + vVec[2]**2)\n", "gamma = 1/np.sqrt(1 - (vVec[0]**2 + vVec[1]**2 + vVec[2]**2)/c**2)\n", "Ep = gamma*mP*c**2/qP\n", "pp = gamma*mP*vMag*c/qP\n", "#\n", "dZ = rVec[2] - rVec0[2]\n", "EdZ = Evec[2]*dZ\n", "print(\" \")\n", "print(\"Final position ({:0.2e}, {:0.2e}, {:0.2e}) m.\".format(rVec[0],rVec[1],rVec[2]))\n", "print(\"Final velocity ({:0.2e}, {:0.2e}, {:0.2e}) m/s.\".format(vVec[0],vVec[1],vVec[2]))\n", "print(\"Speed {:0.2e} m/s and gamma factor {:0.2e}.\".format(vMag,gamma))\n", "print(\"Energy {:0.2e} eV and momentum {:0.2e} eV.\".format(Ep,pp))\n", "print(\"Expected energy gain {:0.3e} and final energy {:03e}.\".format(EdZ,Ep + EdZ))\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\")\n", "plt.show()\n", "#\n", "plt.plot(rX,rZ,\"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(\"z\")\n", "plt.show()\n", "#\n", "plt.plot(rY,rZ,\"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(\"y\")\n", "ax.set_ylabel(\"z\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot position in 3D." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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SawFg1p1+vz/U/NpPQHeYyBqz5rdjw3xFtDiGLdLY9SOjKPOLV8tBXPE7BBGE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ZVl9YlWinnQAQOK3Wms72lThhececrTGMIA1VYyJIamT21VPrWnHIc9EWZQvb29jR5zKeq/NQZj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\nFDElayIiIiJF7CuD8Z7bW4C6PwAAAABJRU5ErkJggg==\n", "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": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0ZQVQa9eurcX0gx9UweyP739/9jpe85rZy++22+bbcbvbzV7Ha15jP+yH/bAf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\ndu0+dzstt77MsT/v6bZ9X9q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hpWRfl4YQ5iYxtwKnA9dJ+jOwMTCMeEagWYuR4Ac/iLc33oBuPj3BzKzZVUrx\ndAyxQLmMeFjtY+BvyWMAhBDOk7QUcU6m7sDTwC4hhDmp7Qwn9mDdCXQCHgKOzuxrKHAp8Sy7BUns\nwqInhLBA0u7J/p8jzid1A3BGKmampB2TfCcA04AzQwjXLs6TYFaKddfNOwMzs+qk4JGlZUFSP2Di\nxIkTfdjOWs1LL8HGG8ceKzOzSpU6bNc/hFDT0vurlLPtzKyZTZ4cz9br3x9uuw3mzWtwFTMzw8WT\nWZu1+upxWoMePWDIEFhnnXhZmFmz8s7MzKy8uXgya6Mk2GGHWEDV1MBWW8UpD1ZbDc44Az77LO8M\nzczKk4snM6NvX7jlFnjrLTjgAPjrX+E4nxtqZlZUpZxtZ2atoHdvuPBCOP10+N//8s7GzKw8uXgy\ns+9Ybrl4MzOz7/JhOzNrkjff9DX0zKxtcvFkZiWbMSNOcdC/f7ym3vzsxZPMzKqYiyczK1nXrnD3\n3fHQ3j77wAYbwHXXwZw5Da9rZlbpXDyZWckkGDQIHn0Uxo2LxdOhh8Jaa8FFF3muKDOrbi6ezGyx\nbLll7IV65RXYfns48UT46U/zzsrMrOX4bDszaxYbbAA33gh/+AN88UXe2ZiZtRwXT2bWrHr3jjcz\ns2rlw3Zm1urmzs07AzOzpnPxZGatau5c2GQTOOooeO+9vLMxMyudiycza1Xz58MvfgF33QVrrw2H\nHQZvv513VmZmjefiycxa1ZJLwsknw7vvwp//DPfdB+utBwcdBK+/nnd2ZmYNc/FkZrno0gVOOCEW\nUSNGwGOPQZ8+cPzxeWdmZlY/F09mlqvOneHYY+Ohu8svh759887IzKx+nqrAzMpCp05w5JF5Z2Fm\n1jD3PJmZmZmVwMWTmVWUc86B117LOwsza8tcPJlZxfj0U7jySthwQzjwQHjzzbwzMrO2yMWTmVWM\nFVeMBdNFF9WenXfwwfDOO3lnZmZtiYsnM6soSy4JxxwDb70F558PDz4Y54n65S9h8uS8szOztsDF\nk5lVpM6d4bjjYq/Tn/8M99wTiykzs5bmqQrMrKIttVScbPOII2DOnLyzMbO2wMWTmVWFLl3izcys\npfmwnZm1GfPm5Z2BmVUDF09m1ia89Rb07g2XXAKzZ+edjZlVMhdPZtYmdO4MO+4YLzy87rpw/fXu\niTKzpnHxZGZtwv/9H1x3HbzyCgwYAIccAhttBHfcAQsW5J2dmVUSF09m1qasvz6MHg0TJ8Kaa8I+\n+8Dmm8O7wGT8AAAgAElEQVS//513ZmZWKVw8mVmb1K8fPPAAPPUULL00dPC5x2bWSP64MLM2bZtt\nYgFlZtZY7nkyMzMzK4GLJzOzBsyaBTNn5p2FmZULF09mZg04/3xYa604R5QvAWNmLp7MzBpw8MHw\n4x/HOaL69IHbb/f0BmZtmYsnM7MGrLpqnCPqxRdhgw1gv/3iXFGPP553ZmaWBxdPZmaNtNFGcO+9\n8MQT0K4dbL897LILfP553pmZWWty8WRmVqIf/CBOqnnHHXGOqO7d887IzFqT53kyM2sCCfbeO97M\nrG1xz5OZmZlZCVw8mZm1IM8PZVZ9XDyZmbWQOXPiRYf32QfeeSfvbMysubh4MjNrIR06wGmnwbPP\nxvmhfvMb+PLLvLMys8Xl4snMrIW0awcHHghvvAGnngqXXQZrrx3/zpuXd3Zm1lQunszMWliXLnD6\n6fDmm7DHHnDssdC3b5wvyswqj4snM7NWsvLKcaby55+Hrl3hP//JOyMzawrP82Rm1sr694dnnvH1\n8cwqVcX0PElaWdJISdMkfS3pRUn9MjFnSfo4Wf6IpLUzyztJuizZxleS7pS0YiZmWUm3SJohabqk\nayR1ycSsKul+SbMkTZF0nqR2mZhNJD0l6RtJ70k6qbmfEzOrXBK0b593FmbWFBVRPEnqDjwLzAZ2\nAvoAJwLTUzEnA8cAhwNbArOAMZI6pjZ1IbAbMBjYFlgZuCuzu1uT7Q9KYrcFrkztpx3wALHXbiBw\nEPAL4KxUzDLAGOBdoB9wEnCmpMOa/CSYmZlZWaiI4gn4LfB+COGwEMLEEMJ7IYRHQwjvpmKOA84O\nIdwXQvgvcCCxONoTQFJX4BBgeAjhyRDCC8DBwNaStkxi+hCLs0NDCBNCCM8BxwL7SeqV7GcnYH3g\n5yGEl0MIY4DfA0dLKhwG3R9YItnOpBDCaOBi4ISWeXrMrNo8/jgceSRMm5Z3JmaWVSnF04+BCZJG\nS5oqqSbdiyNpDaAX8FjhsRDCTGAc8L3koc2JvUXpmNeB91MxA4HpSWFV8CgQgAGpmJdDCOmPtDFA\nN2DDVMxTIYR5mZj1JHUrtfFm1vZMnQq33QbrrAOXXOKpDczKSaUUT2sCRwGvAzsCfwMulnRAsrwX\nscCZmllvarIMoCcwJymq6orpBXyaXhhCmA98kYkpth9KjDEzq9N++8WpDX72MzjuONhiCxg7Nu+s\nzAwqp3hqB0wMIfw+hPBiCOFq4GrgyJzzMjNrMSusAFddBePGxcHlW20Fhx4Kn32Wd2ZmbVulTFXw\nCTAp89gk4KfJv6cAIvYupXt8egIvpGI6Suqa6X3qmSwrxGTPvmsPLJeJ2SKTS8/UssLfng3EFDV8\n+HC6dVv0yN6QIUMYMmRIfauZWRXbYotYQF19NZxyCjz8MLz9NnTs2PC6ZtVm1KhRjBo1apHHZsyY\n0ao5VErx9CywXuax9YD3AEII70qaQjxD7iVYOEB8AHBZEj8RmJfE3J3ErAesBhQ6w8cC3SX1TY17\nGkQszMalYk6R1CM17mlHYAbwairmHEntk8N+hZjXQwj1vsIjRoygX79+9YWYWRvUvn0cQD54cJxk\n04WTtVXFOhRqamro379/q+VQKYftRgADJf1O0lqShgKHAZemYi4ETpP0Y0kbAzcBHwL3wMIB5NcC\nF0jaTlJ/4Drg2RDC+CTmNeLA7qslbSFpa+ASYFQIodBj9DCxSBqZzOW0E3A2cGkIYW4ScyswB7hO\n0gaS9gWGAee3xJNjZm3HCivArrvmnYVZ21YRPU8hhAmS9gLOJU4L8C5wXAjhtlTMeZKWIs7J1B14\nGtglhDAntanhwHzgTqAT8BBwdGZ3Q4lF2aPAgiT2uNR+FkjanTho/TnifFI3AGekYmZK2pHY6zUB\nmAacGUK4dvGeCTMzM8ubQgh552BAMlv6xIkTJ/qwnZktlk8+gZVWyjsLs9aTOmzXP4RQ09L7q5TD\ndmZm1gjPPw+rrw6//S18/XXe2ZhVJxdPZmZVZNNN4Ywz4MILYaONYMyYvDMyqz4unszMqkjHjnDq\nqfDyy7DGGrDzzjB0aJyx3Myah4snM7MqtM468OijcOONcV6o9deP80QtWJB3ZmaVz8WTmVmVkuDA\nA+G112DPPWHYMHj//byzMqt8Lp7MzKpcjx5w/fXxWnm9e+edjVnlc/FkZtZGrLJK3hmYVQcXT2Zm\nZmYlcPFkZmZAPKxnZg1z8WRmZrzySjwj7xe/gC++yDsbs/Lm4snMzNhggziVwT/+Ef/997/nnZFZ\n+XLxZGZmSHDIIfDqqzBwIAweDD/7mSfXNCvGxZOZmS208spw991w223w5JOxF2rkSPA15M1quXgy\nM7NFSLDvvrEXaued4dBD4d13887KrHy4eDIzs6J69IBbboFJk2DNNfPOxqx8uHgyM7N6rbVW3hmY\nlRcXT2ZmZmYlKLl4kjRf0uOSlss83lPS/OZLzczMKsG8eXlnYNa6mtLzJKATMEHShkWWmZlZG1FT\nA+utB48+mncmZq2nKcVTAAYD9wJjJf0ks8zMzNqIHj1gjTXgRz+Co4+Gr7/OOyOzltfUnqf5IYTj\ngF8Dt0s6Dfc6mZm1OautBg8/DJdeCtdfD/36wcSJeWdl1rIWa8B4COEqYBfgeOCmZsnIzMwqSrt2\nsdeppga6dIkzlJ97Lsz3KFirUk0pnt4DFv6XCCE8DgwEVm2upMzMrPKsvz6MHQsnnginnAI77eQC\nyqpTh1JXCCGsUeSxtyT1BXoWHpM0BPhnCGHW4qVoZmaVomPH2Ou0887w8svQvn3eGZk1v5KLp7qE\nEL4l9koVXAmMA95prn2YmVll2G67eDOrRi05SaYHkJuZmVnV8QzjZmZmZiVw8WRmZq3urbfgo4/y\nzsKsaVw8mZlZqxs2DDbbDB58MO9MzErn4snMzFrdTTfBgAGw667w61/DnDl5Z2TWeE25MPA1krZr\nROh7wNySMzIzs6rXowfcey+cfz5cfDF8//vwjs/NtgrRlJ6nFYCHJH0g6S+SNi0WFELYKITwweKl\nZ2Zm1UqCE06AZ5+Fzz+Hvn1h9Oi8szJrWMnFUwjhJ8BKwNnAFkCNpFcknSKpd/OmZ2Zm1W6LLeKl\nXXbZBfbdF26/Pe+MzOrXpDFPIYTpIYSrQgjbAasDNwAHAG81X2pmZtZWdOsGo0bFnqc998w7G7P6\nLdYM45KWADYHBgC9ganNkJOZmbVBEvzsZ3lnYdawJvU8SfqhpKuJxdINwExgd2CV5kvNzMzMrPyU\n3PMk6SNgOeAh4HDg3hDC7OZOzMzMzKwcNeWw3ZnAHSGEL5s5FzMzszrNmwf//W+cXNMsT0052+5q\nF05mZtbarr46npl30UUQQt7ZWFu2WAPGzczMWsthh8Vr4h1/PEyYAFddBZ07552VtUW+PIuZmVWE\nJZaIM5KPGgV33RVnJX///byzsrbIxZOZmVWU/faD556Ls5Jvvjk89VTeGVlb4+LJzMwqzmabxUN3\nG20EgwbByJF5Z2RtiYsnMzOrSD16wMMPw/DhsGnRq6yatQwPGDczs4rVoQOcd17eWVhb454nMzMz\nsxK4eDIzMzMrgYsnMzMzsxK4eDIzs6o1dmycXHO2r8BqzcjFk5mZVa2PP4abb47TGXz2Wd7ZWLVw\n8WRmZlVr8GB44gl4800YMABefTXvjKwaVGTxJOm3khZIuiDz+FmSPpb0taRHJK2dWd5J0mWSpkn6\nStKdklbMxCwr6RZJMyRNl3SNpC6ZmFUl3S9plqQpks6T1C4Ts4mkpyR9I+k9SSc19/NgZmYNGzgQ\nxo+HpZeG730P/vWvvDOySldxxZOkLYDDgRczj58MHJMs2xKYBYyR1DEVdiGwGzAY2BZYGbgrs4tb\ngT7AoCR2W+DK1H7aAQ8Q58gaCBwE/AI4KxWzDDAGeBfoB5wEnCnpsCY33MzMmmz11eHZZ2PxtPPO\ncMsteWdklayiiidJSwM3A4cBX2YWHwecHUK4L4TwX+BAYnG0Z7JuV+AQYHgI4ckQwgvAwcDWkrZM\nYvoAOwGHhhAmhBCeA44F9pPUK9nPTsD6wM9DCC+HEMYAvweOllSYdHR/YIlkO5NCCKOBi4ETmvs5\nMTOzxllmGbj3Xth//3jzNfGsqSqqeAIuA+4NISzS6SppDaAX8FjhsRDCTGAc8L3koc2JvUXpmNeB\n91MxA4HpSWFV8CgQgAGpmJdDCNNSMWOAbsCGqZinQgjzMjHrSepWSoPNzKz5LLEEXHst3HUXbLNN\n3tlYpaqY4knSfsBmwO+KLO5FLHCmZh6fmiwD6AnMSYqqumJ6AZ+mF4YQ5gNfZGKK7YcSY8zMLAcS\n/PSn8a9ZU1TEte0krUIcr7RDCGFu3vmYmZlZ21URxRPQH1gBqJEW/lZoD2wr6RjiGCQRe5fSPT49\ngcIhuClAR0ldM71PPZNlhZjs2XftgeUyMVtk8uuZWlb427OBmKKGDx9Ot26LHtkbMmQIQ4YMqW81\nMzOzNmHUqFGMGjVqkcdmzJjRqjlUSvH0KLBx5rEbgEnAuSGEdyRNIZ4h9xIsHCA+gDhOCmAiMC+J\nuTuJWQ9YDRibxIwFukvqmxr3NIhYmI1LxZwiqUdq3NOOwAzg1VTMOZLaJ4f9CjGvhxDqfYVHjBhB\nv379Gng6zMzM2qZiHQo1NTX079+/1XKoiDFPIYRZIYRX0zfiVASfhxAmJWEXAqdJ+rGkjYGbgA+B\ne5JtzASuBS6QtJ2k/sB1wLMhhPFJzGvEgd1XS9pC0tbAJcCoEEKhx+hhYpE0MpnLaSfgbODS1CHF\nW4E5wHWSNpC0LzAMOL/FniQzM1ts8+fDUUfB88/nnYmVs4oonuoQFrkTwnnEQudKYi9RZ2CXEMKc\nVNhw4D7gTuAJ4GPinE9pQ4HXiL1d9wFPAUek9rMA2B2YDzxHLNJuAM5Ixcwk9jT1BiYAfwHODCFc\n2+TWmplZi/v6a3jpJdh+e0+maXVTCKHhKGtxkvoBEydOnOjDdmZmOZo1K17W5fHH4fbbYc89887I\nGpI6bNc/hFDT0vur5J4nMzOzZtelC/zzn7FoGjwYrr8+74ys3FTKgHEzM7NW07Ej3HordO8OhxwC\nX30Fw4blnZWVCxdPZmZmRbRvD1dcAV27wnHHQbt2cMwxeWdl5cDFk5mZWR0kOO886NYNttoq72ys\nXLh4MjMzq4cEp52WdxZWTjxg3MzMzKwELp7MzMzMSuDiyczMzKwELp7MzMwWw6ef5p2BtTYXT2Zm\nZk00bRpsuCGcfXbemVhrcvFkZmbWRD16wPDhcPrpcUoDaxs8VYGZmdliOOUUmD0bTj45zkx+/PF5\nZ2QtzcWTmZnZYjrzTPj229gL1akTHHVU3hlZS3LxZGZmtpgkOPfc2AP1q1/BMsvA/vvnnZW1FBdP\nZmZmzUCCESNg5kw4+GBYay343vfyzspagosnMzOzZiLBVVfBpptC//55Z2MtxcWTmZlZM+rQAY47\nLu8srCV5qgIzMzOzErh4MjMzMyuBiyczMzOzErh4MjMza0Uh5J2BLS4XT2ZmZq3kN7+BE07IOwtb\nXC6ezMzMWknv3nDhhXDxxXlnYovDUxWYmZm1kl/9Ct55J17/bvXV4Sc/yTsjawr3PJmZmbWi886D\nn/4UhgyBiRPzzsaawsWTmZlZK2rXDkaOhI03hj33hClT8s7ISuXiyczMrJV17gx33w3z58deqNmz\n887ISuHiyczMLAcrrxwLqDffhJdfzjsbK4UHjJuZmeVkwAB4911Yeum8M7FSuOfJzMwsRy6cKo+L\nJzMzM7MSuHgyMzMzK4GLJzMzM7MSuHgyMzMrQ/Pm5Z2B1cXFk5mZWZl56SVYf32YNCnvTKwYF09m\nZmZlZs01oVMn2HtvmDUr72wsy8WTmZlZmVl6abjzzjgH1Akn5J2NZbl4MjMzK0N9+sBFF8FVV8WZ\nyK18uHgyMzMrU4cdBnvtFf9+9FHe2ViBiyczM7MyJcHVV8cLCR9wQLyQsOXPxZOZmVkZW355GDkS\nnngC/v73vLMx8IWBzczMyt4Pfwhjx8KWW+adiYGLJzMzs4owYEDeGViBD9uZmZmZlcDFk5mZmVkJ\nXDyZmZmZlcDFk5mZmVkJXDyZmZlVqJkz4YMP8s6i7fHZdmZmZhVqjz3i38cfjxNqWutwz5OZmVmF\nOvVUePLJOImmtR4XT2ZmZhXqRz+CIUPgxBPh88/zzqbtqIjiSdLvJI2XNFPSVEl3S1q3SNxZkj6W\n9LWkRyStnVneSdJlkqZJ+krSnZJWzMQsK+kWSTMkTZd0jaQumZhVJd0vaZakKZLOk9QuE7OJpKck\nfSPpPUknNedzYmZmBnDBBTB3Lpx8ct6ZtB0VUTwB2wCXAAOAHYAlgIcldS4ESDoZOAY4HNgSmAWM\nkdQxtZ0Lgd2AwcC2wMrAXZl93Qr0AQYlsdsCV6b20w54gDhebCBwEPAL4KxUzDLAGOBdoB9wEnCm\npMOa/hSYmZl9V69e8Mc/wrXXwvjxeWfTNiiEkHcOJZPUA/gU2DaE8Ezy2MfAX0III5L7XYGpwEEh\nhNHJ/c+A/UIIdycx6wGTgIEhhPGS+gCvAP1DCC8kMTsB9wOrhBCmSNoF+CewUghhWhJzBHAusEII\nYZ6ko4CzgV4hhHlJzJ+An4QQNqijTf2AiRMnTqRfv37N/IyZmVk1mz8f+vWDLl3g2Wfb3uDxmpoa\n+vfvD/H7u6al91cpPU9Z3YEAfAEgaQ2gF/BYISCEMBMYB3wveWhzYm9ROuZ14P1UzEBgeqFwSjya\n7GtAKublQuGUGAN0AzZMxTxVKJxSMetJ6taE9pqZmdWpfXsYMSJePPiBB/LOpvpVXPEkScTDb8+E\nEF5NHu5FLHCmZsKnJssAegJzkqKqrphexB6thUII84lFWjqm2H4oMcbMzKzZbL89PPYY7LJL3plU\nv0qc5+lyYANg67wTMTMzKyfbb593Bm1DRRVPki4FdgW2CSF8klo0BRCxdynd49MTeCEV01FS10zv\nU89kWSEme/Zde2C5TMwWmdR6ppYV/vZsIKao4cOH063bokf2hgwZwpAhQ+pbzczMrE0YNWoUo0aN\nWuSxGTNmtGoOFVM8JYXTT4AfhBDeTy8LIbwraQrxDLmXkviuxHFKlyVhE4F5SUx6wPhqwNgkZizQ\nXVLf1LinQcTCbFwq5hRJPVLjnnYEZgCvpmLOkdQ+OexXiHk9hFDvKzxixAgPGDczM6tDsQ6F1IDx\nVlERY54kXQ78HBgKzJLUM7ktmQq7EDhN0o8lbQzcBHwI3AMLB5BfC1wgaTtJ/YHrgGdDCOOTmNeI\nA7uvlrSFpK2JUySMCiEUeoweJhZJI5O5nHYinll3aQhhbhJzKzAHuE7SBpL2BYYB57fE82NmZmat\np1J6no4kDgh/IvP4wcQiiRDCeZKWIs7J1B14GtglhDAnFT8cmA/cCXQCHgKOzmxzKHAp8Sy7BUns\ncYWFIYQFknYH/gY8R5xP6gbgjFTMTEk7Enu9JgDTgDNDCNc2qfVmZmZWNipynqdq5HmezMzMmsbz\nPJmZmVmzuPde+PWv886i+rh4MjMzq1JTpsRr302alHcm1cXFk5mZWZU68EBYeWX485/zzqS6uHgy\nMzOrUp06xcN2N98MkyfnnU31cPFkZmZWxX75S+jeHf7617wzqR4unszMzKpYly5w/PFwzTVxDJQt\nPhdPZmZmVe7oo6FDB7jiirwzqQ4unszMzKrcssvCQQfBHXeAp3dcfJUyw7iZmZkthrPOgqWWAinv\nTCqfiyczM7M2YPnl886geviwnZmZmVkJXDyZmZmZlcDFk5mZmVkJXDyZmZmZlcDFk5mZmVkJXDyZ\nmZm1MQsWwCOPwDvv5J1JZXLxZGZm1sbMmwdDhsCVV+adSWVy8WRmZtbGdOwIgwfD6NGecbwpXDyZ\nmZm1QfvuC5Mnw/PP551J5XHxZGZm1gZtuy2suGLsfbLSuHgyMzNrgzp0gL33jsXTggV5Z1NZXDyZ\nmZm1UfvsAx984EN3pXLxZGZm1kZtvTUsuyzcf3/emVQWF09mZmZtVIcOcOSR0KtX3plUlg55J2Bm\nZmb5+eMf886g8rjnyczMzKwELp7MzMzMSuDiyczMzKwELp7MzMzMSuDiyczMzKwELp7MzMzMSuDi\nyczMzJgyxde5aywXT2ZmZsbYsbDvvvDxx3lnUv5cPJmZmRn9+8e/Eybkm0clcPFkZmZmrLoqrLAC\nTJyYdyblz8WTmZmZIcHmm7vnqTFcPJmZmRkQD93V1OSdRflz8WRmZmYAbLhhPOtu+vS8MylvLp7M\nzMwMgPXXj39ffz3fPMqdiyczMzMDYN11YbnlYNq0vDMpbx3yTsDMzMzKw1JLxcJJyjuT8uaeJzMz\nM1vIhVPDXDyZmZmZlcDFk5mZmVkJXDyZmZmZlcDFk5mZmVkJXDyZmZmZlcDFk5mZmVkJXDyZmZnZ\nQgsWwGabwejReWdSvlw8mZmZ2ULt2sE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PBA4Gngw8GPhMZ3OnNevfr4l9MvCR1na2AL5IvTDoPsBLgZcBR7Ri7g8sBa4G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\nST38f0lOMBq+0lYVAAAAAElFTkSuQmCC\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\")\n", "plt.show()\n", "#\n", "plt.plot(vX,vZ,\"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_z\")\n", "plt.show()\n", "#\n", "plt.plot(vY,vZ,\"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_y\")\n", "ax.set_ylabel(\"v_z\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot velocity in 3D." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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syzjhhBMqfk6qBRJrhCXo+3YykaZfYNkinUgkoCgKPB5PmhVN35TdKqrBsqYva6KqalEi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\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ax.plot(vX,vY,vZ)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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 }