{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook explains PyHEADTAIL's ideal transverse feedback implementation.\n", "\n", "Dec 2018, Adrian Oeftiger" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# general imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from __future__ import division, print_function\n", "\n", "import numpy as np\n", "np.random.seed(42)\n", "\n", "from scipy.constants import m_p, c, e\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# sets the PyHEADTAIL directory etc.\n", "try:\n", " from settings import *\n", "except:\n", " pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PyHEADTAIL imports" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PyHEADTAIL v1.13.0\n", "\n", "\n" ] } ], "source": [ "from PyHEADTAIL.particles import generators\n", "from PyHEADTAIL.trackers.transverse_tracking import TransverseMap\n", "from PyHEADTAIL.feedback.transverse_damper import TransverseDamper\n", "from PyHEADTAIL.trackers.longitudinal_tracking import LinearMap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PySussix imports\n", "\n", "Sussix is a tune analysis tool: https://cds.cern.ch/record/702438/files/sl-note-98-017.pdf .\n", "If you do not have PySussix, its python interface, find it under https://github.com/PyCOMPLETE/PySussix ." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "try:\n", " from PySussix import Sussix\n", "except ImportError:\n", " print ('ERROR: This interactive test needs the PySussix module. Trying PySUSSIX')\n", " from PySUSSIX import Sussix\n", " print('PySUSSIX found')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setting up the machine and functions" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Basic parameters.\n", "n_turns = 500\n", "n_macroparticles = 1000\n", "\n", "Q_x = 64.28\n", "Q_y = 59.31\n", "Q_s = 0.0020443\n", "\n", "C = 26658.883\n", "R = C / (2.*np.pi)\n", "\n", "alpha_x = 0.\n", "alpha_y = 0.\n", "beta_x = 66.0064\n", "beta_y = 71.5376\n", "alpha_0 = [0.0003225]\n", "\n", "# HELPERS\n", "def gimme():\n", " ones = np.ones(2, dtype=float)\n", " trans_map = TransverseMap(\n", " [0, C], \n", " 0 * ones, beta_x * ones, 0 * ones, \n", " 0 * ones, beta_y * ones, 0 * ones, \n", " Q_x, Q_y)\n", " long_map = LinearMap(alpha_0, C, Q_s)\n", " bunch = generate_bunch(\n", " n_macroparticles, alpha_x, alpha_y, beta_x, beta_y,\n", " long_map)\n", " return bunch, trans_map, long_map\n", "\n", "def generate_bunch(n_macroparticles, alpha_x, alpha_y, beta_x, beta_y, linear_map):\n", " intensity = 1.0e11\n", " sigma_z = 0.06\n", " gamma = 3730.26\n", " gamma_t = 1. / np.sqrt(alpha_0)\n", " p0 = np.sqrt(gamma**2 - 1) * m_p * c\n", "\n", " beta_z = (linear_map.eta(dp=0, gamma=gamma) * linear_map.circumference / \n", " (2 * np.pi * linear_map.Q_s))\n", "\n", " epsn_x = 3e-6 # [m rad]\n", " epsn_y = 3e-6 # [m rad]\n", " epsn_z = 4 * np.pi * sigma_z**2 * p0 / (beta_z * e) \n", "\n", " bunch = generators.generate_Gaussian6DTwiss(\n", " macroparticlenumber=n_macroparticles, intensity=intensity, charge=e,\n", " gamma=gamma, mass=m_p, circumference=C,\n", " alpha_x=alpha_x, beta_x=beta_x, epsn_x=epsn_x,\n", " alpha_y=alpha_y, beta_y=beta_y, epsn_y=epsn_y,\n", " beta_z=beta_z, epsn_z=epsn_z)\n", " \n", " return bunch\n", "\n", "def calc_sussix_spec(x, xp, y, yp, q_x, q_y, n_lines=1):\n", " # Initialise Sussix object\n", " SX = Sussix()\n", " SX.sussix_inp(nt1=1, nt2=len(x), idam=2, ir=0, tunex=q_x, tuney=q_y)\n", "\n", " tunes_x = np.empty(n_lines)\n", " tunes_y = np.empty(n_lines)\n", "\n", " SX.sussix(x, xp,\n", " y, yp,\n", " # this line is not used by sussix:\n", " x, xp)\n", "\n", " os.remove('sussix.inp')\n", "\n", " return SX.ox[:n_lines], SX.oy[:n_lines]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Let's go" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Creating resistive transverse damper:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dampers active\n" ] } ], "source": [ "damping_rate = 50 # in turns\n", "\n", "# create transverse feedback instance\n", "damper = TransverseDamper(damping_rate, damping_rate)\n", "\n", "# create bunch\n", "bunch, trans_map, long_map = gimme()\n", "\n", "# simulate initial kick by offset of 100um\n", "bunch.xp -= bunch.mean_xp()\n", "bunch.yp -= bunch.mean_yp()\n", "bunch.x -= bunch.mean_x() - 1e-4\n", "bunch.y -= bunch.mean_y() - 1e-4\n", "\n", "# assemble one turn map\n", "one_turn_map = list(trans_map) + [long_map, damper]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We track for a number of turns to evaluate the damping of the kicked bunch:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# prepare empty arrays to record transverse moments\n", "x = np.empty(n_turns, dtype=float)\n", "xp = np.empty_like(x)\n", "y = np.empty_like(x)\n", "yp = np.empty_like(x)\n", "\n", "# actual tracking\n", "t = np.arange(n_turns)\n", "for i in t:\n", " for m in one_turn_map:\n", " m.track(bunch)\n", " x[i] = bunch.mean_x()\n", " xp[i] = bunch.mean_xp()\n", " y[i] = bunch.mean_y()\n", " yp[i] = bunch.mean_yp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's evaluate the damping time:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Horizontal reconstructed damping time: -48.994 turns\n", "Vertical reconstructed damping time: -48.994 turns\n" ] } ], "source": [ "# evaluation of dipolar bunch moments\n", "j_x = np.sqrt(x**2 + (beta_x * xp)**2)\n", "exponent_x, amplitude_x = np.polyfit(t, np.log(2 * j_x), 1)\n", "\n", "j_y = np.sqrt(y**2 + (beta_y * yp)**2)\n", "exponent_y, amplitude_y = np.polyfit(t, np.log(2 * j_y), 1)\n", "\n", "print ('Horizontal reconstructed damping time: {:.3f} turns'.format(1/exponent_x))\n", "print ('Vertical reconstructed damping time: {:.3f} turns'.format(1/exponent_y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, the reconstructed damping times fit the initial setting of the transverse resistive damper. The centroid motion and the fit look as follows:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(t, x, label='horizontal dipolar moment', alpha=0.8)\n", "plt.plot(t, y, label='vertical dipolar moment', alpha=0.8)\n", "ylim = plt.ylim()\n", "plt.legend(loc=0);\n", "plt.xlabel('Turns')\n", "plt.ylabel('Centroid motion [m]')\n", "plt.twinx()\n", "plt.plot(t, np.exp(amplitude_x + (exponent_x*t)) / 2., color='turquoise', label='horizontal fit')\n", "plt.plot(t, -np.exp(amplitude_x + (exponent_x*t)) / 2., color='red', label='vertical fit')\n", "plt.ylim(ylim)\n", "plt.legend(loc=4)\n", "plt.yticks([]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A purely resistive damper (standard setting of the `TransverseDamper`) has zero reactance part and should therefore not affect the tune of the beam. Let's confirm this by frequency analysis using `PySussix`. We investigate the fractional tune:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Horizontal fractional tune: 0.280 vs. reconstructed 0.280\n", "Vertical fractional tune: 0.310 vs. reconstructed 0.310\n" ] } ], "source": [ "spec_x, spec_y = calc_sussix_spec(x, xp, y, yp, Q_x%1, Q_y%1)\n", "print ('Horizontal fractional tune: {:.3f} vs. reconstructed {:.3f}'.format(Q_x%1, spec_x[0]))\n", "print ('Vertical fractional tune: {:.3f} vs. reconstructed {:.3f}'.format(Q_y%1, spec_y[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\implies$ nice, indeed we have no tune shift for the default resistive damper." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Damper Phase Scan\n", "\n", "Let's scan the phase of the damper in order to vary the resistive and reactive components of the feedback system.\n", "\n", "Here, the complex tune shift $\\Delta Q_x$ imparted by the damper is defined with respect to the complex oscillation\n", "\n", "$$\\langle x \\rangle \\propto \\exp( -i\\omega_x t) = \\cos(\\omega_x t) - i\\sin(\\omega_x t) = \\exp\\bigl[-i \\, 2\\pi \\, (Q_{x0} + \\Delta Q_x)\\, n_{turn}\\bigr]$$\n", "\n", "i.e. a positive imaginary tune shift corresponds to exponentially increase." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n", "Damper in horizontal plane active\n", "Damper in vertical plane active\n" ] } ], "source": [ "damping_rate_x = 50 # in turns\n", "damping_rate_y = 25 # in turns\n", "phases = np.arange(0, 360, 30) # in degrees\n", "\n", "tune_shifts_x = np.empty(len(phases), dtype=np.complex128)\n", "tune_shifts_y = np.empty_like(tune_shifts_x)\n", "\n", "for k, phase in enumerate(phases):\n", " # create transverse feedback instances\n", " # (separately because of different beta functions,\n", " # which are needed now for the reactive component)\n", " damper_x = TransverseDamper.horizontal(\n", " damping_rate_x, phase=phase, local_beta_function=beta_x)\n", " damper_y = TransverseDamper.vertical(\n", " damping_rate_y, phase=phase, local_beta_function=beta_y)\n", "\n", " # create bunch\n", " bunch, trans_map, long_map = gimme()\n", " \n", " # simulate initial kick by offset of 100um\n", " bunch.xp -= bunch.mean_xp()\n", " bunch.yp -= bunch.mean_yp()\n", " bunch.x -= bunch.mean_x() - 1e-4\n", " bunch.y -= bunch.mean_y() - 1e-4\n", " \n", " # assemble one turn map\n", " one_turn_map = list(trans_map) + [long_map, damper_x, damper_y]\n", " \n", " # prepare empty arrays to record transverse moments\n", " x = np.empty(n_turns, dtype=float)\n", " xp = np.empty_like(x)\n", " y = np.empty_like(x)\n", " yp = np.empty_like(x)\n", " \n", " # actual tracking\n", " t = range(n_turns)\n", " for i in t:\n", " for m in one_turn_map:\n", " m.track(bunch)\n", " x[i] = bunch.mean_x()\n", " xp[i] = bunch.mean_xp()\n", " y[i] = bunch.mean_y()\n", " yp[i] = bunch.mean_yp()\n", " \n", " # evaluation of rise time / imaginary tune shift\n", " j_x = np.sqrt(x**2 + (beta_x * xp)**2)\n", " exponent_x, amplitude = np.polyfit(t, np.log(2 * j_x), 1)\n", " im_x = exponent_x / (2*np.pi)\n", " \n", " j_y = np.sqrt(y**2 + (beta_y * yp)**2)\n", " exponent_y, amplitude = np.polyfit(t, np.log(2 * j_y), 1)\n", " im_y = exponent_y / (2*np.pi)\n", " \n", " # evaluation of real tune shift\n", " spec_x, spec_y = calc_sussix_spec(x, xp, y, yp, Q_x%1, Q_y%1)\n", " re_x, re_y = Q_x%1 - spec_x[0], Q_y%1 - spec_y[0]\n", " \n", " # storing complex tune shifts for current phase\n", " tune_shifts_x[k] = re_x + 1j*im_x\n", " tune_shifts_y[k] = re_y + 1j*im_y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, the complex tune shift moves on a circle in the complex tune plane: the imaginary part corresponds to the damping/growth rate inflicted on the beam centroid (resistive action of the feedback), while the real part indicates the frequency shift of the centroid motion (reactive action of the feedback). The radius of the circle depends on the damping rate ($\\frac{1}{2\\pi d_{rate}}$) while the complex angle corresponds to the feedback phase:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(12, 6), sharex=True, sharey=True)\n", "\n", "plt.sca(ax[0])\n", "plt.title('horizontal complex tune plane')\n", "plt.plot(tune_shifts_x.real, tune_shifts_x.imag)\n", "plt.scatter(tune_shifts_x.real[0], tune_shifts_x.imag[0], color='red')\n", "plt.xlabel(r'$\\Re\\{\\Delta Q_x\\}$')\n", "plt.ylabel(r'$\\Im\\{\\Delta Q_x\\}$')\n", "plt.text(0, 0, 'damping rate\\n{} turns'.format(damping_rate_x), color='green', \n", " horizontalalignment='center', verticalalignment='center')\n", "\n", "plt.sca(ax[1])\n", "plt.title('vertical complex tune plane')\n", "plt.plot(tune_shifts_y.real, tune_shifts_y.imag)\n", "plt.scatter(tune_shifts_y.real[0], tune_shifts_y.imag[0], color='red')\n", "plt.xlabel(r'$\\Re\\{\\Delta Q_y\\}$')\n", "plt.ylabel(r'$\\Im\\{\\Delta Q_y\\}$')\n", "plt.text(0, 0, 'damping rate\\n{} turns'.format(damping_rate_y), color='green', \n", " horizontalalignment='center', verticalalignment='center');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the real and imaginary parts of the complex tune shift separately for both planes demonstrates the contribution of resistive and reactive feedback component:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(phases, tune_shifts_x.real, label='horizontal')\n", "plt.scatter(phases[0], tune_shifts_x.real[0], color='red')\n", "plt.plot(phases, tune_shifts_y.real, label='vertical')\n", "plt.scatter(phases[0], tune_shifts_y.real[0], color='red')\n", "plt.legend()\n", "plt.title('Reactive action of the feedback')\n", "plt.xlabel('Damper phase [deg]')\n", "plt.ylabel(r'$\\Re\\{\\Delta Q\\}$');" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(phases, tune_shifts_x.imag, label='horizontal')\n", "plt.scatter(phases[0], tune_shifts_x.imag[0], color='red')\n", "plt.plot(phases, tune_shifts_y.imag, label='vertical')\n", "plt.scatter(phases[0], tune_shifts_y.imag[0], color='red')\n", "plt.legend()\n", "plt.title('Resistive action of the feedback')\n", "plt.xlabel('Damper phase [deg]')\n", "plt.ylabel(r'$\\Im\\{\\Delta Q\\}$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `TransverseDamper` class implements an ideal in-place transverse feedback -- for a more realistic feedback implementation (much closer to the LHC ADT for example) please have a look at the `feature/multibunch_feedback` branch of PyHEADTAIL at https://github.com/PyCOMPLETE/PyHEADTAIL/tree/feature/multibunch_feedback (which should be merged into develop over the course of the next months)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }