{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*This notebook was created by [Sergey Tomin](http://www.xfel.eu/organization/staff/tomin_sergey/) which was inspired by questions from E.R. Source and license info is on [GitHub](https://github.com/iagapov/ocelot/tree/dev/docs). June 2017.* " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial N7. Lattice design. Matching. Twiss back tracking.\n", "### Outline\n", "* FODO lattice (undulator section) with desiring max and min twiss parameters. \n", "* Back tracking through chicanes \n", "* Matching of twiss parameters in matching sections\n", "\n", "### Introduction \n", "In this tutorial we are going to design the simplest FEL lattice for external seeding option. \n", "The desire lattice is:\n", "- matching section - modulator - chicane - modulator - chicane - FODO.\n", "\n", "FODO in that case is undulator section:\n", "- undulator - QF - undulator - QD - undulator - QF - .... \n", "\n", "where QF, QD - focusin and defocusing quadrupoles. \n", "\n", "**And suppose we know**: \n", "1. max and min values for the betas in the undulator section.\n", "2. chicanes geometry and parameters are defined. \n", "3. twiss parameters on the entrance of the matching section. \n", "\n", "We can solve this task in many ways (and even more simply), *but to cover all topics we will do it in a few steps*:\n", "\n", "1. the matching of twiss parameters in FODO lattice to find desired amplitudes of the beta functions. \n", "2. back tracking of the beta through *modulator - chicane - modulator - chicane* \n", "3. matching quadrupoles in the matching section\n", "\n", "\n", "#### Optics design and matching\n", "\n", "Optics design is the art (still) and a few people in the world can do really good design (and author of this notebook is not one of them (so far :)). \n", "\n", "The matching techniques barely help you if your initial geometry or initial conditions are poor. In this example, we are not aiming to make a good design but just show an example of usage some matching functions. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initializing ocelot...\n" ] } ], "source": [ "# the output of plotting commands is displayed inline within \n", "# frontends, directly below the code cell that produced it.\n", "%matplotlib inline\n", "\n", "from time import time \n", "\n", "# this python library provides generic shallow (copy) \n", "# and deep copy (deepcopy) operations \n", "from copy import deepcopy\n", "\n", "# import from Ocelot main modules and functions\n", "from ocelot import *\n", "\n", "# import from Ocelot graphical modules\n", "from ocelot.gui.accelerator import *\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 1. FODO lattice matching \n", "### Design the simplest FODO lattice" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# example of the FODO\n", "U = Undulator(nperiods=50, lperiod=0.04, Kx=1)\n", "D = Drift(l=0.5)\n", "QF = Quadrupole(l=0.25, k1=1)\n", "QD = Quadrupole(l=0.25, k1=-1)\n", "\n", "M1 = Marker()\n", "cell = (M1, QF, D, U, D, QD, QD, D, U, D, QF)\n", "\n", "# suppose we have 5 cells or 10 undulators\n", "fodo = cell*5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Periodic solution for FODO lattice\n", "**Note**\n", "\n", "* In the most cases to find twiss periodical solution we do not need to put the initial conditions and we can use following command to calculate twiss parameters:\n", "**tws = twiss(lat)** \n", "\n", "**BUT**\n", "\n", "* To take into account undulator vertical focusing effect we have to define the energy of the electron beam. and in that case we have to define initial condition like that: \n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hhOi00uphUkoVATuBDzHjlpqBHUCVf00TQgghhLBDSj1MSqluSqnfA9XAAWA38GOl1ECt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\nIFvhafbz4VdeUZ09u/y8Bx/0vu/AX+huvrncoFNPVT1woLH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"text/plain": [ "<matplotlib.figure.Figure at 0xa6af908>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create MagneticLattice object\n", "lat_fodo = MagneticLattice(fodo)\n", "\n", "tws0 = Twiss()\n", "# by default the all parameters are zero and \n", "# that what we need to force the twiss function \n", "# to calculate periodic solution\n", "\n", "# print(tws0)\n", "\n", "# And we need to define the beam energy\n", "tws0.E = 1 # GeV\n", "\n", "tws = twiss(lat_fodo, tws0=tws0)\n", "\n", "plot_opt_func(lat_fodo, tws, legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Matching" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial value: x = [1, -1]\n", "Optimization terminated successfully.\n", " Current function value: 0.000031\n", " Iterations: 41\n", " Function evaluations: 80\n", "QF.k1 = 1.07104011822\n", "QD.k1 = -0.857945636259\n" ] }, { "data": { "image/png": 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PEdUwKaVaKKVeBIqAPGAv8Bul1Pla68W2gSuFEEIIIRqNSGuYnsFMYzIMaAkMBO4ENiql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\npvESqEwuUZ6SS32iE8UCGOARYG3A+9yEKdegYO2SJYmf7y9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"text/plain": [ "<matplotlib.figure.Figure at 0x7c3d400>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# constrains\n", "constr = {M1:{'beta_x':15, 'beta_y':2}, 'periodic':True}\n", "\n", "# variables\n", "vars = [QF, QD]\n", "\n", "# initial condition for twiss\n", "tw0=tws[-1]\n", "\n", "match(lat_fodo, constr, vars, tw0, verbose=False)\n", "\n", "# results \n", "print(\"QF.k1 = \", QF.k1)\n", "print(\"QD.k1 = \", QD.k1)\n", "\n", "\n", "tws0=Twiss()\n", "tws0.E = 1 # GeV\n", "\n", "tws = twiss(lat_fodo, tws0=tws0)\n", "\n", "# let's variable *tws_fodo* will be the twiss \n", "# parameters on the FODO entrance \n", "tws_fodo = tws[-1]\n", "\n", "plot_opt_func(lat_fodo, tws, legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 2. Chicanes. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# undulator + chicane + undulator + chicane\n", "modulator = Undulator(nperiods=10, lperiod=0.1, Kx = 2)\n", "\n", "# Chicane from CSR example with small modifications \n", "\n", "b1 = Bend(l = 0.5, angle=-0.0336, e1=0.0, e2=-0.0336, gap=0, tilt=0, eid='BB.393.B2')\n", "b2 = Bend(l = 0.5, angle=0.0336, e1=0.0336, e2=0.0, gap=0, tilt=0, eid='BB.402.B2')\n", "b3 = Bend(l = 0.5, angle=0.0336, e1=0.0, e2=0.0336, gap=0, tilt=0, eid='BB.404.B2')\n", "b4 = Bend(l = 0.5, angle=-0.0336, e1=-0.0336, e2=0.0, gap=0, tilt=0, eid='BB.413.B2')\n", "\n", "d = Drift(l=1.5/np.cos(b2.angle))\n", "\n", "start_csr = Marker()\n", "stop_csr = Marker()\n", "\n", "# define chicane frome the bends and drifts\n", "chicane = [start_csr, Drift(l=1), b1, d, b2, \n", " Drift(l=1.5), b3, d, b4, Drift(l= 1.), stop_csr]\n", "\n", "\n", "# For sake of buity add randomly couple of the quadrupoles\n", "\n", "D1 = Drift(l=0.5)\n", "echo = (D1, QF, D1, modulator, D1, QD, chicane, QF, D1, modulator,D1, QD, chicane)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Chicane parameters\n", "For example, one wants to know R56 of the whole chicane. It can be easily calculated" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R56 = -4.14432493493 mm\n" ] } ], "source": [ "lat_chic = MagneticLattice(chicane)\n", "# in that case energy is not important we do not have \n", "# energy dependant elements here\n", "R = lattice_transfer_map(lat_chic, energy=0)\n", "print(\"R56 = \", R[4,5]*1000, \"mm\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backtracking though chicanes.\n", "We know twiss parameters on the entrance of the FODO\n", "but for backtracking we need to \n", "* invert alphas \n", "* and invert the lattice (change the order of the element)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IdCGXjgaediWBPwCDgPrAzXlevzUwFrvkT8jN/QgL0y4EX8jbeqWzipSTRo2y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\nk19LOoc5OTlMmTKlSt3ChQsZMWJEgx7fqgKsyuDqBOAI732VCTHe+9X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"text/plain": [ "<matplotlib.figure.Figure at 0xb864630>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# inverting alphas\n", "\n", "tws2 = Twiss()\n", "tws2.alpha_x = -tws_fodo.alpha_x\n", "tws2.alpha_y = -tws_fodo.alpha_y\n", "tws2.beta_x = tws_fodo.beta_x\n", "tws2.beta_y = tws_fodo.beta_y\n", "\n", "# invert the lattice\n", "echo_inv = echo[::-1]\n", "lat_echo_inv = MagneticLattice(echo_inv)\n", "\n", "# calculate twiss \n", "tws_echo = twiss(lat_echo_inv, tws0=tws2)\n", "tws_echo_inv_end = tws_echo[-1]\n", "\n", "# show the twiss parameters of INVERTED echo\n", "plot_opt_func(lat_echo_inv, tws_echo, legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "So twiss parameters on the entrance of the echo lattice are: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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o5SbZRft3sCTXGGO8ZQlWkjvoIOjSxZWj0YK1YwesXu3K/ftDK/sbCES/JdES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\nvxxcSOOwgOKaWGjJEnOzdMWSJUQtmxTQPzGNSqG37ND117ODvBt8vhd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"text/plain": [ "<matplotlib.figure.Figure at 0xb9f6908>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# inverting alphas again is needed\n", "tws_e = Twiss()\n", "tws_e.beta_x = tws_echo_inv_end.beta_x\n", "tws_e.beta_y = tws_echo_inv_end.beta_y\n", "tws_e.alpha_x = -tws_echo_inv_end.alpha_x\n", "tws_e.alpha_y = -tws_echo_inv_end.alpha_y\n", "\n", "lat_echo_fodo = MagneticLattice((echo, fodo) )\n", "\n", "tws_all = twiss(lat_echo_fodo, tws_e)\n", "\n", "plot_opt_func(lat_echo_fodo, tws_all, legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 3. Matching section" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Q1 = Quadrupole(l=0.3, k1=1)\n", "Q2 = Quadrupole(l=0.3, k1=1)\n", "Q3 = Quadrupole(l=0.3, k1=1)\n", "Q4 = Quadrupole(l=0.3, k1=1)\n", "\n", "\n", "m1 = Marker()\n", "m2 = Marker()\n", "dm = Drift(l=1.5)\n", "match_sec = (m1, dm, Q1, dm, Q2, dm, Q3, dm, Q4, dm, m2)\n", "\n", "lat_m = MagneticLattice(match_sec[::-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Matching\n", "As it was mentioned above, matching will not give you desired values if your geometry of initial conditions are poor. Because our goal is not a good design but showing the concept of OCELOT usage, we choose very relax condition. \n", "Twiss parameters on the entrance of the matching section:\n", "\n", "- beta_x = 5 \n", "- beta_y = 5\n", "- alpha_x = not defined\n", "- alpha_y = not defined\n", "\n", "the twiss parameters on the exit of matching section are defined by echo section" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial value: x = [1, 1, 1, 1]\n", "Optimization terminated successfully.\n", " Current function value: 214921323.823277\n", " Iterations: 106\n", " Function evaluations: 197\n", "Q1.k1 = 2.35585335163\n", "Q2.k1 = -1.31552921354\n", "Q3.k1 = -0.916460317653\n", "Q4.k1 = 1.33264967947\n" ] }, { "data": { "image/png": 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ff8zxxx9f5/aHH34YM+Oss85KcGTbRoWSSKYrL4fTTqtpaNi5M0ydCh07Jjcu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\n3vLzgdsA3P1aM2sAbiZ8K+6PwEJ331vGOkVEpMJ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"text/plain": [ "<matplotlib.figure.Figure at 0xaf64358>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# constrains\n", "constr = {m1:{'beta_x':5, 'beta_y':5}, \n", " m2:{'beta_x':tws_e.beta_x, 'beta_y':tws_e.beta_y, \n", " 'alpha_x': -tws_e.alpha_x, \"alpha_y\":-tws_e.alpha_y}}\n", "\n", "# variables\n", "vars = [Q1, Q2, Q3,Q4]\n", "\n", "# initial condition for twiss\n", "\n", "match(lat_m, constr, vars, tw0, verbose=False)\n", "\n", "for i, q in enumerate(vars):\n", " print(\"Q\"+str(i+1)+\".k1 = \", q.k1)\n", "\n", "tws0 = Twiss()\n", "tws0.beta_x = tws_e.beta_x\n", "tws0.beta_y = tws_e.beta_y\n", "tws0.alpha_x = -tws_e.alpha_x\n", "tws0.alpha_y = -tws_e.alpha_y\n", "\n", "tws = twiss(lat_m, tws0)\n", "plot_opt_func(lat_m, tws, legend=False)\n", "plt.show()\n", "\n", "tws0 = tws[-1]\n", "tws0.alpha_x = -tws[-1].alpha_x\n", "tws0.alpha_y = -tws[-1].alpha_y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## FINAL Lattice" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9xhjjNUuwTMqxBMt7kWzTI0fg88/d9vDhyf/QgDEmOdh/VSbl5OTAgAFuO5IJ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\nxTrGd6xZCxYsoKioiPHjx7c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QrVuExwAPqurOKF0vsUW6BwtcL1ZxsZumob7e+6kgjDHG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"text/plain": [ "<matplotlib.figure.Figure at 0xb848240>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cell = (match_sec, echo, fodo)\n", "# fodo quadrupoles\n", "\n", "lat = MagneticLattice(cell)\n", "\n", "tws = twiss(lat, tws0)\n", "plot_opt_func(lat, tws, legend=False)\n", "plt.show()" ] }, { "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 [conda root]", "language": "python", "name": "conda-root-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": 2 }