{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "*This notebook was created by Sergey Tomin (sergey.tomin@desy.de) and [Igor Zagorodnov](http://www.desy.de/~zagor/) for Workshop: [Designing future X-ray FELs](http://www.xrayfels.co.uk/). Source and license info is on [GitHub](https://github.com/ocelot-collab/ocelot). Updated January 2018. *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial N4. Wakefields.\n", "## Chirper.\n", "Influence of corrugated structure on the electron beam.\n", "This example based on the work: [I. Zagorodnov, G. Feng, T. Limberg. Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL](https://arxiv.org/abs/1607.07642). \n", "\n", "Gerometry of the corrugated structure. The blue ellipse represents an electron beam\n", "propagating along the z axis.\n", "\n", "\n", "\n", "## Wakefields\n", "In order to take into account the impact of the wake field on the beam the longitudinal wake function\n", "of point charge through the second order Taylor expansion is used.\n", "In general case it uses 13 one-dimensional functions to represent the longitudinal component of the wake\n", "function for arbitrary sets of the source and the wittness particles near to the reference axis.\n", "The wake field impact on the beam is included as series of kicks.\n", "\n", "The implementation of the wakefields follows closely the approach described \n", "in:\n", "* [O. Zagorodnova, T. Limberg, Impedance budget database for the European XFEL,\n", "in Proceedings of 2009 Particle Accelerator Conference,(Vancouver, Canada, 2009)](http://bib-pubdb1.desy.de/record/93956/files/tu5rfp060%5B1%5D.pdf)\n", "* [M. Dohlus, K. Floettmann, C. Henning, Fast particle tracking with wake \n", "fields, Report No. DESY 12-012, 2012.](https://arxiv.org/abs/1201.5270)\n", "\n", "#### This example will cover the following topics:\n", "* Initialization of the wakes and the places of their applying\n", "* tracking of second order with wakes\n", "\n", "#### Requirements \n", "* beam_chirper.ast - input file, initial beam distribution in [ASTRA](http://www.desy.de/~mpyflo/) format (was obtained from s2e simulation performed with ASTRA and [CSRtrack](http://www.desy.de/fel-beam/psviewer/index.html)).\n", "* wake_vert_1m.txt - wake table of the vertical corrugated structure (was calculated with [ECHO](http://www.desy.de/~zagor/WakefieldCode_ECHOz/))\n", "* wake_hor_1m.txt - wake table of the vertical corrugated structure (was calculated with [ECHO](http://www.desy.de/~zagor/WakefieldCode_ECHOz/))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wake Table format\n", "\n", "We use the same format of the wakes as implemented in ASTRA and the description of the format can be found in [M. Dohlus, K. Floettmann, C. Henning, Fast particle tracking with wake \n", "fields, Report No. DESY 12-012, 2012.](https://arxiv.org/abs/1201.5270)\n", "\n", "Second order Taylor expansion of the longitudinal wake ($w_z$) in the transverse coordinates\n", "\n", "$$\n", "w_z(x_s, y_s, x_o, y_o, s) = \n", "\\begin{bmatrix}\n", " 1 \\\\\n", " x_s\\\\\n", " y_s\\\\\n", " x_o \\\\\n", " y_o\n", "\\end{bmatrix}^T \n", "\\begin{bmatrix}\n", " h_{00}(s) & h_{01}(s) & h_{02}(s) & h_{03}(s) & h_{04}(s) \\\\\n", " 0 & h_{11}(s) & h_{12}(s) & h_{13}(s) & h_{14}(s)\\\\\n", " 0 & h_{12}(s) & -h_{11}(s) & h_{23}(s) & h_{24}(s) \\\\\n", " 0 & h_{13}(s) & h_{23}(s) & h_{33}(s) & h_{34}(s)\\\\\n", " 0 & h_{14}(s) & h_{24}(s) & h_{34}(s) & -h_{33}(s)\n", "\\end{bmatrix} \n", "\\begin{bmatrix}\n", " 1 \\\\\n", " x_s\\\\\n", " y_s\\\\\n", " x_o \\\\\n", " y_o\n", "\\end{bmatrix} ;\n", "$$\n", "where $x_s$ and $y_s$ transverse coordinates of the *source* particle and $x_o$ and $y_o$ are transverse coordinates of the *observer*, $s$ is distance between *source* and *observer*. Thus to describe longitudinal wake we need 13 functions $h_{\\alpha \\beta}$. \n", "\n", "The transverse components are uniquely related to the longitudinal wake by causality and Panofsky-Wenzel-Theorem.\n", "\n", "For each of these coefficients, we use the representation in [O. Zagorodnova, T. Limberg, Impedance budget database for the European XFEL](http://bib-pubdb1.desy.de/record/93956/files/tu5rfp060%5B1%5D.pdf) \n", "\\begin{equation}\n", "h(s) = w_0(s) + \\frac{1}{C} + R c\\delta(s) + c\\frac{\\partial}{\\partial s}\\left[L c \\delta(s) + w_1 (s) \\right]\n", "\\end{equation}\n", "where $w_0(s)$, $w_1(s)$ are nonsingular functions, which can be tabulated easily, and constants $R$, $L$, and $C$ have the meaning of resistivity, inductance, and capacitance, correspondingly.\n", "The functions $w_0(s)$, $w_1(s)$ can be represented by table, e.g. [$s_i$, $w_0^i$].\n", "\n", "Now we can describe whole table how it is saved in a file. \n", "\n", "$N_h$| $0$ \n", "--------------|-----------------\n", " $N_{w_0}$ | $N_{w_1}$\n", " $R,\\: [Us]$ | $L,\\: [Us^2]$\n", "$C,\\: [1/Us]$ | $10\\alpha + \\beta$ \n", "$s_1,\\: [m]$ | $w_0(s_1),\\: [U]$ \n", "$s_2,\\: [m]$ |$w_0(s_2),\\: [U]$ \n", " ... | ... \n", "$s_{N_{w_0}},\\: [m]$ | $w_0(s_{N_{w_0}}),\\: [U]$ \n", "$s_1,\\: [m]$ | $w_1(s_1),\\: [U]$ \n", "$s_2,\\: [m]$ |$w_1(s_2),\\: [U]$ \n", " ... | ... \n", "$s_{N_{w_1}},\\: [m]$ | $w_1(s_{N_{w_1}}),\\: [U]$\n", " $N_{w_0}$ | $N_{w_1}$\n", " $R,\\: [Us]$ | $L,\\: [Us^2]$\n", "$C,\\: [1/Us]$ | $10\\alpha + \\beta$ \n", "$s_1,\\: [m]$ | $w_0(s_1),\\: [U]$ \n", " ... | ... \n", " $N_{w_0}$ | $N_{w_1}$\n", " $R,\\: [Us]$ | $L,\\: [Us^2]$\n", "$C,\\: [1/Us]$ | $10\\alpha + \\beta$ \n", "$s_1,\\: [m]$ | $w_0(s_1),\\: [U]$ \n", " ... | ... \n", "|\n", "\n", "\n", "\n", "In the very first line, $N_h$ is number of $h_{\\alpha\\beta}(s)$ functions in the table. After that, a typical table repeated $N_h$ times describing every $h_{\\alpha\\beta}(s)$ function. \n", "\n", "\n", "Every table starts with $N_{w_0}$ and $N_{w_1}$ which are number of points of $w_0(s_i)$ and $w_1(s_i)$ functions.\n", "Next two lines are included $R$, $L$, $C$ and entry $10\\alpha + \\beta$ which describes the subscript of the auxiliary function $h_{\\alpha\\beta}(s)$. Next $N_{w_0}$ lines described function $w_0(s)$, and after that next $N_{w_1}$ lines described function $w_1(s)$.\n", "\n", "And to describe next $h_{\\alpha\\beta}(s)$ we repeat procedure. \n", "\n", "The unit $U$ is $V/(A\\cdot s)$ for $\\alpha\\beta = 00$, $V/(A\\cdot s \\cdot m)$ for $\\alpha\\beta = 01, ... 04$ and $V/(A\\cdot s \\cdot m^2)$ for all other coefficients.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Import of modules" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initializing ocelot...\n" ] } ], "source": [ "# the output of plotting commands is displayed inline within frontends, \n", "# directly below the code cell that produced it\n", "%matplotlib inline\n", "\n", "# this python library provides generic shallow (copy) and deep copy (deepcopy) operations \n", "from copy import deepcopy\n", "import time\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", "\n", "# load beam distribution\n", "# this function convert Astra beam distribution to Ocelot format \n", "# - ParticleArray. ParticleArray is designed for tracking.\n", "# in order to work with converters we have to import \n", "# specific module from ocelot.adaptors\n", "from ocelot.adaptors.astra2ocelot import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Layout of the corrugated structure insertion. Create Ocelot lattice " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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NVlr+t79Bamr8YqlZE+68cx2ffmrjXzNmQLducNNNsG1b/OJwrrSCblG5fM466yxOOOEEZs2axRNPPMEdd9wRdEiumNatgxEjoGVLGDs2r8Bh0SK45x6bGxWU44+H2bPhqqsgO9tadl26wLffBheTc9HwRBUSs2bNYt26dVx77bW75kHVrVs34KjcvmRk2PhP8+Zw332QmWmTbn/8EcaMgYYNg47QpKbCf/4DkyZB69Y2Rnb00XDttfD770FH59zeVdpEJRKfo7gmT55Mjx49yM7OZtasWVx77bUMHz687P4DXKls3w4PPQQtWtj4z6ZN0K8fTJ0Kr7wCrVoFHWHRjj7augBvvNEKOe6/Hzp2hIkTg47MuT2rtIkqbGbMmEHXrl057rjj6N+/P9WqVePMM88MOixXSFYWvPCCtUquuAJ++QW6d7cquwkTrEst7KpUgX/+00rjO3aExYttrcDhwy3hOhc2lTZR5a0JULZHcc2YMYNu3brx+eefM2nSJGrXrs0NN9xQdv8BLiqq8O670LkznH8+LF0KbdvC+PE2d+m444KOMHqHH27l87feCklJ1lXZvr0lXOfCpNImqjDJyspi7ty5dO7cmUgkQtOmTTnmmGMA2L59O927d2fr1q28/fbb/PWvfw042srnq69spYcBA6wooUkTePpp+/qMM6Lr4g2b5GS45RZb1aJbN6taPPlk+NOfbEFc58LAE1UIzJ8/n99//50PPviArKws0tLSGDt2LEOHDiU5OZm//OUvXHXVVTz99NM89NBDQYdbacydm8wpp8Cxx8LkyXDAATamM38+XHghhGDt35hp3962F/nXvyAlBZ55Bg49FN58M+jInPNEFQrTp0/n0EMP5brrrqNWrVpcc801PPDAAxx55JEAHH300YwdO5aHHnqIxMQw78xSMSxeDOedB6eeehDvvw/Vq9u6eYsXw9VX2xhPRZSYCNdfDzNnwjHHwM8/w8CBMHiwbeLoXFA8UYXAjBkzGDJkCEuXLmXz5s189NFHuwop1q1bx5VXXsmdd97Ji7kbFrky8fPPcNlltmbeSy/ZuM3VV9tk3dGjbQJtZdC6NXz5JTz4oJW1v/qqjce9/HJ0467OxYonqhCYPn06bdu23e18ZmYmF1xwAffffz8jRoxg3LhxZGRkBBBhxbZhg63W0KKFrcOXnW1de59+upL774fKOJ0tEoHLL7dxuD59bELzuefamNzq1UFH5yobT1QhMHPmTNq0abPb+ZSUFN577z06dOhAYmIi3333HdWrVw8gwopp61a4916brHvXXTbx9YwzYNYsK5Zo2ND3yGjWDD7+GJ54wlqUb79tY1dPPeWtKxc/nqhCYO3atUUmKlc2du60N96WLW0dvvXroVcvKzMfP97W6XN5RGz9wrQ0OPVU2LgR/vxnm+C8bFnQ0bnKwBOVqzSys+H11y0RDRsGq1bZvKgJE+DzzyGndsXtQaNG1qJ64QVbu/Djj61a8OGH7f/WubLiicpVeKrw0Ue2zcU558CCBXDIIbbU0ZQp1jIoz3Oh4knEKiJ//BHOPtvWOrz8cttWZOHCoKNzFZUnKlehffedFQPkrsPXoIGtwPDjj7Z4bKw3Lqws6tWD116D//3Pvv7qK1uO6b77bJkp52LJ/0xdhTR3Lpx5pnXnff451Kpl220sWmTbbyQlBR1hxTBokCX9Cy6wPa5GjLCFb9PSgo7MVSSeqFyFsnw5XHSRjZ2MHw9Vq9qGhUuWWOFEtWpBR1jx1K4Nzz4L771n41jff29jf3fcATt2BB2dqwg8UbkK4ddfbW+lli2ttDwSsdXAFy+20vP99w86woqvf39rSV1yiSWom2+29QOnTQs6MlfeeaJy5drmzXDbbTYX6v77bZ+oIUOs6++RR2xMysVPzZo2BvjppzYHa+ZMK2K56SbrGnSuJEKTqESkpYhsE5EX8p07V0SWicgWEXlTRALc0NuFSWYmPPCArSYxapQlrJNPtk/vL71kVX0uOMcfb6taXHWVla7fdZft1fXtt0FH5sqj0CQq4GHgh9xvRKQd8BhwPlAP+B14JJjQXFhs2waPPWbr0V11lS2WetRRtkPt++/b2IgLh9RU+M9/YNIk+3nNnWuFFtdea6uAOFdcoUhUIjIY2AB8mu/0ecA7qvqlqmYANwNnikiNIGKMh/T0dE4++WTatWtHw4YNefrpp4MOKTQ2boS774amTeGvf7UVEdq1g7fesi04evUKOkK3J0cfDTNmwI032tjh/fdDhw5WjelccYgGvGCXiNQEpgB9gD8Dh6jqH0XkLeBrVb0n330zgF6qOrXQcwwDhgE0aNDg8MmTJ+/2OtnZ2VQJ+f4MJ598MgMHDuScc85h6tSp3HLLLRR1LXuzbds2IiGYHLRhwwZq1apV6uf55ZcEnnqqJi+9VJOMDLuuQw/N5JJLNtK//5Yy3RMqVtcQpLBdw+zZyYwceQDz5qUAcO65mxg58jdq1Njz+1DYrqEk/Br2rXnz5lNVtWuRN6pqoAfwX2BkztejgRdyvv4U+Guh+64Ceu/t+dq3b69FycjIKPJ8WMycOVMPPvhgVVVduXKlvvfee9q9e/eonycs17lkyZJSPX7BAtVhw1STk1VtbQnV445T/fBD1ezsGAW5D6W9hjAI4zVkZqreeqtqUpL9XBs3Vv3ggz3fP4zXEC2/hn0Dpuge3tcD/egtIp2AvsD9RdycARTeAagmsDlGLx6fo5gmT55Mjx49yM7OZtasWVx77bUMHz48JpdankydassctW4Njz9uZc5nnmkrTHz2GZx4oi93VN4lJ8Mtt1jhS7dusGKFFcJceCH89lvQ0bkwCrqPqDfQFFguIj8DI4BBIjINSAMOy72jiDQHUoAF8Q+z7M2YMYOuXbty3HHH0b9/f6pVq7Zr88SKThU++QROOAG6drWFYxMTbYXuuXNh3DgrcXYVS/v28PXX8K9/QUqKTRpu184majuXX9CJ6nGgBdAp5xgDvAf0A14EBohITxFJBW4D3lDV2LSo8nqUyvYophkzZtCtWzc+//xzJk2aRO3atbnhhhticqlhlZVla8V162ZJ6pNPbNv3ESMgPR2efNJaVq7iSkyE66+3+VbHHGO7LJ95pq3D+MsvQUfnwiLQRKWqv6vqz7kH1t23TVXXqmoa8FcsYf0C1AAuDTDcMpOVlcXcuXPp3LkzkUiEpk2bcswxxwDw/vvvM3r0aADWr19Pv379Aow0NjIzbT+otm1tBe6pU20X3TvusCWQ7r0XGjYMOkoXT61bw5dfwoMPWln7a6/ZBo0vv+wbNLrgW1QFqOpoVf1jvu9fUtUmqpqqqqeraoXswZ4/fz6///47H3zwAVlZWaSlpTF27FiGDh1Kt27dmJazBs0///lP/va3vwUcbclt2mTdPE2b2n5QCxfa6gUPP2zl5jfd5EsdVWaRiG0ZMnu2rXi/bh2cey5cdFE9fvwx6OhckEKVqCqr6dOnc+ihh3LddddRq1YtrrnmGh544AGOPPJI6taty7p161i5ciWLFy+md+/eQYcbtZ9/toVhmzSBkSPt+44dbQWJBQvg0ktt8VjnwD68fPyxdf3WrAlffFGNjh3t98S7AysnT1QhMGPGDIYMGcLSpUvZvHkzH330UYFCioMOOojLL7+cUaNGBRhl9BYtssm5TZvaZN2NG21i7gcf2ATQIUNsjMK5wkSsmGbhQptrpQqPPmpLY91zj68bWNnsM1GJyJfFPD6KR8AV0fTp02nbtu0eb+/WrRs1a9akY8eOcYyq5KZPhyuvrEvr1rbcUWYmnHEGfPONLXV00kleYu6K58AD4Y471jFrlpWwb95sK1y0aePjV5VJcT7PdsOKGvZGsIm7rgRmzpxJmzZt9nj79OnTufvuu+MYUfRUbUmce+6xbd+hOklJMHSoVXXtJQ87t0/t2tlajh9/DNddZ+NY554L//0v/PvftkyTq7iKk6i+VtVn93UnETk3BvFUSmvXri3y/M8//8ywYcPo168fBx98cJyjKp6sLFtv7+674YecJYVTU2Hw4I2MHr0fjRoFG5+rWE44wVrsTz9t+119952VtZ91lv0OtmgRdISuLOyz609V+xTniVT1xNKH4/KrX78+b7/9NpdddlnQoewmMxPGjrUS4kGDLEkdcADcfruVmN9002+epFyZSEiAiy+28aubb7ZCnP/9z1rtI0bA+vVBR+hizYspXFQ2bYL/+z/bqPDii61q7+CDbf7LsmXwj3/Y1uTOlbXq1W3TzAUL4IILbLmt++6zgosHH7TvXcUQVaISkf1E5GYReUNEPsp/lFWALhzWrLF5TgcfbGNOq1fbVg0vvGCfbC+/HKpVCzpKVxk1amTLL02dCr1723qBV15pSzS99ZYXXFQE0RYHvw4kAOOBrbEPx4XNkiXWgnr66byS4J49rfLq5JO9es+FR5cutnDx22/bh6kFC6zatFcvK7jo0iXoCF1JRZuojgTqqGq5bFSrKlKB31k1hh8dZ8ywCr7XXrOtxAFOO80m7HqFlQsrETj9dPsQNWYM3HorfPGFLXZ8/vlw55342Gk5FO0Y1SSgXBYaRyIRdu7cGdM38zBRVXbu3FmqTRNVbZ7TySfblu6vvGLL2gwdCmlp1o3iScqVB8nJ1v23aJGVsycmwnPPQatWVoCRkRF0hC4a0baoLgTeF5HvgDX5b1DV22IVVFlISUkhMzOT7du3Bx3KPm3bto0tW7ZE/bhIJEJKSkrUj8vOtiR0zz1W7gs23jRsGFxzjS195Fx5tP/+1nU9fLh1V//vf7b48ZNPWoXqn/5Eme4S7WIj2kR1J9AYWErBTQ1D30yJRCJULScLykUiEVJTU8v8dbZvhxdftIVi582zc3Xq2CfRyy6zr52rCFq0sH3OJk+2FtZ338Ff/gIPPGCJ7ESfXBNq0SaqwUArVf2pLIJx8bF5s22z8e9/w6pVdq5JE5uDctFFNmHXuYromGNsKa9XX7UW1uzZ0K+fdXffe6+tgOHCJ9oBjSVAuSykcDB/vn2aPPhg+3fVKvvDfO4568u/4gpPUq7iE4HBg60X4e67oUYNWyi5Y0frIvQV2sMn2kT1PPC2iAwRkePzH2URnCu9zEwrijjuOFvI89//tpn7PXrAO+/ArFlWDZWUFHSkzsVXlSpWxbpokSUoEasUPOQQ+Oc/YatPwAmNaBPVZUAD4C5gbL7jyRjH5Upp8WL7I2zc2LbTmDjRCiT+/Gf4/nv46is49VSr6nOuMjvwQHjkEesGPOUU6xr/+9/tg91LL+VNz3DBiWqMSlWblVUgrvR27LDqvcceg08+yTvfsSNccgmcdx7st19w8TkXZm3bwrvv2t/OdddZb8N558F//mM9ET16BB1h5VWc/ahuL84TicitpQ/HlcTSpba8UZMmcPbZ9odWpYrNf/rmG5u8e+mlnqScK46+fWHaNFt0uUEDW3C5Z09bfHnRoqCjq5yK0/FztYg0E5HmezuAK0sSgIi8ICI/icgmEVkgIhfnu62PiMwTkd9F5HMRCedeFwHYuRPefNOqlZo3h7vusi3eDz3U9uhZvRqeeQaOPNKXOXIuWgkJVgG7YAHccout0P7GG/b3de21vkJ7vBUnUaUCi4pxRD/T1PwTaKqqNYHTgDtE5HAROQB4A7gZqA1MAV4t4WtUGCtWwKhRtr37wIEwYYLNwj/vPPjyS5gzx+ZB7b9/0JE6V/5Vr27LMC1cCBdeaB8Q77/f5mX95z82F9GVveLsRxVR1YScf/d2lGjtbFVNU9XM3G9zjhbAmUCaqr6uqtuA0cBhIrLnrXArqKwseO89GDDAEtRtt1lpeatWtq3BqlW2innPnt56cq4sNGxoCzNPnWoVtOvX26ot7drB+PG+QntZkzCsfScij2DLM1UFpgPHYqtgJKvq8Hz3mwOMUtVxhR4/DBgG0KBBg8MnT54cp8jLxoYNG6hVqxZr1iTw2ms1ePXVGqxebXUvSUlKv35bGDJkM0ceuS20iSn3Gsozv4ZwCNs1qMJnn1Xlrrtqk56eDMARR2zl73//jY4di25ihe0aSqKsr6F58+ZTVbVrkTeqaigObPuQHsA/gCSs7P3uQveZDFy4t+dp3769lmdZWfitra8AAB/JSURBVKrPPPOTnnGGakKCqv1ZqDZvrnrPPapr1gQdYfEsWbIk6BBKza8hHMJ6Ddu3qz74oGqdOnl/p3/8o+ry5bvfN6zXEI2yvgZgiu7hfT00s2hUNUtVJwGNgOFABgXXEyTn+83xji0e1qyxSYaHHAIXXlifN9+0brxBg+Cjj6yP/IYbbM6Hcy54SUm2YeiiRbb/VXKydcG3amU7XW+ukO9UwQhNosonERujSgMOyz0pIqn5zlcI2dnw6adWUt6okU0yTE+Hhg13cOedsHy5rfZ8wgk+Mde5sKpVK29h53POsQ1G77wTWraExx+3AgxXOoG+/YnIgSIyWESqi0iCiPQDhgCfYbsItxeRQSJSBbgFmKWq84KMORbWrrUFMFu3tjkb//ufJa3TT4f334eJE1fy97/bHA7nXPnQrJktdjt5sk0LWbPGJtp36gSffFLNV7gohVIlKhGZICLHluIpFOvmWwmsB/4PuFpV31LVtcAgrKhiPdAdW729XFK1nUaHDLHW0w03WJdBo0ZW/rp8ed68KN8fx7ny6+ij4euvbY3Npk1t09Fhw+rRsSM8+6yXtJdEaVtUg4FTROR1EWkf7YNVda2q9lLVWqpaU1U7qOoT+W7/RFXbqGpVVe2tqktLGW/c/fabzbs49FDo3dt+eXfssDXF3n7buvpuucXKX51zFYMI/OEPMHeuLb9Uv/5O0tJsLlaLFvae4LsMF1+pEpWqblDVkcDVwO0i8oyINI5NaOWXqjX/zz8fDjrIZrLPm2ddef/4hyWnd9+1eVGJ0e4I5pwrN6pUsflWEyeu4OmnbT3BlSvtPaFJE3s/8G1F9q20XX+jRORN4BVsn6o04B4RGb73R1ZMGzbAgw9Chw62gOULL1gzv18/W35l2TLb/vpgXwjKuUolOdlaU3Pm2MLRRx9tk4bvvNPeDy69FJYsCTrK8Cpt19/3wMWq2lNVz1HVe1X1XOCkGMRWLqjattZ/+pO1nq680vqkDzzQdhBdtMiWORo40Pd8cq6yi0TgtNOsx+Wrr6xXZds2ePRRqxIcPBimTw86yvApbdffB6r6axE3DSvN85YHmzbZL1fnzlbh88wzttFanz7w2mu2Jt8//2kLxjrnXGE9etg49Zw5ttNBJGJVg126wIkn2tSVECwcFAplUp6uqmvK4nmDpmprfQ0bZq2nSy+FmTPhgANgxAhbafmTT2xeVHJy0NE658qDdu3sg+6SJTaelZoKH39sU1e6dbMPvllZQUcZrJglKhFpKCJfisifY/WcYbF0qW2j0b49dO0KTzwBW7ZAr162A+jKlTYvqmXLoCN1zpVXjRtbheDy5TaWXbeufTD+wx9szuWYMdZNWBnFLFGp6irgOGBWrJ4zSOvWWddejx42ke+mm+DHH6FOHbj6avt64kSbF5VS0g1OnHOukNq1rRpw2TJ45BEbPli8GIYPt8KLu+6qgPth7aPJWNqqv0dEJP9zpKjqD6V5ziD9/rvNcxowAOrXt669yZNt07TBg+Gdd2xDwvvvtzJT55wrK1WrWnKaP9/elzp3tlL23N28R4ywLX7KtbQ0GDnSLmgvStuimgC8LiINROR64NNSPl/c7dwJH34IF1wA9epZC+ndd21Jo3794LnnbCmUl1+GU0/1sSfnXHwlJlr339SptkB1nz42Wfi++6y356KLbGJxubF2LTzwgI2jtG9vCyWuXr3Xh5Q2UX0I/AosBwTbpiP0VOH77+Gqq2wJo5NOgueftx/+EUfkbeU+YYJN2q1RI+iInXOVnYgtUP3JJzBlihVtZWXZho6HHmprhX79ddBR7kFmJowbZ0EedJC9+U6daiv6XnKJdV3tRWnXRfgCeBz4b87xLvBjKZ+zzCxcCC++aMeiRXnnW7a0rdzPPdcLIpxz4Xf44VYNuGiRtayeftpK3d9+28bVR46E/v0D3nUht0Xw7LPWd5k7sJaQYN1TF1xg4yxVquzzqUqbqHqq6g4AERkMPAucWsrnjKmff7a5CS++CD/kGz2rV8/Gnc47z1qgYd0p1znn9uSQQ6zoa/Ro60175BGYNMmOdu1s8eshQ+K82MDy5bYsz3PP2QBbrk6dbMLYkCH2BhyFYiUqERkK3Az8AjyCbcHxr5zbnlHVH1R1nYicGdWrl5HNm2H8ePu/+vRTdi2vX706nHmmJafjj/d19pxzFUO9erYc04032h5Y999vdQpDh1oF4bXXwsUX23tgmcjIsK69Z5+1cujcmcr169sb7gUXQMeOJX764r5V34GtNiHAfdgitOuxreHHicgVOVtzBL6A/YbFm2l54EbWbNsPsE8Sp55q3XoDBkC1agEH6JxzZaRGDbjuOrjiCpvj+a9/WaHFNdfAbbfBZZfZbTHZKTwrCz7/3FpO48ZZ2TRYV94ZZ1iW7Ns3Ji2C4j5DKjBBVVVE1gA/AC1UNT1nUdqngLdKHU0M1Nu6jK+py7T9+7Lt1EF0/Mfp1G51QNBhOedc3OQugnvBBVbFfM89Vmhxxx3wf/9nlYLXXVfCJd7mzrXk9MILttpBrp497QXPPhv22y9WlwIUv+rvW+DKnK+nAV+qanrO97OwLeJDITOpOkmRLI5c/wG9n7+Y2m3rWT/fww/vswTSOecqksKL4J56qq1u8cgjVjg2ZEgxF8H99VdqPPeclUUfeijcfbclqebNbYBs8WL48kvrX4xxkoLiJ6pLgfNFZAlWMPGGiByVs0X86cC6mEdWUq2bIj/9ZB21/frZT+rzz+Hyy60W/ZhjbJ2SpUuDjtQ55+KmRw9btGD27LxFcF95xRbB7dcPPvus0CK4q1bZB/y+faF+fQ4YPdoq0mrWhL/8xTLfokUwalSZr74tGsXyvCLSATgG6JRztAWqYftQvQzMBeap6oLYh1o8HTp00NmzZ+edWL/e2r7jxtnM3vyLZXXpAoMG2dG6dfyD3YP09HSaNWsWdBil4tcQDn4N4RDGa1ixwoouHn/c1i4FGNR+Prd0HE+HheORH77Pu3NiIr8fcwzVhg+3JlrVqjGPR0SmqmrXom6LapRLVWcDu7JAzvJJrYHOWOK6AugIRFd7WJb2399m7Z5/vlWmvP++Ja333oNp0+y46SZrzuYmrY4dvV7dOVehNW4M/75PGXXKVGbfNp66k8fTes5cmGO370iqSuTkk0g4ayCceiprNmwILNmWqhxDVbOxVtRc4KVoHy8iKVi5e1+gNrAI+LuqfpBzex/gYaAJ8B1woaouK3HA1avDOefYsXWrraU/bpzNkvvxRztuvx1atLA69kGDrE/Wk5ZzrqLYudO67caPhzffZL8VK3YtKbStai3eTxjAcxln8tGOE6n5XTWuOhKGC8CGwEIOct4yWKJcAfQC9sPmar0mIk1F5ADgjZxztYEpwKsxe+WqVa0J++yztpjfhx/aRlMHHmgDg/feazsiNmliy318+aVvCuOcK5+2bbMBqosusrlNxx8PDz5o/X+5m+t9/DFVNv7CaeufY8grZ9CmczXWrIG//91aX7feWpv8oypxpaqhOrAqwkHYvK2v851PBbYCbfb2+Pbt22up7NypOnGi6pVXqjZqpGrji3YceKDqsGGqb72lumlT6V5nL5YsWVJmzx0vfg3h4NcQDoFcw4YNqi++qHrWWaqpqQXfy1q1Uh05UvXbb1Wzsop8eHa26kcfqfbpU/Ch3burPvmk6ubNsQ0XmKJ7eF+PqpiirIlIPWAZNt41HEhW1eH5bp8DjFLVcYUeNwxLbDRo0ODwyftY4LDYsrNJmTWLahMmkDphAknLl++6SRMT2dalC1t79mRrz55sb98+ZgtrbdiwgVq1asXkuYLi1xAOfg3hEK9rSFi7lmoff0y1jz6i6jffIDt27Lots317tvTrx+8nnsiOQw6Jakjjxx+TefbZZD74oA4ZGfY+l5qazYABGfzhD5vp2HF7qUdImjdvvsdiisBbULkHkAR8AjyW8/1Y4O5C95mMjVOVXYtqT7KzVWfMUB09WvWoo1QjkYIfM+rUUR08WPWpp1RXrizVS/knyHDwawgHv4Z9WLRI9d57VY8+WlUk7z0pElHt1Uv1P/9RXbq01C+zZMkS3bJF9ZlnVHv0KPj217Gj6gMPqP72W8mfn720qEKx2l1O9eDzwHbg8pzTGUDNQnetCWyOY2h5ROCww+wYNQo2bLCFBD/6yMa3li2zSQmvvGL3b9fOJieceCIce2yZlHM65yohVZg504ohxo+nwMBRSortBTJwoK0ZV7duTF+6WjWbgzV0qC1QMXasDfPPmgVXXmmL4J51ls37PfbY2NWhBZ6oRESw1lM9oL/mrMaOzc0amu9+qdgKGGlxD7IotWrllbOr2h4iH35oievzz21FyLQ0m1yckmI/tdzE1b69VxI654ovKwu++SYvOaWn591Wsyaccoolp5NOitsGem3b2nJMd95phdNPPGGF1C+8YEfLlpawhg6NerH03QSeqIBHsYnDfVV1a77z44F7RWQQ8B5wCzBLVecFEOPeiUCrVnZccYVtEvbNN3mJa9o0+wl+/LHdv0EDS1j9+tms7xh/6nHOVQCZmbZcxPjx8NZbtg99rnr1bBPCgQPhuOPsw3BAUlJseb+zz7b8+dRTdixcaPti3XSThXrxxdbYS0gowYvsqU8wHgdwMKDANqyrL/c4L+f2vsA8rNpvItB0X89ZZmNUpbFmjVXfXHCBav36BTt3RVQPP1z1b3+zasPMTO+TDwm/hnCoVNewaZPqq6/aeHeNGgXfK5o1U73uOtVJk6w6Oc6i+Tns2KH6zjuqp52mmpCQdwlNmtgw//Lluz+G8lL1Fwu7LaEUNqrWp5w7tvXVV/bJKVf16mzp3p3UM86wFleU1TlhEcYlY6Ll1xAOFf4a1q61vrPx422f+fzvBx07Wqtp4MDAV8wp6c9h9Wp45hl48sm8HksR66X8y19sodykpBguoeRiQMR+4Tp2hBEjbA+XL7/MS1w//kjqp59aoQZA06Z5Y1t9+pTJysTOuThbtixvvGnSpLzdXUVs4ezc5FTGi73Gw0EH2aThG2+04fsnnrDL/uADO+rVsy1J9sYTVdCqVbOPFiedZN+vXMnaF1+k7vTpNqa1dCk89pgdCQnQvXte4urWrYQdvs65uFK14qrc5DRtWt5tSUn29zxwoK2WU79+cHGWoUjEPmv36QO//grPP29Ja+5c2y9rbzxRhU2jRmSccw51R460Sp9p0/KKMr75xnY/+/prK5Hff3/7qecmriZNgo7eOZdr40ZrLX3+OY3GjSu4tVBqKvTvb8mpf/9K11NywAG26/DVV9vb2hNPWPfgnniiCrOEBGs1desG//gHbNpkbefcxLV4Mfzvf3YAtGmTV03Yq5f9MTjn4mP9ehtz/uILO6ZP39WllwRQp461mAYOtGpfn1uJCBx9tB2eqCqKmjWtzvP00+37xYvzxrY++wzmzbPjgQdsL+oePfISV8eOMVviyTkHrFtniWniREtMM2cW3HkwMdEWtu7Vi586dKDB2WfbORc1/18rz1q0gOHD7dixA779Ni9xTZliyeuzz2wUs149m8Rw4on2bwXtB3euzKxda4VPuYmpcHVxcrKNIffqZcdRR+3q1diWnu5JqhT8f66iSEqCnj3tuP12+7T3ySd5iWvVqrwp42BJ7ogj7OjeHTp18q4I5/Jbs8YSUm5i+vHHgrenpFiLqXdvS0xHHul/Q2XEE1VFVacO/OEPdqhaaU3u2NYXX1i34eLF8PLLdv/EROsezE1eRxxhY15eVegqi9Wr88aXJk6E+fML3l61qrWSchPTEUdAlSpBRFrpeKKqDETg0EPtuOYa6yZMS4Pvv8870tKswnDaNBgzxh5XvTp07Wotrtzk1bBhuZyA7NxuVqwomJgWLSp4e7VqNqcpNzF162bdey7uPFFVRklJ1tXXqZPtagyQkQFTpxZMXsuX2x/wxIl5j23QoGCrq1u3Slda68qppUsLJqb8C7uCfTDr0cOSUu/ecPjh9rfiAueJypnq1fMGgXP9/DP88IMlre++s69/+skWyHzrrbz7tWlTMHl17Bj/+J3LT9USUe740hdf2GoQ+dWsaWO6uYmpc2cveAgp/6m4Patf3/a0GTDAvs/Otu6R/K2u6dPzyuKfe87ul5xMg7Zt7U0gt1jjkEO8PN6VHVX73cyfmFauLHifWrVsu53cD2SdOvkYbDnhicoVXySSt53JH/9o5zIzbde0/Mlr3jyqzJxp80py1apl3YT5W15eIu9KStWKHfInpp9+KnifOnUKJqYOHTwxlVOeqFzppKTkrZ5x2WV2buNGfnrnHRqsWGFdht99Z92I+ffkAmjcOK/FdcQRNiZQvXow1+HCTdXKw3PHl7780srH86tbNy8p9eplu2x7K75C8ETlYm+//dh2zDGQuyWAqs3jyt/q+uEHq7pasQLGjbP7RSJWmZi/1dW+vQ9oV0Zr11pLfdYsDvzwQyv0+fXXgvepVy+vIq9XL9ty1itSKyRPVK7siUCjRnaceaady8qyca38yWvWLJgzx46nnrL7Va0KXboUTF7NmvkbUkWxbZu1lGbPtp9/7r/5Wku7Vqw86KCCialVK/89qCQ8UblgJCRY10y7dvCnP9m5rVthxoy8KsPvv7dJyZMn25GrTh3ramzbNm/MrFUreyPzrp5wys62qrv8yWj2bFiwIG8vpvyqV7cxpY4dWdu0KXXPOstWU/HEVCl5onLhkTvz/6ij8s6tW5dXIp+bwH79FSZMsCO/atWsujB/8mrVClq2tOTmb3LxsX69JaH8CWn2bJurV1gkYtMbOnbclZjo0AEOPnjXh46M9HTqlvMdfl3peKJy4VanTsGNJVXtk/nUqfZpPPdYuLDAuMZu9t+/YOLK/7UXcJTM9u1WeVe4265wWXiu+vULJqMOHaxV7OvjuX0INFGJyOXAhUAH4GVVvTDfbX2Ah4EmwHfAhaq6rIincZWJCDRtakdh69dbwspNXPkT2fr1eRWIhR10UMHklXt4C8zkFsMU7rabN8+W4yqsalXr0i3cSqpbN/6xuwoh6BbVauAOoB+w62OViBwAvAFcDLwD3A68ChwZQIyuvNh//7yCi/xUrTy+cPJauNAmia5enbcgaT5NIxFLiEW1xBo3rphzcjZvtmKWwq2kDRt2v6+IjRsVTkgtWlTM/xsXmEATlaq+ASAiXYFG+W46E0hT1ddzbh8N/CoibVR1XtwDdeWbiK1R2KCBTQDNLyvL1jTMn7xyv166FJYssaPweFhKio2HFdUSO/DA8LfGdu60JF04IRVe/y5X7dq7J6R27bzb1MVF0C2qPWkH7FrWQFW3iMjinPO7JSoRGQYMA2jQoAHpe/pjKyc2bNjg1xBvuUkmn42//MIBmzaRlJ6+60hcutT+/eUXW3E+LW23p8quXp0dTZuyo1kzO3K+3tmsGdk1a8brigD7OSz7/nuS580jef78XUfSwoVEMjN3u78mJ7O9RQu2t2nDjtat2d66NdvbtCGrqOS7dq0dcbiGcvW7VAS/htIJa6KqDhT+C9gI1Cjqzqr6OPA4QIcOHbRZOa8QSk9Px68heOlAo+7di75x8+Y9jodFNmwgZc4cUubM2f1xBx6Y1wpr2RKaNLFuxEaNbAuVlJSSBbtpU94eY4sW7fo3a/ZsEtatK/oxTZrs1kqSVq1ISUqihFGUiQrxu+TXUCphTVQZQOGPnjWBzQHE4tzuatSwichduhQ8r2ol9fnHwnKT2cKF8MsvduSfF5ZfvXp588GysqyLLiur4NeFz+3caYmzCAm5sRbutmvf3tZfdK4cCGuiSgOG5n4jIqlAi5zzzoWXCBxwgB1HH13wtuxsq57LX8ixYoWVc69YYQUda9bsvoZdcaSkWBFDixY2dpbz74pq1Wjco0f4x8yc24ugy9MTc2JIABJEpAqwExgP3Csig4D3gFuAWV5I4cq1SMS6+Ro3hj59dr89K8uqE3/6yVpmiYlWPZeQsO+va9YsclWOnenpnqRcuRd0i+ofwKh83/8RuFVVR+ckqYeAF7B5VIMDiM+5+ElIsHGqhg2DjsS5UAm6PH00MHoPt30CtIlnPM4558LHV/B0zjkXap6onHPOhVrQY1Qxt2rVKrp27Rp0GKWyY8cOksr5ZoF+DeHg1xAOfg3F0mVPN1S4RNWwYUOmTJkSdBil4pMDw8GvIRz8GsKhrK9BRKbt6Tbv+nPOORdqnqicc86Fmicq55xzoeaJyrkwql/fVpQo7lG/ftARO1dmPFE5F0bRrvdXkvUBnSsnPFE555wLNU9UzjnnQs0TlXPOuVDzROWccy7UPFE555wLNU9UzjnnQs0TlXPOuVDzROWccy7UPFE555wLNU9UzjnnQs0TlXPOuVDzROWccy7UPFE555wLNU9Uzjnnwk1VK9TRtGlTBcr06NWrV5k+/9ChQ/0aAo4/6GvYnJqqCsU+RqWmFvk8o0aNKvP/p7I+/BrCccThGqbs6X1dVJWKpEOHDjp79uygwyiV9PR0mjVrFnQYpeLXEA5+DeHg17BvIjJVVbsWdZt3/TnnnAs1T1TOOedCzROVc865UPNE5ZxzLtQ8UTnnnAs1T1TOOedCzROVc865UPNE5ZxzLtQ8UTnnnAs1T1TOOedCzROVc865UPNE5ZxzLtQq3KK0IrIZmB90HKV0APBr0EGUkl9DOPg1hINfw74drKp1i7ohsQxfNCjz97QCb3khIlP8GoLn1xAOfg3hEOQ1eNefc865UPNE5ZxzLtQqYqJ6POgAYsCvIRz8GsLBryEcAruGCldM4ZxzrmKpiC0q55xzFYgnKuecc6Hmico551yoVZhEJSK1RWS8iGwRkWUicm7QMUVDRFJEZGxO7JtFZLqInBx0XCUlIi1FZJuIvBB0LCUhIoNFZG7O79NiEekZdEzREJGmIvK+iKwXkZ9F5CERCfW8SRG5XESmiEimiDxT6LY+IjJPRH4Xkc9F5OCAwtyrPV2DiBwpIh+LyG8islZEXheRBgGGukd7+znku88oEVER6RuPmCpMogIeBrYD9YDzgEdFpF2wIUUlEVgB9AL2A24GXhORpgHGVBoPAz8EHURJiMgJwD3An4AawLHAkkCDit4jwC9AA6AT9nt1aaAR7dtq4A7gqfwnReQA4A3sb6I2MAV4Ne7RFU+R1wDsj1XNNQUOBjYDT8c1suLb0zUAICItgLOAn+IVUKg/YRWXiKQCg4D2qpoBTBKRt4HzgRsDDa6YVHULMDrfqXdFJB04HFgaREwlJSKDgQ3A18AhAYdTErcCt6nqtznfrwoymBJqBjykqtuAn0VkAhDqD26q+gaAiHQFGuW76UwgTVVfz7l9NPCriLRR1XlxD3Qv9nQNqvpB/vuJyEPAF/GNrnj28nPI9RAwEvswFBcVpUXVCshS1QX5zs0k5H+YeyMi9bDrSgs6lmiISE3gNuC6oGMpCRFJALoCdUVkkYiszOk2qxp0bFH6LzBYRKqJSEPgZGBCwDGVVDvs7xnY9aFuMeX47xtrpZerv20AETkb2K6q78fzdStKoqoObCx0biPWbVPuiEgS8CLwbNg+MRbD7cBYVV0RdCAlVA9Iwro2emLdZp2BfwQZVAl8gb2RbwJWYt1lbwYaUclVtL/vjsAtwPVBxxINEakO3AVcHe/XriiJKgOoWehcTawfuFwRkQjwPDbednnA4URFRDoBfYH7g46lFLbm/Pugqv6kqr8C/wb6BxhTVHJ+hz7ExnVSsVWv98fG3cqjivT3fQjwAXCVqn4VdDxRuhV4XlXT4/3CFSVRLQASRaRlvnOHUc6a1iIiwFjsU/0gVd0RcEjR6o0NFi8XkZ+BEcAgEZkWZFDRUNX1WAukPC/ZUhtojI1RZarqOmzgvtwk20LSsL9nYNeYdAvK39/3wcAnwO2q+nzQ8ZRAH+DKnCrSn7HfsddEZGRZv3CFSFQ5fdZvALeJSKqIHAOcjrVMypNHgbbAAFXduq87h9Dj2BtIp5xjDPAe0C/IoErgaeAKETlQRPbHujreDTimYstpBaYDw0UkUURqAUPJN84TRjmxVgESgAQRqZJTUj8eaC8ig3JuvwWYFcZu8T1dQ8444WfAw6o6Jtgo924vP4c+QHvy/r5XA5dgFb5lS1UrxIF9inwT2AIsB84NOqYo4z8Y+xS/DevqyD3OCzq2UlzTaOCFoOMoQdxJWEXTBuBn4AGgStBxRXkNnYCJwHpss7vXgQODjqsYvy9a6Bidc1tfYB7WNTsRaBp0vNFcAzAq5+v8f9sZQccb7c+h0P2WAn3jEZMvSuuccy7UKkTXn3POuYrLE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlQ80TlnHMu1DxRORdSIjIxZ/PJL0v4+BQRyRCRHSJyR6zjcy5ePFE5F26Xq+qxJXmg2jp/1bGV+J0rtzxROeecCzVPVM7FmYiMFJFVIrJZROaLSJ8oHrtURK4XkVkiskVExopIPRH5IOf5PslZSNe5CsMTlXNxJCKtsX3GuqlqDWxl+aVRPs0g4ARsB+gB2P5Gf8f2nYoAV8YqXufCIDHoAJyrZLKAFOBQEVmrqktL8BwPquoaABH5CvhFVafnfD8e247BuQrDW1TOxZGqLsL2txoN/CIir4jIQVE+zZp8X28t4vvqpQrSuZDxROVcnKnqS6rag7w9yMrrFvHOxYUnKufiSERai8jxIpKCbZK5FesOdM7tgScq5+IrBbgb23X3Z+BArBDCObcHvsOvcyElIh8BRwFTVPW4Ejw+BRu/SgL+paq3xjhE5+LCE5VzzrlQ864/55xzoeaJyjnnXKh5onLOORdqnqicc86Fmicq55xzoeaJyjnnXKj9P0+7sOf1BKdiAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "D00m25 = Drift(l = 0.25)\n", "D01m = Drift(l = 1)\n", "D02m = Drift(l = 2)\n", "\n", "# Create markers for defining places of the wakes applying \n", "w1_start = Marker()\n", "w1_stop = Marker()\n", "\n", "w2_start = Marker()\n", "w2_stop = Marker()\n", "\n", "w3_start = Marker()\n", "w3_stop = Marker()\n", "\n", "w4_start = Marker()\n", "w4_stop = Marker()\n", "\n", "w5_start = Marker()\n", "w5_stop = Marker()\n", "\n", "w6_start = Marker()\n", "w6_stop = Marker()\n", "# quadrupoles\n", "Q1 = Quadrupole(l = 0.5, k1 = 0.215)\n", "\n", "# lattice\n", "lattice = (D01m, w1_start, D02m, w1_stop, w2_start, D02m, w2_stop, \n", " w3_start, D02m, w3_stop, D00m25, Q1, D00m25, \n", " w4_start, D02m, w4_stop, w5_start, D02m, w5_stop, \n", " w6_start, D02m, w6_stop, D01m)\n", "\n", "# creation MagneticLattice\n", "method = MethodTM()\n", "method.global_method = SecondTM\n", "lat = MagneticLattice(lattice, method=method)\n", "\n", "# calculate twiss functions with initial twiss parameters\n", "tws0 = Twiss()\n", "tws0.E = 14 # in GeV\n", "tws0.beta_x = 22.5995\n", "tws0.beta_y = 22.5995\n", "tws0.alpha_x = -1.4285\n", "tws0.alpha_y = 1.4285\n", "tws = twiss(lat, tws0, nPoints=None)\n", "# ploting twiss paramentrs.\n", "plot_opt_func(lat, tws, top_plot=[\"Dx\"], fig_name=\"i1\", legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load beam file" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# load and convert ASTRA file to OCELOT beam distribution\n", "# p_array_init = astraBeam2particleArray(filename='beam_chirper.ast')\n", "\n", "# save ParticleArray to compresssed numpy array \n", "# save_particle_array(\"chirper_beam.npz\", p_array_init)\n", "p_array_init = load_particle_array(\"chirper_beam.npz\")\n", "\n", "plt.plot(-p_array_init.tau()*1000, p_array_init.p(), \"r.\")\n", "plt.grid(True)\n", "plt.xlabel(r\"$\\tau$, mm\")\n", "plt.ylabel(r\"$\\frac{\\Delta E}{E}$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization of the wakes and the places of their applying " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from ocelot.cpbd.wake3D import *\n", "\n", "# load wake tables of corrugated structures\n", "wk_vert = WakeTable('wake_vert_1m.txt')\n", "wk_hor = WakeTable('wake_hor_1m.txt')\n", "\n", "# creation of wake object with parameters \n", "wake_v1 = Wake()\n", "# w_sampling - defines the number of the equidistant sampling points for the one-dimensional\n", "# wake coefficients in the Taylor expansion of the 3D wake function.\n", "wake_v1.w_sampling = 500\n", "wake_v1.wake_table = wk_vert\n", "wake_v1.step = 1 # step in Navigator.unit_step, dz = Navigator.unit_step * wake.step [m]\n", "\n", "wake_h1 = Wake()\n", "wake_h1.w_sampling = 500\n", "wake_h1.wake_table = wk_hor\n", "wake_h1.step = 1\n", "\n", "wake_v2 = deepcopy(wake_v1) \n", "\n", "wake_h2 = deepcopy(wake_h1)\n", "\n", "wake_v3 = deepcopy(wake_v1) \n", "\n", "wake_h3 = deepcopy(wake_h1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Add the wakes in the lattice\n", "Navigator defines step (dz) of tracking and which, if it exists, physical process will be applied on each step.\n", "In order to add collective effects (Space charge, CSR or wake) method add_physics_proc() must be run.\n", "\n", "**Method:**\n", "* Navigator.add_physics_proc(physics_proc, elem1, elem2)\n", " - physics_proc - physics process, can be CSR, SpaceCharge or Wake,\n", " - elem1 and elem2 - first and last elements between which the physics process will be applied.\n", "\n", "Also must be define unit_step in [m] (by default 1 m). unit_step is minimal step of tracking for any collective effect. \n", "For each collective effect must be define number of unit_steps so step of applying physics process will be \n", "\n", "dz = unit_step*step [m]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tracking with Wakes .... \n", "z = 15.0 / 15.0 : applied: .0 : applied: Wake\n", " time exec: 1.3371977806091309 sec\n" ] } ], "source": [ "navi = Navigator(lat)\n", "\n", "# add physics proccesses\n", "navi.add_physics_proc(wake_v1, w1_start, w1_stop)\n", "navi.add_physics_proc(wake_h1, w2_start, w2_stop)\n", "navi.add_physics_proc(wake_v2, w3_start, w3_stop)\n", "navi.add_physics_proc(wake_h2, w4_start, w4_stop)\n", "navi.add_physics_proc(wake_v3, w5_start, w5_stop)\n", "navi.add_physics_proc(wake_h3, w6_start, w6_stop)\n", "\n", "# definiing unit step in [m]\n", "navi.unit_step = 0.2 \n", "\n", "# deep copy of the initial beam distribution \n", "p_array = deepcopy(p_array_init)\n", "print(\"tracking with Wakes .... \")\n", "start = time.time()\n", "tws_track, p_array = track(lat, p_array, navi)\n", "print(\"\\n time exec:\", time.time() - start, \"sec\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Longitudinal beam distribution" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100000\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "tau0 = p_array_init.tau()\n", "p0 = p_array_init.p()\n", "\n", "tau1 = p_array.tau()\n", "p1 = p_array.p()\n", "print(len(p1))\n", "plt.figure(1)\n", "plt.plot(-tau0*1000, p0, \"r.\", -tau1*1000, p1, \"b.\")\n", "plt.legend([\"before\", \"after\"], loc=4)\n", "plt.grid(True)\n", "plt.xlabel(r\"$\\tau$, mm\")\n", "plt.ylabel(r\"$\\frac{\\Delta E}{E}$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Beam distribution" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# by default the beam head on the left side\n", "show_e_beam(p_array, figsize=(8,6))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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KPPpo+PFH/5hq7PwvIETOOOMMjj32WPLy8nj66ae58847gw4p9D74AA4/HE49FaZMgW3b7MP1rrsgNxfWrIFFi2D2bGsLmToVZs2yktcnn8Cjj8IFF0DLlvbB+NvfWqeAP/0Jli9PCfryAjNzpv0cv/nGSjoffQT77Zec995nH/u97rOP/a5+9as9mTIlOe/twskTVUjk5eWxZs0ahg8fTkqKfUBmZ2cHHFV4zZkDJ58MP/uZfYi2bQsPPgg//GB3/n/6E/TtW/2UPU2aWAnrssvg//4Pli2Dp56y16xaBffcA0OG7MWoUY2vYf/dd63k+cMPNovEe+/ZmKhk6tTJSlYHHgjffZfGccfZDcWaNcmNw4VDo01UIsnZamr69OkcccQRlJaWkpeXx/Dhwxk2bFjifgD1VF4enHWWVdW9/ro1to8aZXf+V1xhVX+1kZkJl1xid/DTp8MZZ0BRUYTbboOePW3WBdW4Xkoovf++tUkVFsJ559nPuPkOC+skR/v28PHHMGLEj2RkWDVtz57wz382jt+FK9doE1XY5ObmMmDAAAYPHsyJJ55Is2bNOO2004IOKzQ+/hhOOcVKPC+8YD3F/vhHa0cZOTJ+H6YiVuU1fjz861/L6dsXliyxxHXssTBvXnzeJ4ymT4cTT7SekRdeCM89B+npwcaUlgbDhq0nLw+OOspKu+ecYzcrja2k25g12kSlmpytpnJzcxk4cCBTp05l2rRptG7dmuuuuy5xP4B6Yv58a8A/9FB47TXrEn3lldbu9NBDVuWXKAcdVMRnn8Fjj0Hr1vD221YV9cgjDe+O/uOP4YQTrCT129/C3/5mHU7CYt994Z134Omn7abkxReto8UPPwQdmUuGEP0pNl4lJSXMmzePfv36EYlE6Ny5M4cffjgAW7du5eCDD2bz5s1MmDCBSy+9NOBok0PVeu71728JokULuPFGWLwYHngA9torOXGkpMCwYfDVV1bK2LLFSnInn9xwPiRnzLAekxs3wtlnw7PP2nWHTSRi8wh+9JG1YX38MRxySMMu5TrjiSoEFixYwKZNm5g8eTIlJSXMnTuXMWPGcMEFF5Cens4ll1zClVdeybPPPssjjzwSdLgJt26dfWD+/vdWDXX++Zag7r47sSWonWnTxj7Ax4+3Lu8TJ1o72RtvBBNPvHzxhY1X2rABfv1rawcKY5KqqHdv67E5YIDNL3jYYdab0zVgqtqgtj59+mhVCgoKqtwfBmPHjtWcnBzde++9NSsrS3v16qUvvfTST8/PnTtXI5GIfvfdd7s8V1iuc9GiRbV63YcfqnbubBWnWVmqzz8f58BiUN01fPut6qBB5RW8w4erbtuW5OBqaGe/h2++UW3Xzq7h1FNVt25NYmAxqO4aCgstblBNTVX9xz+SHFgMavv/ECaJvgZgplbzue4lqhDIzc3l7LPPZvHixWzcuJEpU6b81JFizZo1XHHFFdx1112MGzcu4EgT67nn4MgjrfQ0YID1wDvvvKCj2lHHjjb7xejR1qnjf//XSiWrVgUdWc0tX26dQ1autDbAf/7TOi7UJ82aWQl3+HCbi/C88+yxa3g8UYXArFmz6Nmz5w77i4qKOP/887n//vu59tpreemllygoKAggwsR78EFrAyopsaUgpk+3AZ9hlZIC119vVU577GFf+/e3gbJht3attUnl59tYsldegYyMoKOqnZQUm9B25EgoLbUegf/5T9BRuXjzRBUCX3zxBT169Nhhf0ZGBhMnTiQnJ4fU1FQ++eQTshrYLJ2qNg7qqqvs8f33Wwkl6G7RNXXEEfDZZ9YrcelSexzmma8KC+EXv7AB0z17WltbQ/iTGjkSrrvOSla//rVNbOsaDk9UIbBq1aoqE1VDV1pqXc1vu816dD3zTHnCqk/23NNKVJdeavME/u531jOw8rLsQdu2zT7EP/zQes1NmVL7AdJhI2JVsVdcYdd52mnWnd01DKFJVCLSXUS2iMjYCvvOEZElIlIoIq+KSOsgY3TxU1ICF11kC/Clp9vKsBddFHRUtZeRAY8/bl3q09NtrNVJJ1kPxjAoLbUEOnmyJacpU5LXxT9ZRGzowh/+YMMITj7ZqpBd/ReaRAU8CsyIPhCR3sCTwG+BdsAm4LFgQnPxpGqlj7//3aYumjjRJpVtCH73O7uTz862ZHDooTa9U9Cuu85mhs/MtGSVrAlmk03EBmhfcIENbTjlFBsD5+q3UKxHJSJnAeuAD4FoE/q5wGuq+n7ZMbcA80SkuapuDCZSFw833mgzHzRtauOQjjgi6Iji6/DDbYn1k0+2tqCDD7a5AgcNqv05S0th9WrrrVd5W7HCljEZOtSq9Cq77z7rcJCWZh0nBgyofRz1QSRif1+rV9tN0Akn2OBgn+O5/hINeC4YEWkBzASGABcD+6jqeSLyH+BDVb23wrEFwFGq+lmlcwwFhgK0b9++//QqyvulpaU0qcua2Um0ceNGmtdy8rotW7YQCcHcN+vWraNVq1Y77H/qqZaMHt2a1FTlySdXMnhweCdsq+4aaqqgQLjqqra8804zUlOVO+5YzW9+s/Nemz/+GOHll7P47rtUVq5M5YcfUli5MpVVq1LYtm3nsxxHIsrgwZs477yNHHnkZiIRGDs2wq237g3AAw/8wCmnFNb6eoJS299DYaFw9tntmTMng379tjBu3AqaNAnm866uf0thkOhr6Nq162eqWvVtVHUDrJK1AQ8C15d9PwoYW/b928CllY5dBgza2fnq44DfymoysLc6YbnOqgYHjhlTPkh27NgAgopRPAY4FherXnNN+XWPGKFaUrLjcSUlqk8/rdq6dfUzR7Zpo5qTo3rccaoXXaR6002qjz6q+s9/qp59tmpaWvmxXbuqXn21akpKqYLqAw/U+VICU5ffw/Llqp062c/k9NOr/tkngw/43TV2MuA30Ko/ETkAOAboV8XTBUCLSvtaAF7tVw+98ootowE2mey55wYbT7KkpFjVW48eNmfgX/4CX39d3l4EtsDjsGFWPQU22eopp1hvwujWvr2toVWds86yjgTPPANPPGGT9t5/P4Bwww3Wu7Ixat/elrM//HCrfh0xwqpBXT1TXQZLxgZcBRQCK8q2AmAz8DlwNzCuwrFdga1A852d00tU4bjOindf06erZmTYXe3IkcHFFKt430G+9ZZqq1b2czjwQNUvv1S98krVSMT2tW+v+q9/qZaW1u19iotVX3/dShCXXba2zucLWjx+D2+/bdMsgepjj8UhqBh5iWrXCGuJCngK+FeFx9cCnYFhQFvgIxE5EktctwMvq3ekqFfy8+FXv7LxRZdeagMzG6shQ2zm71/8Aj7/HHr1sv2RiI0fu+02myW+rlJSrGv8SSdBfv5aROp320g8HH20dbC48EIb49ajBwweHHRUrqYCbXVX1U2quiK6YSWqLaq6SlXnApcC44AfgObAZQGG62K0fr19KK9aZXPhPfxwbKseN0Q9elgV35FH2uNDD7WZLe6/Pz5JylXvggus6q+kxBbCXLgw6IhcTQXfPawCVR2lqudVePwPVe2kqpmq+ktV/THI+BItPz+fE044gd69e9OhQweeDfNcPLtQXAxnnglffmklhxdftAlcnQ24fecda5uaNg0OOCDoiBqPe+6xkuaPP1o74IYNQUfkaiJUiaqxO+OMMzj22GPJy8vj6aef5s477ww6pFpRhdtvb8OUKTZ25fXXoWXLoKMKl9RU6Ns3XKvoNgYpKfCPf9g8h19+aZ16SkqCjsrtiv+bhEReXh5r1qxh+PDhpJStXJddT0coPvwwjB3bgowMePVV6NIl6IicK9eiBUyYYAtgvv463HRT0BG5XWm8iUokOVsNTZ8+nSOOOILS0lLy8vIYPnw4w4YNS+APIDGmTLFlOsC6Sh92WLDxOFeVffax+SVTUuDee62U5cKr8SaqkMnNzWXAgAEMHjyYE088kWbNmv20eGJ98c038Jvf2HQ/l1++lnPOCToi56p39NE2pg/g4outU4sLp8abqKqfACC+Ww3l5uYycOBApk6dyrRp02jdujXXXXddAn8A8bVhgzVOr1sHv/wlXHVVSKYNd24nhg2zgehbttgwipUrg47IVaXxJqoQKSkpYd68efTr149IJELnzp05/PDDAZg0aRKjRo0CYO3atRx33HEBRlq10lJbBnzePOjdG55/3jsJuPpBxJZkOfxw+O47OP102Lo16KhcZf5xEgILFixg06ZNTJ48mZKSEubOncuYMWO44IILGDhwIJ9//jkA99xzDzfeeGPA0e7o1lvhtdescfo//4FazqfrXCDS0216pb32svWrLr88psoQlwSeqEJg1qxZ9OrVi2uuuYZWrVpx9dVX89BDD3HIIYeQnZ3NmjVr+O6771i4cCGD6rJWRAK8+CLcdZc1Sr/4InTrFnREzsWuXTubj7JJE3j6aZsv0YWHJ6oQyM3N5eyzz2bx4sVs3LiRKVOmbNeRYs899+Tyyy9nZMjmH8rNtSlpwCb6POaYQMNxrk4GDLBplsCWtH/33UDDcRXscq4AEXm/hufaoqo/r2M8jdKsWbO4/PLLq31+4MCBzJkzh/333z+JUe3cqlXW+Lx5syWrK64IOiLn6u7cc+0G7L77bJqlTz+Frl2DjsrVZFKbgdicezsj2LpSrha++OILevToUe3zs2bNYvTo0UmMaOe2bbPpkZYsgYMOgscf9zn8XMMxerTNWjFpkvVk/fBDn4cxaDVJVB+q6nO7OkhEfNRMLa1atarK/StWrGDo0KEcd9xx7L333kmOqnrDh1u1yB57lNfrO9dQRKdZOvRQmDvXerS+8ortd8HYZaJS1SE1OZFX+8XfHnvswYQJE4IOYzvPPGPdedPT4eWXbVE/5xqali1tmqWDDrIerTffbBPaumB4ZwpXYx9/bAMkwar7Dj002HicS6SK0yyNHg3jxgUdUeMVU6ISkZYicouIvCwiUypuiQrQhcN338Gpp9pgyMsvh9/9LuiInEu8o4+GB8ta3y++2Ba+dMkX6wpB44EU4BVsyXjXCGzaZD38VqyAQYPgf/836IicS57LLrO2qscft+nBPv7YewImW6yJ6hCgjapuS0QwiaaqSAPunqYJGE6vWj5hZ9euVhWSlhb3t3EutERs8tpFi+C//7WFFz/6CFq1CjqyxiPWNqppQM9EBJJokUiE4uLihHyYh4GqUlxcTCTOk+zdfTf86182LdKECdCmTVxP71y9kJpqM6/06QPz59sYq2318na9foq1RHUhMElEPgG2m2dYVW+PV1CJkJGRQVFREVvrwYyTW7ZsobCwMObXRSIRMjIy4hbHq69abycR667bu3fcTu1cvdOihS20ePDB8Pbb1rHo6ad9DGEyxJqo7gI6AouBikPgal1MEZGxwBAgE1gB/FlV/1b23BDgUaAT8Alwoaouqc37RCIRmjZtWtswkyoSiZCZmRloDHl5Nn4ErFvuL34RaDjOhcLee1t39aOOgjFjoHt3uP76oKNq+GJNVGcB+6rq93GM4R7gYlUtEpEewLsiMgtYArwM/B54DbgDeAFrJ3MJtGIFnHwyFBbalDL1aFks5xJu4EAYO9aq/264wWZdP/fcoKNq2GJt0FgExLVmVlXnqmpR9GHZ1g04DZirquNVdQswCuhblsxcgmzaZNPGfPstHHKIV204V5XTTrOJmMHmupziA3QSKtZE9TwwQUTOFpGjK251CUJEHhORTcB84HtgEtAb+CJ6jKoWAgvL9rsEKC2F88+HGTOgc2dbW6qe1JY6l3RXXw3XXgvFxZa4Zs4MOqKGS2LpBSci+dU8papap5EFIpICHAoMAu4FngBWqeoNFY6ZDjytqv9X6bVDgaEA7du37z99+vS6hBK4devW0SqAvq/33rsbTz7ZiqysUl56aTndu9e+8BzUNcSTX0M4hPkaSkvh2muzefXVLNq0KeHFF5fTpUvxDseF+RpqKtHX0LVr189UdUBVz8WUqJJBRJ4AvsSq/9JU9bIKz80GRqnqS9W9PicnR2fPnp34QBMoPz+fLl26JPU9x4yB3//epouZPBmOPbZu5wviGuLNryEcwn4N27ZZm+5//wtduths63vssf0xYb+GmqDVRcoAACAASURBVEj0NYhItYlql1V/InJHDd/ktlgDq0YqlqTmAn0rnD+zwn4XR2+/DZeWLeTy+ON1T1LONSZpaTYQfsAAyM+H44+HtWuDjqphqUkb1VUi0kVEuu5sA2JeOk9E2orIWSKSJSIpInIccDbwDjZNUx8ROV1EmgC3AnmqOj/W93HVy821OfyKi62+/ZJLgo7IufonKwsmTrTu6l98Yclqw4ago2o4atI9PRP4BlsccWe21OL9FRiGtUdFsC7pV6nqfwBE5HTgEWAsNo7qrFq8h6vG4sVwwgmwcSP85jdw771BR+Rc/dW2rdVO/OxntjLwL34Bb7wBzZrV7PWrV8PChVYqy8+3/89vv4V16yzpRbdNm6wUl54OGRm2ZWZaN/lOnaBjR/vatSv062dLltR3NVmPKmFLgajqKuConTz/FuDd0RNg9Wo47jgbMzV4MDz3HMR59iXnGp2OHcuT1Qcf2CS2r72243FLl9r8mZ9/DrNm2dfly2v+PsXFsLnStODzq6lr2m8/G/s1YAAcdhj071///tdjHfDrAqIKJSX2Bxr9mpJid1VpabGNdSostLu9r76C/fe31UvjOPOSc41a167lyeqtt2xg8NVXpzF1Krz3nm1LqphfJyvLqg67dLHhIdGvrVvb9E3RrVkz+/8vKirfNmywpXiWLrVS2NKlMG+eVUMuWGDb2LH2Pm3b2sS6v/iFtUc3b57Mn07teKIKyNq1VsxfutRKNRW35cvbs3WrVclt2GBfdzVFYbQqICvL/phbtiz/uvvu9sfZti1kZ9sf7Cef2HQwkyc3jKoB58Jkv/0sSQ0aZG1XEyfutd3zrVrZ6sH9+tl24IHQrVvNSzrp6TtWKebk7Hjc1q0we7aNjZwxw2L69lt49lnb0tIsWV10kfVcDOsNqyeqBCopgW++sT+U2bPtDmfRIktQ69bt7JVNqtybkmJbaqp9LSmxP8TiYusiu22blZZWrqzy5dtp3drqz30peecSIycH3nzTqthLSkoYNCiFo46yeQJzcux/ONHS062qr39/69mramtrvf66bR99BJMm2damjc3vedFF0Lfvrs+dTJ6o4qSkxBLRJ5/Y9tln8OWXsKWaLiaZmVZFsPfe0L69jbuIblu3fs9++7WnRQsrljdvDk2aVF+9p2pJqqgICgpg/Xoria1fb9vq1fDDD7atWmWx3ngj9PDWP+cS6sADrZZk8eJv6dYt+HFUIrZUSZ8+Nk/hqlXwz3/aOMq8PFvN+MEHbYb4ESNswdRkJNRd8URVS0VFttLnu+/C++9bsXrjxh2P69TJ7p5ycmyZjG7dbMvOrj7x5OdvIZZxdSJ255SebkmtfftaXZJzLgFSUsLbeSE7G664Av74R+vU8cwzMG6c3WyfcQbss48NWzn//GDjrFOiEpE3gLtV9f04xRNqCxbA+PHwzjtWZK5cWurUye5EDj7Y6p9zcnwVUOdc+IlY6e/AA+HPf7b2q7/+1ZouLr0Ubr0VLrqoJSNHBjP/Z11LVGcBN4rIH4HbVHVOHGIKlZUrbYXbsWN3nHQyJ8caSwcNgkMP9ZKMc67+a9YM/ud/4A9/gJdessT1+edw772tGTsWRo2yGeNTk1gfV6e3UtV1wPUi0gF4RETWA7eo6tK4RBeQwkJb3XbsWGsMLSmx/S1awOmnw4knWoNodnawcTrnXKKkptpEAGeeacuYXHNNEXPnZnDJJVbauusum9UmGcsA1bXqbyTQD2iDLc8xF7hXRD5Q1cfjEF/SFBdb182xYy1JRVeCT0219ZnOO8/GHfiyF865xkTEei7us89yZszows032+Di00+3Zo7Ro61WKZHqWnj7FHhUVVdX3Cki/wFCn6hUrXfe2LHW8+WHH8qfO+wwS06//rWNQ3LOucYsEoGzzrK1t55+Gm6/3TpdDB5scxuOHp24bu116ouiqpMrJ6kyQ+ty3kRbtAjuvBN69rSpRR580JLUvvvCHXfYOKfp02HYME9SzjlXUXq6tWEtXGjJqnlzG5PZr5/d3OdXt2phHSSk06Sq1mDIaXKtWWNLWBx+uHUPv+UW68XXti1ceaV1L58/H26+2cY3Oeecq15Wln2OLlwIV11ls1yMG2ezclxxxfY1VHUVt0QlIh1E5H0RuThe56yrzZutO/kvf2k98i67zBY1a9YMzj3Xpg9atgweeMAmbExGo6BzzjUk2dlw//124//b31p7/8MPW4HgttuqHl8aq7glKlVdBgwG8uJ1ztp65x24+GKb5eHMM2HCBOu5d/zx1h61cqV9Pf745HaxdM65hqpzZ/j7322Nu5NOsllyRo2yhPXww7uer3Rn6pSoROQxEal4jgxVnVGXc9ZV4dzvuW/IJMY+U8SGDVZSeuABKzlNnmwlqaysICN0zrmGa//9bR7B99+38aWrVllVYI8eVjVYWhr7OetaonoDGC8i7UVkBPB2Hc9XZ611DZM4ifUZbVl38m+ZcfN/uHLoZvbYI+jInHOu8TjySOuU9uqr0KuXdbI47zyb/WLyZOt1XVN1TVT/BVYD32IrAB9Rx/PV2ebd2qF9+9KkaAMtXxtrsypmZ1u/yvHjywdIOeecSygR6yOQl2fzCO61l62RdeKJ1q39k09qdp66Jqr3sCXi+wLHAvvV8Xx1FumQjeTm2qqA99xjdX+FhfDCC9ZglZ1tI9X+8Q+bYtw551xCpaTY8iFffQV/+QvstpstIHnIIfZxXN3qxFF1TVRHquozqvolNu/fn+t4vvjp3t3msZ8xw8qcf/2rVZhu3gwvv2yNVdnZtlrYc8/ZSobOOecSpmlTm4190SJbaqhpU/s47t1756+rUaISkQtE5BsR+VBEzhORTBF5FHhARAYCqOoa4LS6XkhCdO4Mw4db3/SlS+Ghh2yd6G3brNXvwgttQNXxx8Pf/matf8455xKiVSu4+26bnX3o0F0PDappiepO4I9lX2/Cqvz2BVYBL4nILwFUNaYOiCKSISJjRGSJiGwUkVkickKF54eIyHwR2SQiU0Vk71jOX6W99rLFV957D5Yvt1HAQ4ZYy95//wuXXGL92ocMgcceg++/r/NbOuec29Gee8KTT9qqwztT00SVCbyhqpOA84ADgaGqOgo4BRhZyzhTgaXAUUBL4BbgRRHpLCK7Ay+X7WsNzAReqOX7VG2PPWyxlbfesmU4//Y3K1WlpNhgrP/5H+jQwUpfDz5opTHnnHPxUVAAzzzDfr87fKeH1TRRfQxcUfb958D7qhqd0SkP6FabGFW1UFVHqepiVS1V1deBfKA/Vo04V1XHq+oWYBTQV0QSs4D67rvbKOHJk21E8HPPWftVejp88IHNEdKpk7VzPf00bNqUkDCcc65BU7Xl0S+5xKYMuvhia5bZCdEadGYXkc7Av7GSzTSsdDMDmAWcAPxVVes8Q56ItAOWAAcAw4B0VR1W4fk5wEhVfanS64ZSNhFu+/bt+0+fPr2uoZSfe+NGmk2dSuYbb9D03XeJlC3rW9KyJRvPPJON551HcceOcXs/gHXr1tGqni8N7NcQDn4N4eDXAJEffyTrlVdo/uKLpH/99U/7t/Tvz8Yzz6Tt9dd/pqoDqnyxqtZ4A3KAS4EnsFLWemAbkAtcj1UD7hvLOSucOw14C3iy7PEYYHSlY6YDF+7sPH369NGEKShQff551YMPVrX7AlUR1VNOUX3rLdXS0ri8zaJFi+JyniD5NYSDX0M4NNprKC5WfeMN1TPOUE1LK//cbNtWdcQI1XnzfjoUmKnVfK7HNNOdqs4GZkcfl02ftB+2eOIBWIeL/YF2sZy37DzPA1uBy8t2FwAtKh3aAojDFIe1lJlpQ6vPOw8+/dQmsHrhBZtMcMIE6NPHpmI/91xfYdE513gtXgzPPmtbtG0/ErFJAC++2FahTUur8enquh5VqarOU9V/qOp1qnqsqsaapAQrPbUDTlfVbWVPzcUGEkePy8TawnbRPyRJDjoInn/efgm3324dM+bMsXrXjh3hT3+yCQadc64xKCqyG/ef/9zWSrr9dvt87NrVFgBcssSGA516akxJChK0HlWMHgd6Aier6uYK+18B+ojI6SLSBLgVyFPVXYxhTrJ27WxRliVLLHENGGCLX91zj43fOvdcG3TsnHMN0ezZ1tlszz1tqro337ROaOecA2+/DV9/DTfdZEODainQRFU2LuoPWLXhChEpKNvOVdVVwOnAXcBa4GBs9otwSk8vrxKcPt2ma1K1qZoOOshWbBw/3hZrcc65+mzDBnjqKfts239/G77z44+2Fv3DD9sY1XHj4OijrcqvjgJdjUlVl2CT2Vb3/FtAYrqjJ4oIHHaYbd9+C488Yr/QDz+0rVMnG3D8+9/b8GznnKsPVG2ozpgxdtMdHaLTsqWVni6+2KZGT8AKtGGo+mu4OnWCP/8ZvvvOElb37pa8RowonyGjQjdN55wLjfXr4fPPLSnddhsdjjnGJj947jlLUkcdZSslLl9us/j075+wZdJ9fdtkyMqyWS6GDbMBxfffb3W3jzwCjz5qPWGuvNKmbUrQL9o553awZYtNuLdggU1tvmCBbd98A6tXb3doOlinsQsvhN/9zm68k8QTVTJFu2eedJI1QD7wgNXjvv66bb17w5VXIkcEvqyXc64h2bQJ5s2zSfW+/NK+//JLm8a8uiV3mza1HnvdukG3bqzs2ZN2F10EqclPG56ogpKTY3W9o0fbrIyPPWZ/REOH0rFVK5uD8LLLrKu7c87VRGkpLFxoqxPOnm3bnDlWQqpqFqJIBPbZB/bbz7Z997Wv3bvb9EYVOkJsys8PJEmBJ6rgZWfDzTfDdddZXfADD5Ayc6YlsL/8BU47Da64wnoNerWgcy5q0yZLRLNmQW5ueXKqahXzlBRLQL1727rwvXpBz56WmDIykh97jDxRhUV6uo25Oucclr/8Mnv++9/w739b8ho/Hvr1g8svh7PP9lkvnGts1q+3ZPTZZ9bBYdYsWxa3qmq7Dh2sm/j++1vNTZ8+lqTqQUKqjieqsBGh6MADbX3m++6DJ56wqsFZs6z754gR9vWyy2xAsXOuYdmwwf7fZ8607bPPqu4dnJJiSahfP9uiyWn33ZMfc4J5ogqzDh3gjjtsVPeLL9pAupkzrUrwvvtsvqzLLrMpS+IwqM45l2SbN1tSmjGjPDEtWLBje1J6uiWhAw8s3/r0aTS1K56o6oMmTeD882379FPr1v7CC/Daa7Z17WqdLy66qEHeTTnXIBQXW4epGTPs//jTT62jQ0nJ9selpVnpaMAAG5s0YIC1KaWnBxN3CHiiqm8OOsgG2d13HzzzjFULLlpknTFuuQXOOAP+8Ac44gjvfOFckLZtg2nTYPJk2k+daklq8+btj4lErB1p4EBLSAMH2uN63J6UCJ6o6qu2beGGG6zN6o034PHHYdIkG5c1bpz16Bk61EphrVsHHa1zjcPKlfZ/OHGiTc66YQMATaLPd+tmyWjgQLvp7NfPlg9yO+WJqr5LSSkfRLx4MTz9tJW05s2Dq6+2ZHbGGdYB46ijvC3LuXgqLbXODhMn2jZz5vbP9+oFJ53Eip492eOUU6BNm2DirOc8UTUknTvDXXfBqFHWdvXkkzBlSnkpq1s3m/rkwgttSn7nXOzWr7f/q0mTbEq0lSvLn2vSxGYMP+kkOPHEn3rmbs7P9yRVB56oGqK0NBsofNppkJ9fvtLmwoXWg/Dmm22gX9++228dOni7lnOVqVoNRbTUNH369sv1dOpUXqsxeDA0axZcrA2UJ6qGrksXW2lz5Ei7CxwzBiZMKJ988sUXy49t3dq6wEbHY/Tta1UXjaQLrHM/KSyEd96xEtOkSbYwalRKis0iHi019e7tN3gJ5omqsUhJgRNOsK2oyCak/OIL26LTr/z4I7z7rm1RkYiVvnJyyke65+RYlYa3d7mGQtVmD5882bb33rP/k6jsbDj+eEtOP/857LZbcLE2Qp6oGqOMjPLR7FGqsGwZ5OWVJ7C8PPvnnT/ftvHjy4/PyrI7yWjiik7Vkp2d/OtxrjYKCmDqVEtMb7xh1eRRItYr78QTbevf32/MAuSJyhkRW8xxr73sHzNqyxarn8/Lsy06I/OKFfDJJ7ZVlJ0NffrQumNHOPRQS2a9e3sXeRe80lL7G/7vfy0xTZ9uY52i2rSB446zktNxx9kQEBcKnqjczjVpsmPpC2DVqu2XEZgzxwY0rloFU6fSEmxgctQee5TP3NyzZ/kMzl4Cc4n0/fc2nmnKFHjrre176EUicMghlpROOMEG3KakBBerq1agiUpELgcuBHKAf6rqhRWeGwI8CnQCPgEuVNUlVZzGBSE727rhHn10+T5VWLoUZs/mxw8+oPX331vymjfPSmArVtjKxhW1aQM9etjWs6d93W8/awMLaO0bV48VFMD771tSeustu5GqaM89y0tMxxzjJf16IuhPguXAncBxwE9dy0Rkd+Bl4PfAa8AdwAvAIQHE6GpKxLrqdurE+l69aN2li+0vLbVeUxVXFo1+v2aNVcFMn779udLSdlzQLbplZ3svK2e2brXq53fesZugjz7avut4s2Y20P3nP7etZ0//26mHAk1UqvoygIgMAPaq8NRpwFxVHV/2/ChgtYj0UNX5SQ/U1U0kYt3ku3SxXlNRqlY1M3++Ja3o1wUL4Lvv7Pt583Y8X4sWlryis0n362ff+1Q0DV9xsa3H9M471hFi2jRbQDAqEoGDD7bS0pAhcNhhPm9eAyBa1fLEyQ5C5E5gr2jVn4g8CKSr6rAKx8wBRqrqS1W8figwFKB9+/b9p1e+O69n1q1bR6tWrYIOo07qeg2yaRNp+fmkLVpk2+LFpOXnk5qfT8rGjTscr5EI27p0YWuvXmzt2ZOtvXpR1LMnpXVoA/PfQwhs28bWjz4ie+5cmnz6KU1mziRSaQXbrfvuy+ZDDmHL4Yez5eCDKW3RIqBgq1fvfw8k/hq6du36maoOqOq5oKv+qpMFrKq0bz3QvKqDVfUp4CmAnJwc7RKtcqqn8vPz8WvAOl9UpgqrV1tJa9asnzb58kvSFy4kfeFCmz4qql278pk3ooOYe/SwqsVkXEPA6s01bNsG33xTXi08d659XbDAqvcq6t7dqvOGDIHBg0lv1450sA48IVVvfg87EeQ1hDVRFQCVb4taADveSrvGRcTaqLKzbXaAqC1brOdhdABzdBDzypXW42vKlPJj09KsraLiGLCcHOua7+0XibVxoyWfaDVvdPvmm+3blirY2rUr6cccA4MGWYLyeSobnbAmqrnABdEHIpIJdCvb79yOmjSx7sUDKtQclJbajPLRwcvRgcyLFpWPC6uoRQsrxfXpA71706R1azvvHnt4AotFcbH93L/6qnyLJqfly6t+jYi1YfbsWT6MoXdv6NGDZatX1/vSiKuboLunp5bFkAKkiEgToBh4BfiLiJwOTARuBfK8I4WLSSRiqx937Qqnnlq+v6DAqpaiA5jz8qw0tmaN9Rr76CMA2kePb9WqfNxXtAt9z57Ww7GxjrvZutWS0aJF8PXXViKKbvn52w+krSgjw3pu7rdf+c+xZ097XN1krqtXJ+wyXP0QdInqZmBkhcfnAbep6qiyJPUIMBYbR3VWAPG5higry3qGHXxw+T5V+OEHS2BlA5i3zJpFk4ULYe1a+PBD2ypq0qT8Q7diN/r99oOWYW4xqYHSUhv3tnixJZ7o14ULLTktXWo/s+p06rT9kILu3S0x7b13403urtaC7p4+ChhVzXNvAT2SGY9rxESs40W7dj8NYv4+P58unTtbAos28FfsSr98edVViGBtaN27b79162ZbGHp/FRbaEIClS+3rkiXw7bf2dckS219xUtbKIhFLOl272rXts0/51q2bz7jv4iroEpVz4VYxgQ0evP1z69eXL5cSbYeJtsmsWmVb5VIY2GwI0aRVNkB6u61Vq9q3iW3ebB1IyrbmeXmWcJYvt0mHo9vatbs+V5s25ePfOne2r127lsednl67GJ2LkScq52qrZUubYfugg7bfX1pqieHrr7ffotVmP/5o24wZVZ+3WTOrVkxJsS01tfz76vatW2fJacOG7U61e3Wxp6dbL8eOHe1rp05WQop+7dgRmlc5GsS5pPNE5Vy8RSLlM9FXLoWpWttPxbaeb7/dfiso2H62hVikpVkvxbJS4MbMTJr36GGrN++5p2177QW77+7LVrh6wxOVc8kkAu3b23bEETs+r2pjjbZuhZIS24qLy7+vuFXc36KFJahK1Yar8/Np7l27XT3nicq5MBGxpOOc+4mX/Z1zzoWaJyrnnHOh5onKOedcqDW4Nqply5YxYECVM8XXG9u2bSOtBrN7h5lfQzj4NYSDX0ONHFjdEw0uUXXo0IGZM2cGHUad+JIA4eDXEA5+DeGQ6GsQkc+re86r/pxzzoWaJyrnnHOh5onKOedcqHmici6Moos11nTbY4+gI3YuYTxRORdGK1cm9njn6hFPVM4550LNE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlwU9UGtXXu3FmBhG5HHXVUQs9/wQUX+DUEHH/Q17AxM1MVaryNzMys8jwjR45M+M8p0ZtfQzi2JFzDzOo+10VVaUhycnJ09uzZQYdRJ/n5+XTp0iXoMOrEryEc/BrCwa9h10TkM1UdUNVzXvXnnHMu1DxROeecCzVPVM4550LNE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlQ80TlnHMu1DxROeecCzVPVM4550LNE5VzzrlQa3CT0orIRmBB0HHU0e7A6qCDqCO/hnDwawgHv4Zd21tVs6t6IjWBbxqUBdXNwFtfiMhMv4bg+TWEg19DOAR5DV7155xzLtQ8UTnnnAu1hpiongo6gDjwawgHv4Zw8GsIh8CuocF1pnDOOdewNMQSlXPOuQbEE5VzzrlQ80TlnHMu1BpMohKR1iLyiogUisgSETkn6JhiISIZIjKmLPaNIjJLRE4IOq7aEpHuIrJFRMYGHUttiMhZIjKv7O9poYgcGXRMsRCRziIySUTWisgKEXlEREI9blJELheRmSJSJCL/V+m5ISIyX0Q2ichUEdk7oDB3qrprEJFDRORNEflRRFaJyHgRaR9gqNXa2e+hwjEjRURF5JhkxNRgEhXwKLAVaAecCzwuIr2DDSkmqcBS4CigJXAL8KKIdA4wprp4FJgRdBC1ISLHAvcCFwHNgZ8BiwINKnaPAT8A7YEDsL+rywKNaNeWA3cCz1TcKSK7Ay9j/xOtgZnAC0mPrmaqvAZgN6zXXGdgb2Aj8GxSI6u56q4BABHpBpwBfJ+sgEJ9h1VTIpIJnA70UdUCYJqITAB+C9wQaHA1pKqFwKgKu14XkXygP7A4iJhqS0TOAtYBHwL7BBxObdwG3K6qH5c9XhZkMLXUBXhEVbcAK0TkDSDUN26q+jKAiAwA9qrw1GnAXFUdX/b8KGC1iPRQ1flJD3QnqrsGVZ1c8TgReQR4L7nR1cxOfg9RjwDXYzdDSdFQSlT7AiWq+lWFfV8Q8n/MnRGRdth1zQ06lliISAvgduCaoGOpDRFJAQYA2SLyjYh8V1Zt1jTo2GL0IHCWiDQTkQ7ACcAbAcdUW72x/2fgp5u6hdTj/2+slF6v/rcBROTXwFZVnZTM920oiSoLWF9p33qs2qbeEZE0YBzwXNjuGGvgDmCMqi4NOpBaagekYVUbR2LVZv2Am4MMqhbewz7INwDfYdVlrwYaUe01tP/v/YFbgRFBxxILEckC7gauSvZ7N5REVQC0qLSvBVYPXK+ISAR4HmtvuzzgcGIiIgcAxwD3Bx1LHWwu+/qwqn6vqquB/wVODDCmmJT9Df0Xa9fJxGa93g1rd6uPGtL/9z7AZOBKVf0g6HhidBvwvKrmJ/uNG0qi+gpIFZHuFfb1pZ4VrUVEgDHYXf3pqrot4JBiNQhrLP5WRFYA1wKni8jnQQYVC1Vdi5VA6vOULa2BjlgbVZGqrsEa7utNsq1kLvb/DPzUJt2N+vf/vTfwFnCHqj4fdDy1MAS4oqwX6Qrsb+xFEbk+0W/cIBJVWZ31y8DtIpIpIocDv8RKJvXJ40BP4GRV3byrg0PoKewD5ICy7QlgInBckEHVwrPAH0WkrYjshlV1vB5wTDVWVgrMB4aJSKqItAIuoEI7TxiVxdoESAFSRKRJWZf6V4A+InJ62fO3AnlhrBav7hrK2gnfAR5V1SeCjXLndvJ7GAL0ofz/eznwB6yHb2KpaoPYsLvIV4FC4FvgnKBjijH+vbG7+C1YVUd0Ozfo2OpwTaOAsUHHUYu407AeTeuAFcBDQJOg44rxGg4A3gXWYovdjQfaBh1XDf5etNI2quy5Y4D5WNXsu0DnoOON5RqAkWXfV/zfLgg63lh/D5WOWwwck4yYfFJa55xzodYgqv6cc841XJ6onHPOhZonKuecc6Hmico551yoeaJyzjkXap6onHPOhZonKuecc6Hmicq5kBKRd8sWn3y/lq/PEJECEdkmInfGOz7nksUTlXPhdrmq/qw2L1Sb5y8Lm4nfuXrLE5VzzrlQ80TlXJKJyPUiskxENorIAhEZEsNrF4vICBHJE5FCERkjIu1EZHLZ+d4qm0jXuQbDE5VzSSQi+2HrjA1U1ebYzPKLYzzN6cCx2ArQJ2PrG/0JW3cqAlwRr3idC4PUoANwrpEpATKAXiKySlUX1+IcD6vqSgAR+QD4QVVnlT1+BVuOwbkGw0tUziWRqn6DrW81CvhBRP4lInvGeJqVFb7fXMXjrDoF6VzIeKJyLslU9R+qegTla5DV1yXinUsKT1TOJZGI7CciR4tIBrZI5masOtA5Vw1PVM4lVwYwGlt1dwXQFusIrK/vSQAAAFpJREFU4Zyrhq/w61xIicgU4FBgpqoOrsXrM7D2qzTgz6p6W5xDdC4pPFE555wLNa/6c845F2qeqJxzzoWaJyrnnHOh5onKOedcqHmics45F2qeqJxzzoXa/wOqdelOCnYKfwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plotting twiss parameters.\n", "plot_opt_func(lat, tws_track, top_plot=[\"Dx\"], fig_name=\"i1\", legend=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wakefields of a Beam near a Single Plate in a Flat Dechirper\n", "\n", "For some FEL applications, e.g. a two-color scheme, only one flat corrugated structure can be used to get a correlated transverse kick along the electron bunch. In that case, we can use analytical approach from [I. Zagorodnov, G. Feng, T. Limberg. Corrugated structure insertion for extending the SASE bandwidth up to 3% at the European XFEL](https://arxiv.org/abs/1607.07642) and [K. Bane, G. Stupakov, and I. Zagorodnov, Wakefields of a Beam near a Single Plate in a Flat Dechirper](https://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-16881.pdf) to calculate described above the wakefield tables. \n", "\n", "
\n", "Note: Due to the use of assumptions in the analytical approach, a transverse kick is infinite if the electron beam distance to the plate wall is zero.
" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# create a simple lattice MagneticLattice\n", "m1 = Marker()\n", "m2 = Marker()\n", "# quadrupoles\n", "Q1 = Quadrupole(l = 0.5, k1 = 0.215)\n", "\n", "lattice = (Drift(l=1), m1, Drift(l=1), m2, Drift(l=2), Q1, Drift(l=2))\n", "method = MethodTM()\n", "method.global_method = SecondTM\n", "lat = MagneticLattice(lattice, method=method)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Describe corrugated structure and add wake to the lattice" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# description of args can be also be shown with Shift+Tab \n", "\n", "wk_tv_kick = WakeTableDechirperOffAxis(b=500*1e-6, # distance from the plate in [m]\n", " a=0.01, # half gap between plates in [m]\n", " width=0.02, # width of the corrugated structure in [m]\n", " t=0.25*1e-3, # longitudinal gap in [m]\n", " p=0.5*1e-3, # period of corrugation in [m]\n", " length=1, # length of the corrugated structure in [m]\n", " sigma=30e-6, # characteristic (rms) longitudinal beam size in [m]\n", " orient=\"horz\") # \"horz\" or \"vert\" plate orientation \n", "\n", "# creation of wake object with parameters \n", "wake = Wake()\n", "# w_sampling - defines the number of the equidistant sampling points for the one-dimensional\n", "# wake coefficients in the Taylor expansion of the 3D wake function.\n", "wake.w_sampling = 500\n", "wake.wake_table = wk_tv_kick\n", "wake.step = 1 # step in Navigator.unit_step, dz = Navigator.unit_step * wake.step [m]\n", "\n", "navi = Navigator(lat)\n", "\n", "# add physics proccesses\n", "navi.add_physics_proc(wake, m1, m2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Track the beam through the lattice" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tracking with Wakes .... \n", "z = 6.5 / 6.5 : applied: Wake\n", " time exec: 0.06728887557983398 sec\n" ] } ], "source": [ "# deep copy of the initial beam distribution \n", "p_array = deepcopy(p_array_init)\n", "print(\"tracking with Wakes .... \")\n", "start = time.time()\n", "tws_track, p_array = track(lat, p_array, navi)\n", "print(\"\\n time exec:\", time.time() - start, \"sec\")" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n"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