From 34aa89728c67d15b92df3d7656ded04ca54271d0 Mon Sep 17 00:00:00 2001 From: polymurph Date: Tue, 20 Sep 2022 20:30:55 +0200 Subject: [PATCH 1/3] workin on quadrupole examplewith C13 --- ...nfinite_lnegth_Quadrupole-checkpoint.ipynb | 2185 +---------------- .../Model_of_infinite_lnegth_Quadrupole.ipynb | 2185 +---------------- 2 files changed, 252 insertions(+), 4118 deletions(-) diff --git a/quadrupole/.ipynb_checkpoints/Model_of_infinite_lnegth_Quadrupole-checkpoint.ipynb b/quadrupole/.ipynb_checkpoints/Model_of_infinite_lnegth_Quadrupole-checkpoint.ipynb index 9415bd8..a4e9cb9 100644 --- a/quadrupole/.ipynb_checkpoints/Model_of_infinite_lnegth_Quadrupole-checkpoint.ipynb +++ b/quadrupole/.ipynb_checkpoints/Model_of_infinite_lnegth_Quadrupole-checkpoint.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 22, + "execution_count": 11, "metadata": { "scrolled": true }, @@ -11,28 +11,29 @@ "name": "stdout", "output_type": "stream", "text": [ - "pole positions\n", - "[[[ 0.01414214]\n", - " [ 0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[-0.01414214]\n", - " [ 0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[-0.01414214]\n", - " [-0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[ 0.01414214]\n", - " [-0.01414214]\n", - " [ 0. ]]]\n", - "pseudo charges\n", - "[0. 0. 0. 0.]\n", - "simulation time = 0.00010000000000013679\n", - "[[0.e+00]\n", - " [0.e+00]\n", - " [1.e-06]]\n", + "N = 10100\n", + "ion has left the boundary!\n", + "n = 1\n", + "simulation time = 9.000900090009e-09\n", + "number of positiions = 2\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "done!\n" ] } @@ -74,6 +75,8 @@ " # K factor for simplification ofcalculating the equations\n", " self.K = 1 / (4 * np.pi * sc.epsilon_0)\n", " \n", + " self.forces= []\n", + " \n", " def check(self):\n", " print('pole positions')\n", " print(self.pPole)\n", @@ -94,78 +97,107 @@ " def calcNewIonPos(self,U,V,f,ion,t_s,t):\n", " \n", " # check if ion has left the r_0 boundary\n", - " if np.linalg.norm(ion.position) >= np.linalg.norm(self.r_0):\n", + " if np.linalg.norm(ion.position) >= self.r_0:\n", " return None\n", " \n", " signLUT = [1,-1,1,-1]\n", " index = 0;\n", " \n", - " # reset force of ion\n", - " ion.F = np.array([[0],[0],[0]])\n", + " # reset force\n", + " F_c = np.array([[0],[0],[0]])\n", " \n", " for Q in self.rodsPseudoQ:\n", "\n", " \n", " # calculate the pseudo charge points of the quadrupole\n", - " eg = signLUT[index] * self.phi_0(U,V,f,t)/2 * self.K * self.R\n", + " Q = signLUT[index] * self.phi_0(U,V,f,t)/2 * self.K * self.R\n", " \n", " # match pseudo charge with ion in z direction\n", " self.pPole[index][2] = ion.position[2]\n", - " \n", + " \n", + " #print('ion position', ion.position)\n", + " #print(self.pPole[index])\n", + " \n", " # calculate force on ion\n", - " ion.F = ion.F + self.coulombForceOnQ1(ion.charge,\n", - " eg,\n", - " self.pPole[index],\n", - " ion.position)\n", + " F_q = self.coulombForceOnQ1(ion.charge,\n", + " Q,\n", + " self.pPole[index],\n", + " ion.position)\n", + " #print(F_q)\n", + " \n", + " F_c = F_c + F_q\n", + " self.forces.append(F_c)\n", " \n", " # update index\n", " index = index + 1\n", - "\n", - " newPosition = t_s**2 * 1 / ion.m * ion.F + ion.position\n", + " \n", + " ion.F = F_c\n", + " # http://lampx.tugraz.at/~hadley/physikm/problems/rvaF/index.en.php\n", + " newPosition = 0.5 * t_s**2 * 1 / ion.m * ion.F + ion.position\n", + " \n", " # velocity component in z\n", " newPosition[2] = newPosition[2] + ion.v_z * t_s\n", "\n", + " #print(newPosition)\n", + " \n", " return newPosition\n", " \n", - "t_step = 1e-9\n", + "N_periodes = 100\n", + "N_points_per_period = 101\n", + "f = 1.1e6 \n", + "t_step = 1 / f / N_points_per_period\n", "t_sim = 0\n", - "N = 100000\n", + "N = N_periodes * N_points_per_period\n", "\n", "# coffein atom 524.50002164 dalton (8.709527e-25 kg)\n", - "ion = Ion(np.array([[0],[0],[0]]), 1000 * sc.e, 8.709527e-25,0.01)\n", + "\n", + "\n", + "ion = Ion(np.array([[1e-10],[1e-10],[0]]), sc.e, 1.661e-27,1)\n", "\n", "# quadrupole\n", - "quad = infiniteLengthQuadrupole(5e-3,15e-3)\n", + "quad = infiniteLengthQuadrupole(0.0101, 0.01)\n", "\n", - "quad.check()\n", + "#quad.check()\n", "\n", "positions = []\n", "\n", - "positions.append(ion.position)\n", "\n", - "for n in range(0,N,1):\n", + "positions.append(ion.position)\n", + "print('N =',N)\n", + "for n in range(0,N-1,1):\n", " \n", - " newPos = quad.calcNewIonPos(1000,5000,1.1e6,ion,t_step,t_sim)\n", + " newPos = quad.calcNewIonPos(2.4764,17.335,f,ion,t_step,t_sim)\n", " \n", " if(newPos is None):\n", - " print('ion has left the boundary')\n", - " exit\n", + " print('ion has left the boundary!')\n", + " break\n", " \n", " \n", " ion.position = newPos\n", - " if n % 100 is 0:\n", + " \n", + " if n % 100 is 0 and 0:\n", " positions.append(newPos)\n", - " \n", + " \n", + " if 1:\n", + " positions.append(newPos)\n", + " \n", " t_sim += t_step\n", "\n", - "\n", + "print('n =',n)\n", "print('simulation time = ', t_sim)\n", - "print(ion.position)\n", + "print('number of positiions = ', len(positions))\n", + "\n", "\n", "if 0:\n", + " print(positions[:10])\n", + "\n", + "if 1:\n", " ax = plt.axes(projection='3d')\n", " #ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], c=positions[:][2], cmap='Greens')\n", - " ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], cmap='Greens')\n", + " ax.scatter3D(quad.forces[:][0], quad.forces[:][1], quad.forces[:][2], cmap='Greens')\n", + " ax.set_xlabel('x')\n", + " ax.set_ylabel('y')\n", + " ax.set_zlabel('z')\n", " plt.show()\n", "\n", "print('done!')\n", @@ -179,12 +211,23 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[1.e-100],\n", + " [1.e-100],\n", + " [0.e+000]]), array([[1.00000000e-100],\n", + " [1.00000000e-100],\n", + " [2.27272727e-007]])]\n" + ] + }, { "data": { - "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ + "print(positions[:2])\n", + "\n", + "\n", "# https://jakevdp.github.io/PythonDataScienceHandbook/04.12-three-dimensional-plotting.html\n", "ax = plt.axes(projection='3d')\n", "#ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], c=positions[:][2], cmap='Greens')\n", @@ -2214,9 +273,17 @@ "ax.set_zlabel('y')\n", "plt.show()\n", "\n", + "plt.plot(positions[:][0],positions[:][1])\n", "\n", - "print(positions)" + "\n" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/quadrupole/Model_of_infinite_lnegth_Quadrupole.ipynb b/quadrupole/Model_of_infinite_lnegth_Quadrupole.ipynb index 9415bd8..a4e9cb9 100644 --- a/quadrupole/Model_of_infinite_lnegth_Quadrupole.ipynb +++ b/quadrupole/Model_of_infinite_lnegth_Quadrupole.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 22, + "execution_count": 11, "metadata": { "scrolled": true }, @@ -11,28 +11,29 @@ "name": "stdout", "output_type": "stream", "text": [ - "pole positions\n", - "[[[ 0.01414214]\n", - " [ 0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[-0.01414214]\n", - " [ 0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[-0.01414214]\n", - " [-0.01414214]\n", - " [ 0. ]]\n", - "\n", - " [[ 0.01414214]\n", - " [-0.01414214]\n", - " [ 0. ]]]\n", - "pseudo charges\n", - "[0. 0. 0. 0.]\n", - "simulation time = 0.00010000000000013679\n", - "[[0.e+00]\n", - " [0.e+00]\n", - " [1.e-06]]\n", + "N = 10100\n", + "ion has left the boundary!\n", + "n = 1\n", + "simulation time = 9.000900090009e-09\n", + "number of positiions = 2\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ "done!\n" ] } @@ -74,6 +75,8 @@ " # K factor for simplification ofcalculating the equations\n", " self.K = 1 / (4 * np.pi * sc.epsilon_0)\n", " \n", + " self.forces= []\n", + " \n", " def check(self):\n", " print('pole positions')\n", " print(self.pPole)\n", @@ -94,78 +97,107 @@ " def calcNewIonPos(self,U,V,f,ion,t_s,t):\n", " \n", " # check if ion has left the r_0 boundary\n", - " if np.linalg.norm(ion.position) >= np.linalg.norm(self.r_0):\n", + " if np.linalg.norm(ion.position) >= self.r_0:\n", " return None\n", " \n", " signLUT = [1,-1,1,-1]\n", " index = 0;\n", " \n", - " # reset force of ion\n", - " ion.F = np.array([[0],[0],[0]])\n", + " # reset force\n", + " F_c = np.array([[0],[0],[0]])\n", " \n", " for Q in self.rodsPseudoQ:\n", "\n", " \n", " # calculate the pseudo charge points of the quadrupole\n", - " eg = signLUT[index] * self.phi_0(U,V,f,t)/2 * self.K * self.R\n", + " Q = signLUT[index] * self.phi_0(U,V,f,t)/2 * self.K * self.R\n", " \n", " # match pseudo charge with ion in z direction\n", " self.pPole[index][2] = ion.position[2]\n", - " \n", + " \n", + " #print('ion position', ion.position)\n", + " #print(self.pPole[index])\n", + " \n", " # calculate force on ion\n", - " ion.F = ion.F + self.coulombForceOnQ1(ion.charge,\n", - " eg,\n", - " self.pPole[index],\n", - " ion.position)\n", + " F_q = self.coulombForceOnQ1(ion.charge,\n", + " Q,\n", + " self.pPole[index],\n", + " ion.position)\n", + " #print(F_q)\n", + " \n", + " F_c = F_c + F_q\n", + " self.forces.append(F_c)\n", " \n", " # update index\n", " index = index + 1\n", - "\n", - " newPosition = t_s**2 * 1 / ion.m * ion.F + ion.position\n", + " \n", + " ion.F = F_c\n", + " # http://lampx.tugraz.at/~hadley/physikm/problems/rvaF/index.en.php\n", + " newPosition = 0.5 * t_s**2 * 1 / ion.m * ion.F + ion.position\n", + " \n", " # velocity component in z\n", " newPosition[2] = newPosition[2] + ion.v_z * t_s\n", "\n", + " #print(newPosition)\n", + " \n", " return newPosition\n", " \n", - "t_step = 1e-9\n", + "N_periodes = 100\n", + "N_points_per_period = 101\n", + "f = 1.1e6 \n", + "t_step = 1 / f / N_points_per_period\n", "t_sim = 0\n", - "N = 100000\n", + "N = N_periodes * N_points_per_period\n", "\n", "# coffein atom 524.50002164 dalton (8.709527e-25 kg)\n", - "ion = Ion(np.array([[0],[0],[0]]), 1000 * sc.e, 8.709527e-25,0.01)\n", + "\n", + "\n", + "ion = Ion(np.array([[1e-10],[1e-10],[0]]), sc.e, 1.661e-27,1)\n", "\n", "# quadrupole\n", - "quad = infiniteLengthQuadrupole(5e-3,15e-3)\n", + "quad = infiniteLengthQuadrupole(0.0101, 0.01)\n", "\n", - "quad.check()\n", + "#quad.check()\n", "\n", "positions = []\n", "\n", - "positions.append(ion.position)\n", "\n", - "for n in range(0,N,1):\n", + "positions.append(ion.position)\n", + "print('N =',N)\n", + "for n in range(0,N-1,1):\n", " \n", - " newPos = quad.calcNewIonPos(1000,5000,1.1e6,ion,t_step,t_sim)\n", + " newPos = quad.calcNewIonPos(2.4764,17.335,f,ion,t_step,t_sim)\n", " \n", " if(newPos is None):\n", - " print('ion has left the boundary')\n", - " exit\n", + " print('ion has left the boundary!')\n", + " break\n", " \n", " \n", " ion.position = newPos\n", - " if n % 100 is 0:\n", + " \n", + " if n % 100 is 0 and 0:\n", " positions.append(newPos)\n", - " \n", + " \n", + " if 1:\n", + " positions.append(newPos)\n", + " \n", " t_sim += t_step\n", "\n", - "\n", + "print('n =',n)\n", "print('simulation time = ', t_sim)\n", - "print(ion.position)\n", + "print('number of positiions = ', len(positions))\n", + "\n", "\n", "if 0:\n", + " print(positions[:10])\n", + "\n", + "if 1:\n", " ax = plt.axes(projection='3d')\n", " #ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], c=positions[:][2], cmap='Greens')\n", - " ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], cmap='Greens')\n", + " ax.scatter3D(quad.forces[:][0], quad.forces[:][1], quad.forces[:][2], cmap='Greens')\n", + " ax.set_xlabel('x')\n", + " ax.set_ylabel('y')\n", + " ax.set_zlabel('z')\n", " plt.show()\n", "\n", "print('done!')\n", @@ -179,12 +211,23 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[1.e-100],\n", + " [1.e-100],\n", + " [0.e+000]]), array([[1.00000000e-100],\n", + " [1.00000000e-100],\n", + " [2.27272727e-007]])]\n" + ] + }, { "data": { - "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ + "print(positions[:2])\n", + "\n", + "\n", "# https://jakevdp.github.io/PythonDataScienceHandbook/04.12-three-dimensional-plotting.html\n", "ax = plt.axes(projection='3d')\n", "#ax.scatter3D(positions[:][0], positions[:][1], positions[:][2], c=positions[:][2], cmap='Greens')\n", @@ -2214,9 +273,17 @@ "ax.set_zlabel('y')\n", "plt.show()\n", "\n", + "plt.plot(positions[:][0],positions[:][1])\n", "\n", - "print(positions)" + "\n" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { From d492ddc05af02086235c095a8c3d59df971f03f9 Mon Sep 17 00:00:00 2001 From: polymurph Date: Sun, 25 Sep 2022 09:29:47 +0200 Subject: [PATCH 2/3] added new calculations for quad model --- ...adrupole_electric_field_calculations.ipynb | 427 ++++++++++++++++++ 1 file changed, 427 insertions(+) create mode 100644 quadrupole/Quadrupole_electric_field_calculations.ipynb diff --git a/quadrupole/Quadrupole_electric_field_calculations.ipynb b/quadrupole/Quadrupole_electric_field_calculations.ipynb new file mode 100644 index 0000000..0372fc7 --- /dev/null +++ b/quadrupole/Quadrupole_electric_field_calculations.ipynb @@ -0,0 +1,427 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\overrightarrow{E} = \\left[\\begin{matrix}- \\frac{x \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{r_{0}^{2}}\\\\\\frac{y \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{r_{0}^{2}}\\\\0\\end{matrix}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$\\overrightarrow{F} = \\left[\\begin{matrix}- \\frac{q x \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{r_{0}^{2}}\\\\\\frac{q y \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{r_{0}^{2}}\\\\0\\end{matrix}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$\\overrightarrow{a} = \\left[\\begin{matrix}- \\frac{q x \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{m r_{0}^{2}}\\\\\\frac{q y \\left(U + V \\cos{\\left (\\omega t \\right )}\\right)}{m r_{0}^{2}}\\\\0\\end{matrix}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sympy import *\n", + "# https://docs.sympy.org/latest/tutorials/intro-tutorial/printing.html\n", + "\n", + "# https://stackoverflow.com/questions/40806591/how-do-i-display-a-full-expression-in-sympy\n", + "from IPython.display import display, Math\n", + "\n", + "U, V, omega, t, x, y, r_0, q, m, v_v, v_p = symbols('U V omega t x y r_0 q m v_v v_p')\n", + "init_printing()\n", + "\n", + "v_ex = Matrix([1,0,0]) \n", + "v_ey = Matrix([0,1,0])\n", + "v_ez = Matrix([0,0,1])\n", + "\n", + "# theory prerequisite\n", + "\n", + "# RF + DC offset of the quadrupole\n", + "phi_0 = U + V * cos(omega * t)\n", + "\n", + "# potential inside a quadrupole at a given point in space\n", + "phi = phi_0 * (x**2 - y**2) / (2 * r_0**2)\n", + "\n", + "# In the first step the electric field is derived from the potiential distribution\n", + "# with the formula E = -\\nabla * phi.\n", + "\n", + "# calculating the partial derivateives for the nabla operation(gradient)\n", + "dx = diff(phi, x)\n", + "dy = diff(phi, y)\n", + "\n", + "v_E = -(dx * v_ex + dy* v_ey)\n", + "\n", + "display(Math(latex('\\overrightarrow{E} = ') + latex(v_E)))\n", + "\n", + "# in the seccond step the lorenz force is determined with the formulafor considering B = 0!\n", + "# F = E * q\n", + "\n", + "v_F = v_E * q\n", + "\n", + "display(Math('\\overrightarrow{F} = '+latex(v_F)))\n", + "\n", + "# With the force the acceleration can be determined with respect to the ions mass\n", + "# a = F / m\n", + "\n", + "v_a = v_F / m\n", + "\n", + "display(Math('\\overrightarrow{a} = '+latex(v_a)))\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(755.0120770093375, 10570.169078130726)\n", + "N = 1100000\n", + "ion has left the boundary!\n", + "n = 1210\n", + "simulation time = 9.999999999999773e-05\n", + "number of positiions = 1\n", + "[-2.0391744630349912e-13, 3.56317754718436e-15, -9.979659008986673e-17, 3.0235407792913644e-18, -7.139985036292582e-20, 7.19867582572237e-22, 4.321977872069379e-24, 8.443545107936075e-26, 2.2137865823636512e-27, 5.297458959531464e-29]\n", + "done!\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy.constants as sc\n", + "import matplotlib.pyplot as plt\n", + "\n", + "class Ion:\n", + " def __init__(self,position, charge, mass, v_z):\n", + " self.position = position\n", + " self.charge = charge\n", + " self.m = mass\n", + " self.v_z = v_z\n", + " self.F = np.array([[0],[0],[0]])\n", + "\n", + "class infiniteLengthQuadrupole:\n", + " def __init__(self,R,r_0):\n", + " # rod radius\n", + " self.R = R\n", + " # rod placement radius\n", + " self.r_0 = r_0\n", + " # rod positions\n", + " self.pPole = np.array([[[ (R + r_0)/np.sqrt(2)],\n", + " [(R + r_0)/np.sqrt(2)],\n", + " [0]],\n", + " [[-(R + r_0)/np.sqrt(2)],\n", + " [(R + r_0)/np.sqrt(2)],\n", + " [0]],\n", + " [[-(R + r_0)/np.sqrt(2)],\n", + " [-(R + r_0)/np.sqrt(2)],\n", + " [0]],\n", + " [[(R + r_0)/np.sqrt(2)],\n", + " [-(R + r_0)/np.sqrt(2)],\n", + " [0]]])\n", + " # rod pseudo charges\n", + " self.rodsPseudoQ = np.zeros(4)\n", + " # K factor for simplification ofcalculating the equations\n", + " self.K = 1 / (4 * np.pi * sc.epsilon_0)\n", + " \n", + " self.forces= []\n", + " \n", + " def check(self):\n", + " print('pole positions')\n", + " print(self.pPole)\n", + " print('pseudo charges')\n", + " print(self.rodsPseudoQ)\n", + " \n", + " def phi_0(self,U, V, f, t):\n", + " return U + V * np.sin(2 * np.pi * f * t)\n", + " \n", + " def coulombForceOnQ1(self,Q1,Q2,r1,r2):\n", + " a = self.K * Q1 * Q2\n", + " r12 = r1 - r2\n", + " mag_r12 = np.linalg.norm(r12)\n", + " # calculate force\n", + " return a * r12 / (mag_r12**3)\n", + " \n", + " def getUV(self, mass_amu, f, a, q):\n", + " U = a * 1.66054e-27 * mass_amu * (2 * np.pi * f)**2 *self.r_0**2 / (8 * sc.e)\n", + " V = q * 1.66054e-27 * mass_amu * (2 * np.pi * f)**2 *self.r_0**2 / (4 * sc.e)\n", + " return U, V\n", + " \n", + " \n", + " def calcNewIonPos_1(self,U,V,f,ion,t_s,t):\n", + " # check if ion has left the r_0 boundary\n", + " if np.linalg.norm(ion.position) >= self.r_0:\n", + " return None\n", + " \n", + " phi_0 = U + V * np.sin(2 * np.pi * f * t)\n", + " a_x = -(float(ion.position[0]) * phi_0) / (self.r_0**2) * ion.charge / ion.m\n", + " a_y = (float(ion.position[1]) * phi_0) / (self.r_0**2) * ion.charge / ion.m\n", + " \n", + " newPosition = 0.5 * t_s**2 * np.array([[a_x],[a_y],[0]])\n", + " newPosition[2] = float(ion.position[2])\n", + " \n", + " # velocity component in z\n", + " newPosition[2] = newPosition[2] + ion.v_z * t_s\n", + " \n", + " # ion position update\n", + " ion.position = newPosition\n", + "\n", + " #print(newPosition)\n", + " \n", + " return newPosition\n", + " \n", + " def calcNewIonPos(self,U,V,f,ion,t_s,t):\n", + " \n", + " # check if ion has left the r_0 boundary\n", + " if np.linalg.norm(ion.position) >= self.r_0:\n", + " return None\n", + " \n", + " signLUT = [1,-1,1,-1]\n", + " index = 0;\n", + " \n", + " # reset force\n", + " F_c = np.array([[0],[0],[0]])\n", + " \n", + " for Q in self.rodsPseudoQ:\n", + "\n", + " \n", + " # calculate the pseudo charge points of the quadrupole\n", + " Q = signLUT[index] * self.phi_0(U,V,f,t)/2 * self.K * self.R\n", + " \n", + " # match pseudo charge with ion in z direction\n", + " self.pPole[index][2] = ion.position[2]\n", + " \n", + " #print('ion position', ion.position)\n", + " #print(self.pPole[index])\n", + " \n", + " # calculate force on ion\n", + " F_q = self.coulombForceOnQ1(ion.charge,\n", + " Q,\n", + " self.pPole[index],\n", + " ion.position)\n", + " #print(F_q)\n", + " \n", + " F_c = F_c + F_q\n", + " self.forces.append(F_c)\n", + " \n", + " # update index\n", + " index = index + 1\n", + " \n", + " ion.F = F_c\n", + " # http://lampx.tugraz.at/~hadley/physikm/problems/rvaF/index.en.php\n", + " newPosition = 0.5 * t_s**2 * 1 / ion.m * ion.F + ion.position\n", + " \n", + " # velocity component in z\n", + " newPosition[2] = newPosition[2] + ion.v_z * t_s\n", + "\n", + " #print(newPosition)\n", + " \n", + " return newPosition\n", + " \n", + "N_periodes = 100000\n", + "N_points_per_period = 11\n", + "f = 1.1e6 \n", + "t_step = 1 / f / N_points_per_period\n", + "t_sim = 0\n", + "N = N_periodes * N_points_per_period\n", + "\n", + "# coffein atom 524.50002164 dalton (8.709527e-25 kg)\n", + "\n", + "\n", + "#ion = Ion(np.array([[1e-10],[1e-10],[0]]), sc.e, 1.661e-27,100)\n", + "ion = Ion(np.array([[1e-10],[1e-10],[0]]), sc.e, 1220 * 1.66054e-27,100)\n", + "\n", + "# quadrupole\n", + "quad = infiniteLengthQuadrupole(0.0101, 0.01)\n", + "\n", + "#quad.check()\n", + "\n", + "positions = []\n", + "\n", + "p_x = []\n", + "p_y = []\n", + "p_z = []\n", + "\n", + "print(quad.getUV(1220,f,0.1,0.7))\n", + "\n", + "\n", + "positions.append(ion.position)\n", + "print('N =',N)\n", + "for n in range(0,N-1,1):\n", + " \n", + " newPos = quad.calcNewIonPos_1(755.0120770093375, 10570.169078130726,f,ion,t_step,t_sim)\n", + " #newPos = quad.calcNewIonPos_1(100,100,f,ion,t_step,t_sim)\n", + " \n", + " if(newPos is None):\n", + " print('ion has left the boundary!')\n", + " break\n", + " \n", + " \n", + " ion.position = newPos\n", + " \n", + " if n % 100 is 0 and 0:\n", + " print(newPos)\n", + " #positions.append(newPos)\n", + " \n", + " if 0:\n", + " positions.append(newPos)\n", + " \n", + " if 1:\n", + " p_x.append(float(newPos[0]))\n", + " p_y.append(float(newPos[1]))\n", + " p_z.append(float(newPos[2]))\n", + " \n", + " \n", + " t_sim += t_step\n", + "\n", + "print('n =',n)\n", + "print('simulation time = ', t_sim)\n", + "print('number of positiions = ', len(positions))\n", + "\n", + "if 1:\n", + " print(p_x[:10])\n", + "\n", + "\n", + "if 0:\n", + " print(positions[:10])\n", + "\n", + "\n", + "\n", + "print('done!')" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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73S468y8V9GgZawSSXlOC/PWvf40vfvGL2LNnD5qbm72eMzIygtLSUu7fJSUlAFDsc6liAEMAQAhxMwwzDSAPwFSAJRUDGOb9e1jgmpIw54nB4/FgZGQEBQUFkjoi+QiHGFwuF1pbW6FWq7F8+XIYDIaw3wPd3FTvsHLlSmRmZsLtdnv1APAbpDQaDXcHjFcoHgtQUdCiRYugVqu5RCZN4LrdbmRlZXHS7Ugip1BNVNFCqJ4Mt9sNpVKJgoICbNq0KebriQXmLDHwjw49PT2Cd+tgHZF8SCUGOntyyZIlWLBgAfR6fdhHEfravb290Gq1nN6BX+UA/BukrFYrenp6MD4+jrGxMa7vQcwsyrkGPrHxE5kVFRVeCT0xicxgiFdZ1Le92xdUYSmE4uJiDA0Ncf8eHh4GgBGfp40AKAUwzDBMEoAszCYhA2EEQAnv3yUC15SEOUkMvtoEX9AQf3x8PGBHJB9Seh2GhoYwMjKC+vp67rqRhPRutxszMzPIzMwUnbSkQpysrCykpKSgoKCA63sYGhoCIYQ7dkjdPIlAsIiHn9ADZiM12j3Z1dWF5ORkjhBDNUXFM8kZLGIIpmFobGxEV1cX+vr6UFxcjJdeegkAXvd52usArgHwMYArAPwtWIWBEDLGMIyJYZizMZt8/CaAJ6S8J1/MKWIQY7kmtiOSDzHEwD+SrF+/3usPH26Owmw2o6WlBUlJSVi5cqXkn6eEJNT3YDAYoNVq0d3dzW2eWMiZowEpGzY5ORkFBQWcPoQ/08JsNnNW9bm5uTFNZAZDqKNEsIghKSkJTz75JC6++GJ4PB5cd911aG5ubmMY5j4ARwghrwN4BsAfGYbpBqAHsIv+PMMw/QAyAagYhtkOYPOpisYP8Hm58m1EkHgE5hAxiNEmSOmI5CPUxjabzTh+/DgqKiqwaNEiwZ+XGjGMjo6iv78ftbW1aG1tlfSzoZCUlOS3efR6vZcvAyWKaCb3wkUkZUTfmRa016Gnpwc2m43rdaARRzwQihhmZmaCipsuueQSXHLJJV6PEUJ+xvt/O4CvCv0sIaQiwONH4F/CDBtzghhCaRMAoKurK+iMyGBQKpWCxEDI7FzFoaEh1NbWBvxjSnFwYlmWM3alkUesdQy+VQAq6412ci9cRCspKNTrQBWZJ06cgNVqRWdnZ1jGslIQKsdAe03mMxJKDGIs1+x2O6xWK1iWldQRyYdCofBL9rndbpw4cQIMw6CxsTHohhEbMdhsNrS0tKCoqIgzaYk3+Pr/8vJyLrlHIwrfsuh8BsMwnIS5oqICn376KfLz8zljWQCi/SKlIFTEMN/l0EACiSGUNgH43AkpLS0NFRUVYW8036PEzMwMWlpaUFZWRuvIQSEmYpiamkJHR0dIw1cpiIaOwTe551sWtdlsGB4ejvmZPR4kyTCMYCJzamoKPT09nA0cJcVw1yQm+ShHDGEg1NHBd0ZkW1ub3x1fCvjXp2d/ISFUIASLGAgh6O3thU6n41yb5jJ8y6KffvopAHDio/laFhVKcPomMqkNHN/dib5XKaYtHo8naIQ53zsrgTgTgxhZM+2I5M+IVCqVEREDfe3W1lZ4PB6sX79e0lk7UMTgcrnQ0tKC9PT0oK3X4SLWykf6u6UScr4dHL8sSs/sc7ksKkbDwLeB47s7UdMWviIzWB7L4/EEvQFYLJa4JkNjgbgRQyjfBMC7I5KW5oDAyUOxsFgssFqtKC0tRWlpqeQQUqiqYTKZ0NraisrKSixYsCDstc0lBCqL0lB8LpdFpVY+hNydaNJWaCoYP3oSI3Diy57nI2JODGK0CUIdkXwIJQ/FYmxsDH19fUhJSUFZWVlY1/C9c9O+DDHiqkiQ6F6J+VQWjbSByjdp6zsVjJDZmZi5ubmc5DkQ5KNECISyXAMCd0TyEc5RgpYNHQ4HGhsbcfjw4bDfB40YKIF5PJ6QlYxQEHt3m0tNVHO5LBrtBirfqWButxtGoxE6nQ6Tk5MwmUzIz88XnAoWjBjC9WI49b27MNuS7QFwMyHkr6cevwXA9QAIgOMArj2lhQgbMfvr0QTjoUOHsH79eskdkXxIPUrQPMWCBQuiUjakOYbDhw9j0aJFYR1HfKHT6WA0GpGXl5fQsDwSjYXYsmi8LOpjmQNJSkriBt84nU4UFxfDbrf7TQVjGCYgMQh5MWzduhWrVq3iP03Qi4FhmFWYVUBWA1gE4H2GYZYBWADgZgCrCCE2hmH+cup5v4/o/Ubyw0Lw1SYIMbmYjkg+pBwlJiYm0N3d7ZenoGsLZwNqtVpYrVasX7/e75pSQV2gpqamkJ+fz4XlGRkZyMvL8/IWTPRRQgqClUWtVitnrR+rsmi8GqiAz5OP2dnZfonMxx9/HO+//z50Oh0uv/xy7Ny5k7vpCXkxvPbaa77EIOjFcOrxlwghDgB9p+TS6wEMYnYfaxiGcQFIBTAa6XuMKjGIkTXTjshA8mMhiDlK0BKn1WpFY2OjoHGnVGKgLtAGgwGpqakRk4Lb7cbx48eRkpKCtWvXwu12eyn4dDodRkZGwLIsF8LGumQYq0iFXxY1m82orKyEwWCIWVk0nsQg5BBNE5kPP/wwent7cfPNN6OtrY0boAsIezHQcjEPgbwYigF8wnveMIBiQsjHDMM8glmCsAF4lxDybqTvMWrEQAiBw+EIqE2Q2hHJh1Kp5JKXQqCKw8LCQq7EKXQNKR8e2qyVkZGBhoYGfPzxx6LXKwSLxYLm5maOEPlHI76Cb/HixVw1YHh4GBaLBUajkbsbp6amRrQOPuIVjfhKmWNRFo13xBAsyrXZbDjrrLNw8cUXx3wtDMPkYDaaWAzACGAPwzBXEUL+FMl1o0YMlAyENqXD4UBra6ukjkg+gjVBUXWkmBHzYvMU1I9BarNWILhcLjQ1NaGmpoZzIA4GWg3weDxwOBwoKCiAXq/n7rY0yZeTk5MwS7hIEIuyaLwjhnD8GIS8GIqL/YyWAnkx0McpqOfCJgB9hBAtADAM8zKAcwDMDWIAhDcfTdotW7Ys7E0mdJRgWRZdXV0wm82CRwehtYU6jtCE6PDwMNasWRPx3ZkeRZxOJzZs2CDZvp5uCBqm0rstTfJR09GcnBzk5eVFJPONFcREJdEoi8aTGEIdSQMpI4W8GF544QXfpwl6MTAM8zqAFxiGeRSzycelAA4BYAGczTBMKmaPEhcCOBLpe4zZ7YZuCrvdjvXr14u6UwaCb1WCjprLy8vDunXrRG2GUBGDx+PBiROzfpy+fgzhwOVy4fjx40hLS0NqamrUcgW+ZTSa5KN+BXSCVG5ubsgu1HgYm4TzGuGUReNJDKHMYgJByIuhuroaYrwYCCFtpyoOJwC4AdxICPEA+JRhmL0Ajp56/BiA/430PcaEGOiAVyoIiTTc5d/tabOS1FFzwYjBarWiubk5qJZCCmiTFlVF6vX6sDaImKqEb++DxWLh1Hsul4v7G/AnXMcTkZKP2LJovByixSDQkRqI2IvhQQAPCjx+D4B7IliyH6JKDAzDcGd+unFbWloi7nNQKpVwu93o6uryGjEvBYGIgVqIrV69GllZWRGtEwDGx8fR29vrpc0ItMGjfbdmmM8nSJWVlXGDYeiEa2p3Ts/u8UC0oxKhsihN1NpsNphMppg7PIUi6/lSYg6GqBIDndLEP/NHowHK4/FgamoKpaWlXiPmpcCXGAgh6OrqgslkEpWjoD8T6LXp9WjOg390CFePEKmOwXcwjNDZ3eVywel0hj2+LxRifVyhw3mpbiY7OzvmZdFg78fpdM6rrtRAiCoxCKkCk5KSIiIGvV6PtrY2aDQaLF26NOzr8InB6XSiubkZ2dnZknIUgT7kdMBtVlYW1q5d6/ecuSJU8j27G41GGI1GtLa2ctqJaBvMxsvSnWVZJCcnx6Userp7MQBRJoaUlBQvQQcQfsTA9zmor6/HyZMnI1obJQaj0Yi2tjZRA2n5oLJo3w+TyWTC8ePHg5Y2ExUxhLp2Zmaml9iKP2aOehVEGpLH07nZ928Ti7KoGCPY+d5ABcShu5LmB6SAiouozwEhJKK2a2D2QzIxMYGZmZmwSpFCOQpq+lJXVxf0wxBog8dr0wQCf02+JUOr1eqlncjMzOQk21KSybGeJ8l/nVARQDTKopE4RM8nxIUYpEQMdEIR/w5M+y/CBZ2dmJSUhMbGxrCy1/zNTeXXNptNlOlLuMnHeBxBAq3BVzthMpmg0+kwMDDgZaGWmZkZsnwXD2II58gSTlk0kmEz8wlRr0r4vUBSEpxOZ8ifJYSgv78fk5OTfiPmI/lgWSwWtLS0IC0tDXl5eWGXtGjEQPMTubm5AeXXvhDa4HNNiBQMviE5rQSMjo7i5MmTQbUTiTxKSIHYsqhKpQpJDPJRQgTEHCWoGEij0UgaMR8KtNOypqYG09PTER1HGIaByWRCd3d3WPkJX2IwGo0YGxvjEmFChDVXkpa+oJWAoqKikNqJ+UIMvghUFh0bG4PZbIbL5RIsiwazjo+RF0M2gKcxO1OCALiOEBJZYw/mwFGC9iVUVVWFNU1aCFQuPTMzwzlC0T9muLDb7ejq6sLatWsl5yd8N/jIyAgGBwdRUlICvV6Pnp4eqNVq5ObmIi8vL24TlqJBOqG0E/S9m81mpKenx+x9xVr5SMlQoVDAbDajqKjIryyqUCgwOTkZNy+GU8rHxwG8Qwi5gmEYFWbbriNGzIkhULmSEILBwUGMjo5GpS+BwuFwoKWlBbm5uV6lw3DHzPEHyNTV1YW1Tro5WJZFR0cH7HY7GhoawLIsR4Y2m82vUYpOh44lor1RfbUTU1NTGBwcxMDAAOc7Qe/E0dROxHOgbVJSkmBZ9MCBA/j1r38Nu92OmZkZfOtb38Ly5csBxMaLgWGYEwC+COBbAEAIcQIIeG5nGOZ7AL536p9ZAPoJIecLPTfmOQaho4TL5UJbWxtUKpWkvoRQYSlNXC5fvpwbL08RDjE4HA40NTWhsLAQubm5YW8ihmHgdDpx8uRJ5OTkYMWKFQDglXvRaDQoLi5GcXEx1yg1MjICo9EIi8XipVicT/kJqi1Yvny51+SoaGsnEjnpmuZgduzYgfHxcaSnp6O0tNTr7xsLLwbMNk1pATzHMEwdgM8A7CaEWITWTgj5LYDfMgyTDOBvAB4N9D7jfpSg7sqhRtf7IpjRCvV6mJiY8EtcUkglBkoyVNp94sSJsO/ebrcbbW1tWL58uVelJRBooguYtTwvKyuDTqfjymr80mEkKrt4Wa7Rvxnfd6KiosJPOxHJcSpexMCybMiZEosXL8a2bdtivhbM7t+1AP6dEPIpwzCPA/gRgJ+G+LnHMdu1+UawC8cU9CjBb2kONicyECjB+P7xqU2cSqUKmriUQgxDQ0MYGRnxIplwE4ETExMwGAxYtWqV5LZz+ppqtZorq7Esy7k9DQ4OQqFQcJspnDN8IrsrfXUFNpsNOp0uLDlzPCOGUDMlhD7bMfJiGAYwTAihocdezBJDQDAM8y0A5QBuCva8uB0lWlpaoFQqw25ppsTA/4DQLkYxNnFiiIFlWS4y8NU7SI04aNu50WhEYWGhYBQTCkK/T4VCgaysLGRlZaGyspJrux4cHMTMzEzMzvDhQsqG1Wg0AYffAAiqnYgnMYQztzIWXgyEEA/DMEMMwywnhHRg1ovhRKC1MQyzDsDtAL5ACAn6YY55xGC1WmEymVBaWirEkKLhuzGFuhil/Lwv7HY7mpubsWDBApSVlUXU70C9HTUaDdauXYuTJ0+GHbZLbbum0cTx48dBCOGiiVBCpFgh3HKlr3bC5XJx5rInT55Eamoql3dJSUmJm8IyXIFTIC+Gn/3sZ7j//vu3hunFAAD/DuDPpyoSvQCuDbL8mwDkAvjg1O/qCCHkeqEnRp0Y+BtoZGQEAwMDXGItEtCIgZ/Z9+1iDPXzgYhBr9ejvb0dK1euDDhaTGzEQL0dysrKuPccSa+E1OfzvSNdLpefEIluJrVaPWeNWoSQnJzspZ2wWq3Q6XRcxcjhcECv1yMnJyemvgyR9EoIeTHcd999uO+++14HwvZiaALQIGbthJBgpOGFmEQM1A2JEIL169fj0KFDEV9TqVTCbrejvb0d+fn5WLFihaQPnNDG5ict161bF9TxSMzmph9UX2+HSIRKkSQIk5OTUVhYiMLCQk6IpNPpOMlvZmYmNzYwVmF4LMiH4ZnLUu3Ep59+CqPRiL6+PiQlJXHHjmhrJ0J1V9Lj3HxH1ImBnvuj5YZE4XQ60d7ejurqaknOTRS+no8ejwdtbW1QKBSi1JbBIgaqyRgfHxckmLmgYOQLkcrLy7n+kampKRw5cgQpKSlcNBFOPiQQ4hGVKJVKJCUloaqqCgC46IHmXdLT07n3FmneRUyOQSYGAQwODqK6utrP4zHcDwjtoZiensbSpUvDIgXAe2PzrdzEDh8NtLlpwpIQEpBg5mLbNb2rTk1Noaamhuum7Ojo4GTNeXl5yMrKiig0T0QHqVqtxsKFC7Fw4UJB7QRfsi01UhJDDNG0+E8Uok4M1dXVfndWuimlfsD4A1pKSkoi+oDSNdBwX2hSlZif54MKoAIlLCnmQsQQDPzQvLS0lJM1T01Nobu720tfIPVDn+jWciHthNFohFar9XpvdGZHqLWGSj6G8zmfi4jLUAKqZZDyCzObzTh+/DgnhOrr64u4Ccpms6GnpycqnpG0x0OMKe1cjBiCwVfWLCTXpgKrUH/TeBGD2Nfgz6AEPn9vvb29sNlsIbUTwfIxc5n8pSImVQlfUC2D2PMdNUDhC6Ei8Y6kIiiWZdHQ0BBWoo06ONH1DQwMiO7xmKsRg9hNKyTX1ul0XKIvmFw7XpWPcOH73ny1E/yZHQqFIqgDNBDcIXo+IS4Rg9hNzW9Y8jVACTWmLhCoH0NZWRmsVmvY2XcaMZw8eRI2mw2NjY2inYyEiIG2hAe7+85FQvGda+FwOATl2nRsQDw8H6NFPsG0EyaTCampqXA6nbDZbIIJWkLInPt7hYu4HiWCgQqMioqKBEfXK5VKOBwOSa9Lrexp+XBgYEDy2ik8Hg+Gh4exaNEi1NfXS/og8jc49bLU6/Woq6vj6vF9fX1ITk7mQvj5ksDylWvTOy6VayuVSmRkZMQ0cohVuVVIO3Hs2DF0dHTA6XR6JTGpIVGgI2osvBhOfU+J2clTI4SQL0frvcftKBGMGGhCMJTASOxRgr/5xFrDB8PMzAx6enqQlZXFlcSkgBKDx+NBa2srkpOTOQNWtVrN3X3tdrtXr0B6ejrsdrvk/IxYRPvuxr/jUrl2Z2cnDAYDtFrtvG65pglalUqF+vp6L4envr4+uN1uvPbaa1yrPH89MfRiAIDdANoBhD/qTQBxO0oIuTgRQtDX14epqamQCUGxxxG+HHndunURf2AmJyfR3d2NxYsXw263h3UN2nZ95MgRLFy4EGVlZZ9vSrMZivZ2wG6HpqICxacUkyzLYmJiAtPT0zh69ChUKhUXTURTZxDL87BKpUJ6ejoKCwtRUFDgJdcGPj+/RyrXjmdnJX0dX4cno9GIf/3rXxgaGkJ9fT2+/vWvc1FBLLwYAHzMMEwJgEsxq4i8NZrvNWE5BmrnlpqaKiohKEaSTMVVUlu6hcCPOhoaGmA2m2G1WsO6lt1ux9jYGGpqarwrGBYLkt54A3A6QVQqKE6ehGfTJpDKSu7um56ejpqaGq7zsLOzkwtj8/Lywp6PEC/QI4RUubYUzIUGquzsbFx66aXo6urCn//8Z+j1eu57MfJiAIBfAvghgKgrqhJylKClSDrbUQxCRQwTExPo6ekR3VQVDLSKoVaruagj3ETg+Pg4xsbGUFJS4lfWZAcHwZpMAP3QqNVQNjXBferOwge/89BXZ0BVi3l5eSEH2fIRbz8GPoLJtT0ejyQDl3ha1IuxjlcoFH5GQdEGwzBfBjBJCPmMYZh/i/b145Z8pIlD2lgl1ZMhEDEQQtDd3Y3p6Wk0NDQEPbvSkmOwD5rNZkNTUxNKS0tRUlLCPR5O23Vvby8MBgMWL17s9z23242kpCQwDAMPy85uILcbzKnXCbZGvs6AEMJFE9SMlYboYjbVXGiiEpJr8w1cNBoNJ7ASIr5EujfxEWcvhq0AtjIMcwmAFACZDMP8iRByVRhvzQ9xzTG0tbXB7XaLmsUgdA3fjelyudDS0oKMjAxRo+YUITYd7bIUUkVKiRhoklGlUmHt2rUYGxuDy+XifB/pHY4pK4MyMxMKnQ6sWg1mehrO88+Hx+PhvkKREcMw3AyI0tJSTtnH31SURKSG6AFf81//QuqVV4JxOODcsQPO3/0u4HPDqUbwDVxoNcDXhZov145HSRQILYcO5BAdIy+GjwHcBQCnIobbo0UKQJyOEm63G8PDw6isrAwqHQ4G36oEPY4sWbJEtLt0sLs+NaYN1GUpNmKw2+1oampCcXExd66kkYoXKTAMkJYGz9atYNraoHA4QL74RSSXlUHJsnC73RgbG0NKSgqn36BHmmCbgK/sEwrR+f4M4YB5/32kXX757P8DUL34IpQffQTbqYSiLyItUwaTa/f09EClUiElJSXiwcliEG7LdTAvhoaGBmzduhUIz4shZoh5xED/gNnZ2SgvLw/7OvyjxNjYGPr6+iQfR4Q2N8uyaG9vh8fjCTqlSkzEQGXSvmVXhmG4u7+fMi4zE2TDBvCvTAjByZMnvQb5sizLvX+Px8MRRDCSEArR+WYnarUabrdb0rTrVB4p0P8qg+hDoq1fEJJrDw4OYnp6GocOHZIk15aKcN2bgMBeDBTheDHwvv93AH8PuLAwEDNioNZmBoMB1dXVGBkZieh6NGLo6OiAxWKRZNLCvwafGBwOB5qbm1FYWIjy8vKgH+BQEQN1lPKVSRNCkJaWhoGBAeh0OuTl5aGgoCCgTwC1v1+0aJHXOVSpVCI5OZkjCKqLoGVgpVIpKprgJ/y0Wi36+/vR2trq5faUkZERuCEMn5OCGMQ6zKf5B5VKhfLycklybakIlcuYmZkJaTE4XxATYqBDaTMyMtDQ0ACbzRZxqOdyuWC1WqFUKrFmzZqwjyN0c9O7u5DVfKCfFYoYKAFOT0/75U5okpFO2HI6nZx8eGZmBllZWcjPz+dG55nNZm4SdzChF/1wsqeSlvxchJRoIjU1Fenp6Vi1ahUn/x0eHobZbEZGRga3qXwJmEA8OcSjYkA3bDC5ttVq5RqkqFxbKsREDKfD3EogBsTAsiyOHDnidfYXI4kOBjpqXqVShaU8pKDEQJu0pAy64TdRUXg8Hq4tnD/cxi/JeOpxlUrF+QTQZqSpqSn09fWBEAKn04nq6uqApCD0fgBwH1YaTdD/0t95oNwEn+h85b9UjDQ8PAyGYT53oqY/i1lyCJWOjUcTVaA7eSi5tlR3bTHJx9NhbiUQA2KgTtC+DVCh5lcGAu1krK+vR3Nzc0RrYxgG/f39YVVGfCMGmmSk2gKKQKQgdD16dxsaGsLY2BjKysowODiIrq4u5ObmIj8/X5KASUw04UsSQuvzFSPxnaj5sjExNZpEEgMfQnJtX3ftQBESha9LuS+C5RjmG2JylEhOTvbaROFMgaKmrw6HQ1InYyC4XC7odDrk5OSEdRThRwyBkoxiSYH//M7OTrhcLk79WVFRAY/HA71ej4mJCXR0dCA1NRUFBQWSSo7Bogn6/263m1tzsI3Fd6IOBFqqS0TbdaghMEII5K49PDwMQFiu7fF4ggrIAjlEz0fERccg9YNBk4JCpq/hfNCoVDojIwOLFi2KKD8xNjYmeAyhd2e+BDgYaE9HVlYWli1b5vV8pVLpVce3WCyYmprC8ePHwbIs8vLykJ+fL6nHwDeacLvdGB0dRVpaGnfsEFMODQR6js/KyuKMTmjb9VyIGIJBrFzb5XKFLFeeDn6PQIyIIRIfAaPRyI1z800K0utK+aDR1uva2lpMTExE5AJls9kwOjrqF8HQJCMAUR9Qu93OeUSEkoTzS44VFRVc5DM0NASz2YzMzEwugSn2rsmyLFpbW5GXl4fS0lKvSIdGE2ISmHysXr3ay8Slv7+fa0W22+1ISUmZN23XgeTaWq0Wer0eRqNRUK4dKMcQ7ZZrhmFKTz2/CLMnuv8lhDwetV8A4hQxiMXw8DCGhoYCJgUDjakTAu3c1Ol0XOu1VqsNixjo3R2AV5IRQGB9QgBMT0/jxIkTWLlypSTPSYrk5GSvEJgmMOlGpOKmQCEtjcZ8SUlsAjMYfKsC1GNjYGAAXV1dXo1f0dQYxFISzSdmq9WKhQsXwuVy+cm11Wq1oEN0LFquMSt0uo0QcpRhmAwAnzEM8x4hJOAUKqmIKzEEuttTkRFNCgb60AiNqRMC3/eA33otxdOBgp9ktNlsISsPwTAxMYH+/n7U19dHpXWaYRguoVZVVQW73Y6pqSl0dXXBbrcjJycH+fn5yMnJgUKhwMzMDFpbWyMqh0pBSkoK1Go1Vq1ahaSkJBiNRuh0OvT29ka1jTyeU6iSk5ORnZ3tJ9fevXs3enp68NOf/hSXXHIJNm3aBIZhYtJyfUoOPQYAhBAzwzDtmO24nH/EQHsdfDc937kplMgo2DQpCpvNxlnD86sFgPQkKD3WrFq1Cjk5ORgcHATwOSnwz+XBQE4NttHr9Vi7dm1EE6qDgbpp09mP1CClq6sLSqUSNpsNq1evjqgcGgiB7tr0ZkDLg/S1o9lGHi9nZt/X4cu1//znP2Pjxo3YvHkzDh48iE2bNgGIacs1XUMFgDUA/C4aCWKWY/AFvdvzf7G+o+ZDIdQdn16PbmSpP89HIMNXfpJRDCnQaIhhGNTX18fNO0GhUHB3ZKrKXLRoEfr6+tDd3Y3c3FwUFBRITmAGAq1y0IiDPjdQlBjNNvJ4RgyBCIgQAqVSiS1btuBLX/pSzNcCAAzDpAPYB+A/CCGmaF47rhEDdYomhGBoaAijo6Neo+bFXCPQxqaj64ONmlMoFCENZQkh6OrqwszMjGCZVErlgXZ/5ufnh908FikGBweh1Wq9JOR8laPJZEJGRgaXwAw3mlGpVIK5CTERmm//A38upZg28rlg1AIIk2CMWq7BMEwyZknhz4SQl8N8SwERV2KgH5gTJ2aPQsGaloQQSRNUoJ/ngyYZU1NT/bQOHo8HKpUKTU1NKCgoQH5+ftC7mdVqRUtLCyorK1FYWCj6PUYLlOAcDgfWrFnjtXF8VY4mkwlTU1OcIpCfwAy3HEoIgdFohNvtBsuycLlcosuh/DZyj8fj583g20Yer7brYBWxQFW4WLRcn8o/PAOgnRDyaDTemy/idpRISkqC1WpFW1sbFi1ahNLSUsl3UN+Iwel0chu1oqJCtB+DEKhBC39KNeCdZKyvr4fNZoNWq0VbWxs8Hg/XFMVvPDIYDNy0q3DbmyMBLUdqNBqsXr066O+FYRhkZWUhKysLS5YsgcPh4DpirVarVwJTLIkrFAro9Xp0dXWhvr4earXaT1wFzP49Q21opVLp1UZOowm+05PD4YhbNBbodex2u2DkG4uWa4ZhzgVwNYDjDMM0nXqpHxNC3ora+wyhNwhLjMDv+qNoamrC9PQ0amtrBc//YtDT04O0tDQsWLCA659YtmwZCgoKRP381NQUdDodli9f7vW4b5KRIlTlgWoKtFot1xSlVCphNBpRV1cnyWYtWqDHl8LCQtFzOQOBJjCnpqZgMBigVqtxzrnnCj7XZrFw/z85OYn+/n7U1dX5KTX55OCrjpUqrqJOT52dnVAqldzw2ry8vKi6UFMcPnwYjY2Ngt/TarX47ne/i/fffz+cS8+5CTUxP0rQjLzRaERVVVXYpAB8XpWgfgz19fWSJKhCVQ2aZPTNdYhRMvI1BfSIpNfroVQq0d7eLurIEU3QCs/ixYujcnzhJzABiDLDHR0dxejoKNasWSOYr6BHjqSkJO7IEY7XBPC509PQ0BBqamo4+30pbeTRQiD3pvmKmB4lqJ4gKSkJZWVlEZ8DGYbB6OgoFApFWPZw/KME7VOwWq2CSkYpSUZKCmq1Ghs3bgTDMJyMOdiRI5qgGoUVK1aEJZwSg2CdqFQA5nQ6sWbNGlHHDn45VMhrgv5/KK8JWkbMyMhARkYGpxAV20YuBqGUvKdTnwQQw4iBjpqnpqpDQ0Nhd1gCn9vDqVSqiPwY6DGnpaUF6enpflOl+EpGMUTmdDrR3NyMhQsXeukmaH27vLycO3IMDAxwR46CggLk5uZGpf6u1+vR2dmJmpqahH04FQoFTCYTlEoljh49yuUFxLY002uE4zUhVK4M1kYOgIuExK4vVEk0kK3bfEVMiMFsNuPYsWPcaDggvBFzFBaLBc3NzVw5Ldw7Li1XHj58GOXl5V5uO+EoGeldeunSpUF1GPwjB8uyXp6FKSkpyM/PR0FBQVhmrePj4xgcHMSaNWuiZvYaDpRKJc4++2wwzOxwHeozYbFYkJ2djfz8fElEGKg7VCiaAII36gVrI5+ZmfGbtykEMdbxMjGEQHp6ut9ouHCnVdMmKHqGnJ6eDntdZrMZBoMBDQ0NXuF2OKSg0+nQ1dWF1atXS/ad5CsA6ZGjtbVV0pHDV00ZaVt6pFi+fLmXIQ3fIMXXvJXmXqRIoQNFE3SEn9Pp9BNXBYJvy7XJZIJOp+PKtTSa4JdrxRjBykeJEFAoFH5ZYakuToQQ9Pf3c+IclUoFl8sVthMUnWeRkZHhRwpS8gnArEhlbGwMa9eujTj77XvkmJqa4o4cge60hBB0dHTA4/HEVU0ZDMEMaXyl0FNTU2hvb4fT6QzbkAaYrcDQhjSazBTjXOW7blqurayshMPhgF6v97KDo5qJM8W9CUiA8lEM+E1Q/PF1YnolfMFPMq5duxYtLS1e35NCCvRaTqcTa9eujbo+Pzk52cv6zWg0QqvVeh05cnNz0dXVhfT0dK+79HyBRqNBaWkpJ17S6/UYHx9HR0cH0tLSuNxEKMKlPTG+yVZ++ziNLCg5iMkbqdVqr78BjSa0Wi3cbjcGBwe5aeT8332wo0QsJl0zDLMFwOMAlACeJoQ8FPSNSUTclY+hIDSXgUJqdyRNMmZkZKC+vp77sADSPRTo2LqMjAw/Y5VYQOjIMTExgU8//RTJycnIyMjg7lLzjRwofA1pZmZmMDU1xVn4UUMa32OVxWLB8ePHsWrVKj8BmdCRg08UbrcbDMOIElfx7eDy8vIwOjoKpVKJnp4e2O12r8Yvq9Uq2JwWo7ZrAPg1gIsw21h1mGGY1+d823WwJqpgCNUEJSVPQasiFRUV3IBbWq6U6qFAjVVKS0sjHpYbLhQKBSYnJ7F69WpkZ2f7JfcKCgpiMkuBD4vFgujN2fYGwzBcuZEmCH0rOfn5+VCr1Thx4gRWr14d0i1JKIHJP25IOXJ4PB6o1WoUFxdz08hpG/mTTz6Jd999F42NjfjCF77AtVgDMZt0DQDdhJDeU7+7l049d24TA+Dv4pSUlBT0KDE8PIzh4eGgTVViiYESjNCoOZqoElvdMJlMaGtrw4oVKyISZ0UCuoZVq1ZxVR6hIwftTKTJvWhWKcxmM1pbW3FB1K4YHL6O2iaTCSMjIxgfH0dGRgYMBgOUSqVol28gMnGVb/KRH9Hdc889MBqN0Gg02L17Nx544AHU1dUBiGnb9ZDP42eJ/kWIQMKPEizLcl10kTZBAZ8TjG+XJf0QLFy4EMeOHUNycjIXxgZSJk5OTqK3txd1dXWSPoDRBK1+BFoD/wNKewm0Wi3nD0lLoZEcOQwGAzo6OrgPe7xB7+hmsxkbNmwAwzCYmprizIJ9DWnEXhMQL64KVZUAZqOBjRs3Rvx+5wLiRgxCm5qKg/Lz87Fy5cqQH9xgEQPN1Nvtdj+C4ScZKyoqsHjxYr9mKP4GAsBNjlq3bl3MjFVCYXR0FCMjI6KrH3zjEKr+i/TIodVq0dvbi/r6+oT0fgCzvSwnT55EXV0dF03yE5jUkKazsxOpqalcAlNKxBRKXEXLoYFavAOVK2PVdh3k8aggbkcJ301vNpvR0tIiqQkqUMTgdrvR3NyMzMxM1NXV+blKCyUZNRoNysrKUFZW5reBCCFISUlBXV1dQvQB1K/SZDJFVP0IVOXo7u6GRqPhyDAQ6YyNjXHHu0SRI1V1BiIm3+7LaDlq02sDs0e58fFxrFq1KmBuIpBDdCzarjHbdLWUYZjFmCWEXQC+LurNiURCVDHUUUhqE5TQH1YoyQhIEy3RDZSfn4+WlhakpKRAoVDg8OHDyMjI4GY6xIMk6NEKAGpra6OmUfA9ctAN1NLSAkKI30zNwcFBTE1NxaQsKxZUFCVW1cnEwFHbYrGgra2NG6AsFE3QYcHxnHTNMMxNAP6K2XLls4SQNlFvSCRi0nYNzIpPfO/uH374IQoLC2EymVBbWxvWXeijjz7COeecA2D2btLe3u4lvQbCUzLabDa0tLR4dSZSjf3k5CR0Op2ovEQkoCPvsrKyRPlLRAu0AqDVamGxWLiwes2aNX4bSCNA5ASAndd2HQ3Q1u36+vqotFDzHbVpByyNNHw1CRQWiwUtLS2oqakJqFFgWRYfffQRrrnmGrS0tIiOfn0w5+rNMT1K8OF2u2Gz2cCyrJ8FezgIZOUWDikYjUa0t7d7Zf3pe6Aa+6qqqqB5iUjfD823FBcXx31iMq0ALFiwACdPnuRMRw4fPsyd2YMdOaKNiYkJrv8jWkcYhueoDcDPUZuff6FHg5aWlpCS96NHj+KHP/whPvnkk3BJYU4iZhGD2+3mzmK0Ccrj8eCcc86JKDT98MMPkZubC4fDgZqamoBJRrGkMDY2hqGhIdTW1kqKAmhegt5lqblqOC7H1AYuVDNWLMGyLNra2qDRaLBkyRIuR0SPHFqtFgDwxX/7N7+fjWbEMDY2hpGREdTX18ctv+NrSJOcnAyLxYLq6uqgf4+mpiZ8//vfx8svv4wlS5ZEsoQ5FzHEnBhoWWn16tXo6upCTU1N2PV1l8uFf/zjH6ioqOA+vNxCJSoZCSHo7e2FyWRCTU1NRB9ClmWh1+uh1WphNBol5SXoAJpE2cABs0eYlpYW5OXloaysLODznE4nsgS0HNEihuHhYUxOTqKuri5heQ2r1Yqmpibk5+fDbDbD7XZzCcysrCzuM9fa2orrr78ee/fuxbJly0JcNSTmHDHEjJJpE9Tk5CQaGhq4JpRwm6DoH0ylUqGysjKgh4LY3voTJ04gOTnZz48hHPANVGm3nlarRX9/PzfuTMjJifZBRGsATThwuVxobm7muiGDIdhRorm5mRNWhXPkGBoawtTUVEJJgeaZVq9ezZG02+2GTqfDyMgI2tvb0dbWBr1ejz179mDPnj3RIIU5iZhFDL29vTAajVi5ciV3B6fJPamDP6mV+OrVq9HR0cGdPcPJJzidTrS0tKCoqChiT0QxoHkJrVbL5SUKCwthMBgwMTGBurq6hJUCHQ4HmpqaUFlZKfp8HCj5ODUxAa1Wi6mpKQDg8hJinKb7+/sxPT2NmpqahHWK0qaslStXeuWZ+CCE4I033sBDD832K2VnZ+P5559HeXl5pC8/5yKGuFYlTpw4gYULF0qSFtP5E9Rc9bPPPkN1dTXUarVkUqDNN1VVVX4Dc+MBl8vFRRIOhwMLFy5EYWFhWHmJSEHzGsHG1QlBTFWCGrVotVrOaZqf2OOjt7cXMzMzWL16dcJIgTbuBSMFAOjr68PXvvY1PP/881izZg0mJiaQk5MTjaTsnCOGmB0lhMRIUo4SLMuio6MDTqcTDQ0NXHhJ27f5I9ZjaawSTSiVShgMBuTm5mLp0qVc1NDR0RFXvQTte4hVXsPXqMVXmUjf59DQEJdETlSHKCWFFStWBCWFwcFBfP3rX8czzzyDNWvWAACKioritcy4I27lSkA8MdBzb05ODlasWOF1LYVCAafTCbVaLfoOQ41VEml/RlvAc3NzuRmdgfIS1OUoXLu3YKDy4traWumOQzMzkl+P74hEqxxarRaffvopCCEoKyvj5MTxJgc+KQQz0B0ZGcGuXbvwm9/8JqB9/OmGmB0l6PQhPuiHPliSi5Y2Kysrvca0A7NJRjoxWqVSobCwMGh9nU5jstvtqK6uTlhSi46eF9u2TRuhpqam4PF4OJKIdPNQJWHYMy+Gh6HxmckBSKtKEEJw8uRJKBQKVFRUcMKqUEeOaMPhcODYsWNYvnx50KPt+Pg4rrjiCjz22GM477zzYrWcOXeUiCsxDA0NcXcJIdAkY01NjVeIK5RktFqtmJychFarBcMwKCgoQGFhIZfdpy5QaWlpfqXNeILmNaSe5SloXkKr1cJms3GbR2pegvY91NXVhX8mbm6G5pTqlA+xxEAIwYkTJ6BSqVBVVeX1N+EfOQwGgyQ3J6kQSwqTk5PYsWMHHn74YVx44YVRXYMPzhxiIITA6XR6PTY6OgqHw4HFixf7PX9wcBBjY2PcSDP+dUKNnHc4HNBqtZicnITL5UJ2djb0er3fuLl4gyoqxZiKiAF/juP09LTovMTQ0BC0Wi1qa2sjy1+89RY0X/2q38NiiIEKqNLS0rB48eKQRrf0yBFOlSMYnE4njh07hqVLlwYl6qmpKezYsQP3338/tmzZEvbricSZTQyTk5MwmUyoqqriHqNNQ2632y/cD0fJaDAYcPz4cWg0Gng8HuTm5qKwsNBLnBIPTE5Ooq+vL2aj6vh5CZ1OJ5iXoCKumZmZ6JQC//AHaL7/ff+1IDgxsCzr1QMiFb5VDmogK/XIQUmhqqoqqKLRYDDg8ssvx09+8hNcdtllktcbBuYcMcS1u9LXENblcqGpqQl5eXl+d5FwSIEKhtatW4e0tDTObJSKU7KyslBYWIjc3NyYnmGHhoYwOTkZ03ZlvrtxVVWVl0EL7ZakDVG1tbXRIcWJCck/IlZVGQy+VQ6qMu3s7ERaWhoXNQU7coglhenpaXz1q1/FnXfeGS9SmJOIWcQAwG/AjNFoxMjICKqrq7kk45IlS/zKPlKVjIQQr3BZaDPy/Qj0ej3S0tI4RWK0yoOEEHR3d3PJzkTV5Wmyk46e50dNEa3p5puheeYZv4dZAA6BiMHj8aC5uRmFhYVeU7qiBb6BLD1yUPUl/8hBp6JXVlYG1a+YzWZcccUVuOmmm3DllVdGfb1BMOcihrgSg9lsRl9fHxYtWoSOjg5RScZQoHoHlmW9VJbB4NtOLabCIWYdbW1tUKvVWLp0acKSnfQOnZOTg4qKCi5q0mq1XnmJ/Px86VWaXbugeeMNv4eFiIGa5yxcuDBu3aIOh4MjCZqozcnJQV9fH5YsWRKUFCwWC3bu3InrrrsOV199dVzWy8OZRQxOp9PLxclms+Ho0aNISkoKmGSUQgpUG0A3QbibMVSFIxTo6PmCgoKww+VogOo/Fi5cKJh0FZOXCIpNm6D5+GO/h32JgR4RS0tL/UrO8YLH44FWq0VHRwcUCgU3LzQ/P98vorTZbLjyyivxta99Dd/+9rcTsdwzlxjoHXVqagrnnXee1509nHwCbXipqKiIqgLNt8JBexsCeS5Qa/ny8vKEKuHo8aGiooIzmgkFmpfQarUghITO/K9ZA01np9/DfGKgYbuUdcQClJwqKiqQn5+PmZkZjhCpuEyj0SAjIwNXXXUVtm/fjhtuuCFRkd6cI4a4JB+pCUlubi5nm0YRDinQVmVfY5VoQK1Wo6SkBCUlJV5ekDQbzq9wzMzM4Pjx4wm1lgc+bwCSqpVITU1FeXk5ysvLucx/T08PbDabl78E9zcJUZKkTVmhwvZYw+12o6mpCeXl5VxzGJ1ZQcfQTU1N4YEHHsDbb7+N5cuXY9myZfB4PFGXoz/22GN4+umnwTAMampq8NxzzyXMVFcKYhoxuFwumEwmtLS0oKqqCgUFBfj44485aza+p7/YpNj4+DgGBgZQW1sb11ZlelanJdeUlBRYLBbU1tYmzEcBAEdO0SRJobxEYWEhiurrkSIwVJgFMK3ToampKWwhV7Tgdrtx7NgxlJWVBY3gXC4Xrr32WjQ2NqKurg5vvvkmHnrooaj+LUdGRnDuuefixIkT0Gg02LlzJy655BJ861vf8n3qmRUxaLVaTpfPF/iEk0+g/g5GoxHr1q2Lu3szf5za2NgY+vr6kJuby4l2ol3hEAMqoAqr7yEIfEfH0bxEXpBeCTE9B7EGjRRCkYLb7cZ3vvMdrFu3Dj/60Y/AMAwuueSSmK3JZrMhOTkZVqs17rZ94SKmn2Kr1cpNquYjnMrDiRMnkJSUhLq6uoROd6bzJtavX891eNIKx8DAQFQqHGJAu0VjbfLC10sogkSXc4UUSkpKgpKCx+PBD37wA6xcuRI//vGPY5pTKC4uxu23346ysjJoNBps3rwZmzdvjtnrRRMx3WEVFRVem4MQAkIIxsbGOGIIBafTiaNHjyIzMxMrVqxIGCnQgTZms9nLj5AaxlZVVeGss87C8uXLuerAkSNHMDAwAJvNFtW1jI+Po6enJ+g4v1iACTAFjAA4efIkOjs7YTAYEOJ4GnVQvURxcXHQKojH48HNN9+MkpIS3HvvvTFPNBoMBrz22mvo6+vD6OgoLBYL/vSnP8X0NaOFmOYY+IawNMk4MzOD8fFx6HQ6aDQaLgQXEiXRBqQlS5Yk1IHX4/Ggra0NqampkhqypFY4xGB4eJhzfor7cSotDUIxkAeAzWTyyktkZmZyisRYdrV6PB40NTVh0aJFQTtXWZbFrbfeivT0dDzyyCNxucHs2bMH77zzDp45JQr7wx/+gE8++QRPPfWU71PPrBwDBd+olWaHq6qquNHuR48e9QvB9Xo9ZyIbjQakcEHv/gsWLJCs3gtU4bBYLMjLy5PUw0FzLCaTCfX19QlpIQ+2SqG8BJ39qVarY+IvQSMFOm0rEFiWxY9+9COoVKq4kQIAlJWV4ZNPPoHVaoVGo8GBAwfQ0NAQl9eOFDGPGJxOp6h8gtVqxcQp30AaadTX1yeUFKhWQoonohj4VjhC9XBQXwmXyyVa3RkLJKWlQajzwwPAGaSUSQVkU1NT4vQSIkBJoaioKGgHLcuyuOeee2A2m/Hb3/427r+7e+65B//v//0/JCUlYc2aNXj66aeFyHHORQwxJYbnn38elZWVou9whBD09PTAZDIhNzfXS/8uRYkYDVD7s1hoJfhgWRbT09OYnJwU7OFgWRbt7e1ITk5OqNQaAJLT0gRDTDcAl0ijFn6nZEC9RAiIJQVCCB544AGMjY3hmWeeSZhRjwj4vXGGYS4D0A7AQggZYxiGIXFM3sSUGF555RW88MIL6OjowAUXXIBt27ahsbFRkLXpOV6j0XiZeDgcDkxOTmJycpJzMyoqKorpWHqa8a+pqYlqGTAUhEbiORwOFBQUeLWqJwI6nQ4LysoiJgY+fPUSYvISLMtyVvXBjnaEEDz88MPo7u7G888/n5DhxBLgRQwMw7wBIAXAMGYnX/+KEPL3eJJDTImBwmaz4Z133sHevXvR3NyM8847D9u2bcOGDRugVCphtVrR1taGRYsWBb0DOJ1OLpnndDqRn5+PoqKiqPoFRsXpKApwu904evQo1Go1nE5nWD0c0YJWq0VfXx82nn9+VImBDzpbksqW1Wo1FznR0JuSQn5+flDrf0IIHn/8cRw7dgwvvPBCwuz5JYD78DIM8yUAtxNCLmQYZiGACwDcBeAOQsjbcVtQPIiBD4fDgffeew979+7FkSNHsHr1ajQ3N+PVV1+VNOeBJvMmJydhs9mQl5eHoqIiZGRkhEUSfAFVbW1tQsNO2m/A77+IRYVDDOhw2TVr1iA1O1uQGFwA3FEeast3cKL+Enq9PuQ8EEIIfvOb3+Bf//oX/vKXvySU3CWATwzrAPw7IeRbvMe+CuAWALsJIYfjsqB4EwMfb7zxBm655RacffbZOHbsGNavX4/t27fjvPPOk/QHpaPwJicnMTMzg9zcXBQVFUnK+J88eRKEkIRqJYDP+x6CzbHkz80U6uGIFmj0VF9fj+TkZKjS0iBEl7EgBj6omzPtpwn0fgkheOaZZ/Duu+9i3759CXMEDwMMwzAKQgjLMIwawD8BHCaE3HTqmyoAtwEwEEJ+G48jRUKJ4ZVXXsEXvvAF5Ofnw+124+DBg9izZw/+8Y9/YM2aNdi+fTsuuOACSU0nvhn/nJycoENdqGlsRkZGSC/CWCOcvgepFQ6xGB0dxdjYmJdeIhAxOAF4YkQM1BYuOzsb5eXlgnmJjIwM5OTkYN++fXjttdfw2muvxaRRyWg04vrrr0draysYhsGzzz6LDRs2RHxdhmHuAZALoJsQ8iTDMDkAXgdwlBCy+9RzrgCwmRDy3YhfUMyaEkkMgeDxePDRRx9h7969+Nvf/oZVq1Zh+/btuOiiiyQlHanz8MTEBKanp/02De36DJXbiAdox2hNTU3YA3EIITAajQErHGJB3bB850jGmxhYlkVraysyMzMFvSJpXuKf//wn7r77blgsFtxzzz3YsWNHTFq+r7nmGnzhC1/A9ddfD6fTCavVGrEM/MYbb8RTTz31JoDfAXgIwLOEkEcZhlmAWXIYAPAcZvMM7xFC7ovsXYjDnCQGPliWxeHDh7Fnzx689957qKqqwtatW7FlyxZJGge6aSYmJmAwGKDRaGA2m7F8+fKE+gYAn1dB6urqopZYDNelamBgAAaDAbW1tX4RRyBicCgUYM3mqKybgpICjeSCYc+ePXj22Wfx+OOP4/3330dFRQWuuOKKqK5nenoa9fX16O3tjVpU+de//hWPPvoo3n33XRUhxMUwTAOAXwO4iBBiAgCGYf4Ts/ldFSHkp1F5YRGY88TAB8uyaGpqwt69e/H222+jtLQUW7duxSWXXCKJuaenp7nwdGZmBqmpqQnpjgSAiYkJDAwMoK6uLqZnYjEuVX19fTCbzQHnSKrT0gSba+waDcgpzUk0QAhBa2sr0tPTQ5LCq6++it/85jd48803Y6o3aWpqwne/+12sWrUKzc3NWLduHR5//PGIytnj4+PQarWoqalhTuUW0gG8B+BSQshYtNYeDuYVMfBBPzx79+7F/v37kZ+fj+3bt+PSSy8N6gI8NTWF7u5u7u5MDUUnJiYwNTWFlJQU7s4a6zLXyMgId46PZ0mNX+Fwu93Iy8uD0+nkLPwD5SYCEYMtOxsYGYnK2gghXF9KZWVl0Ofu378fjz32GPbv3x9zo5wjR47g7LPPxocffoizzjoLu3fvRmZmJu6///6Irut0OqFSqfhVibcA7CSEzDAMcz2APYQQfxOMGGPeEgMftPNx7969eOONN5CZmYmtW7fisssuQ0FBARf6jYyMcJOzA4XTtH9jamoKSUlJKCwsRGFhYdTLXrQ0WlNTk9DSqMvlQmtrKywWC5RKZdAejoDEUFoKnDwZ8VropKqUlBQsWbIk6HPfffdd/PznP8dbb70V9EYQLYyPj+Pss89Gf38/AODgwYN46KGHsH///rCvSassmK1KqAghToZh3gTwEwA/BODkly3jidOCGPigsmqaoVapVLjsssvQ0dGBc889F1/5yldEb0R++K1QKLjwO5KMN7WYdzgcWLVqVUJLo5RQAWD58uXczIZAFY6AxLByJXDkSMRrOXHiBNRqdcgO1g8++AD33nsv9u/fH9f80Be+8AU8/fTTWL58Oe69915YLBb8z//8T1jX8ng8UCqVsNvt0Gg0yYQQNwCcIoblAN6iFYlE4LQjBj7oJKZvfOMbmJ6eRl5eHi677DJs374dJSUlkpJIdrudk2YTQjhptpRkISEE7e3tUCqVWLZsWUJLo3QtSUlJgj0YQhWOxg0bhIlh40bg3XcjXktycrLfTEtfHDx4ED/+8Y+xf//+uDtQNzU1cRWJyspKPPfcc2EdYSgp2Gw2bNmyBf/85z+/Rgh5CQAYhvklgGJCiP8swDjitCYGAHj//fdx9OhR3H777RgfH8e+ffvwyiuvwGaz4dJLL8W2bdtQWVkpaZM6nU6OJNxuNxdJBEtE0Xr8XNBLUEcsGrKHWgutcBQsXChMDNu2AS+8ENZaqLgsKSkpJCl8/PHHuP322/Hmm28mvLwcLigpOJ1OXHbZZWhsbMQDDzzAzzEsJoT0JXKNwBlADIEwOTmJV155BS+//DL0ej0uueQSbN++XfKdnE6jnpiY4BqefKXKdPhKYWGhJNl3LCClDOiLQEeJ4V27kPrkk5JLrZQUlEplyM7RI0eO4Oabb8brr7+e0NkdkYBlWSgUCrAsi8suuwzV1dV4+OGHgdkcg5IQ4kn0GinOWGLgQ6fT4bXXXsO+ffswPj6Oiy++GF/5ylckex+43W5Omm21WpGXl4ecnBz09vairKwsYcNXKFiW5Qb0lJeXS/75QMQwuHs3hq64gqtwiOnhoPkNhmFCknFTUxO+//3v45VXXglZqZhLoETg+9hFF12E2tpaPPbYYwCAU6Qg7JuXIMjE4AOj0Yg33ngDL7/8Mvr6+nDRRRdh+/btkk1oPR4PxsbG0N3dDaVSyVU3pPgORBPUw6CgoCDsqCVg8vHJJ4FrrxXdw0EIQWdnJwghWL58edDfR2trK66//nrs3bsXy5YtC2vdiQCfFEZGRkAIQUlJCY4dO4b3338fd9xxB/95Z5ZRy3yH2WzG/v37sW/fPnR0dODCCy/Etm3b0NDQEJIkLBYLWlpasHLlSmRmZkKv12NiYgImkwnZ2dkoLCyUPMY9XNCjzIIFCyI6mwckhldfBS66yOuxQD0cOTk56OnpAcuyIUmhvb0d1157LV566SWsWrUq7HUnEnfccQeGhoZgtVpRX1+P++77XNFM8w040xycTifwPSVaWlo4T4mzzz7br/xpMpnQ1tYm6FdJp25PTEzAaDQiMzMThYWFyMvLiwlJUM/K4uLioL6IYpCSlib4CbY1NQFLlwb8Ob4cfXx8nEs0BlOadnZ24pvf/Cb+/Oc/o6amJqJ1xxt0wz/xxBM4ePAg/vSnP2HXrl0oLCzEb3/7W6EfkYnhdIDdbuc8JT777DOcc845+MpXvoKNGzfi0KFDAID6+vqQDV+0CWhiYgJ6vR7p6emcNDsaoic6vzHUABaxCEgMHR1ACKNcqt9wOp0oKSnhplIL9XD09fXh61//On7/+99jzZo1Ea87Xujt7fXKgbz00ktYuXIlXnjhBQwNDeGFF16A1WrFsWPHsHHjRv6PnrnE0NTUhO9973uw2+1ISkrCU089hfXr10fr8gmD0+nEBx98gL179+K9994DwzB44IEHcOmll0pSS/KdlfnW+gUFBWH1b1Czl8WLF0fNyDYgMYyPA0Ea2qjojIq6+McHvojs0KFDGBoawnvvvYc//OEPaGxsjMq6A8Hj8aChoQHFxcV48803I7rWvn37cM011+CGG27AL37xCwDAE088gbvuugvbt2/n5klQY1oft+ozlxg2b96MW265BV/60pfw1ltv4eGHH8bf//73aF0+4di3bx9+9atf4bbbbsPbb7+NgwcPcp4S559/viS1JCHES5qtUqlQVFQkun+DDpetqqqKqlw4IDGEaLnu6emB3W73IwVfUL0JwzBgWRb/8z//gy9+8YsRrjowHn30URw5cgQmkykiYtDr9di+fTt27dqFt99+G5WVlXj88ccBALt378Y///lPPP7449i/fz8OHjwo1Ntx5hLDxRdfjOuuuw5XXnklXnzxRbzxxht4IUxRzFzE6OgosrOzueODx+PBhx9+iH379uFvf/sbqqursX37dmzatEmyka3FYuHuqrR/I9CMBup2FIvhsuEQQ29vL6xWK6qrq4OSwvj4OK644gr88pe/xBe/+EVMT0/D4/HEbEDu8PAwrrnmGtx999149NFHI44YOjo6UFFRgbGxMdxwww1YvHgxl0948MEHYTKZYLFYcO+99wpNAj9ziaG9vR0XX3wxN9D2o48+CquWPh/BsiwOHTrEHTeqqqqwfft2XHzxxZJNWWw2G6e6ZBiGK4OmpKRwtnCxmiMplRj6+vowMzOD1atXByWFyclJ7NixAw8//DAuvPDCKK02OK644grcddddXFgfKTHwMTw8jO985zsoKSnB//3f/6G5uZlzoAqA05sYNm3ahPHxcb/HH3zwQRw4cADnnXceduzYgb/85S/43//9X7z//vsSlzv/QT0l6PiysrIyzlNCqp8A31rf5XLB4XBg5cqVMWsskkIMobwdKKamprBjxw7cf//92LJlSxRXGxhvvvkm3nrrLTz11FP4+9//HnViAGYjyNtuuw1HjhxBcnIyDh48GOxYd3oTQzBkZWXBaDSCYRgQQpCVlQWTyRSty89LUE+JPXv24K233kJBQQG2bduGL3/5y5JC6JmZGbS0tKCoqAjT09NwuVxe0uxoQSwx0FF6oUjBYDDg8ssvx09+8hNcdtllUVtnKNx111344x//iKSkJNjtdphMJlx++eVRHzj70EMP4cknn8Q//vGPUG3kZy4xrFy5Er/5zW/wb//2bzhw4AB++MMf4rPPPovW5ec9aN/A3r17OTeirVu34stf/rKXp4Qv6MQsvlckVSBOTEzAbrdzVvPhWutTiCGGgYEBzmciGClMT09jx44duP3223H55ZeHvaZIEauIQafT4corr8STTz6JFStWhHr6mUsM//rXv7B792643W6kpKTgqaeewrp166J1+dMKvp4SarUal112GbZt24YFCxZwm5sayNbV1QVMaLrdbuh0OkxMTIQ1TJePUMQwODgIg8EQkhTMZjOuuOIK3HTTTbjyyislrSHaiBUxALOJYJHVqDOXGOKFJ554Ar/+9a+hVCpx6aWX0u61eQtCCAYHB7l2cQD48pe/jMLCQnR2duL2228X3dVIZcoTExMwm82ctX5OTo4okggoibZYMDg4CL1eL2giy4fFYsHOnTtx3XXX4eqrrxa17jMAMjHEEh988AEefPBB7N+/H2q1GpOTkwl3gI4mCCEYGxvDz3/+c7z44otYuXIltmzZgm3btkn2eBCy1i8qKgrevzE8DM3y5V4PuTZvRt+vfoWpqamQjWY2mw07d+7EN77xDVx33XWi13oGYH4Sg9vtxocffoiNGzfO6eGgO3fuxHe/+11s2rQp0UuJGaxWK7Zt24Y//vGPYBiG85QwGo245JJLsG3bNsmeEoQQGAwGTE5OwmAwICMjA0VFRcjNzfWXZmu1SL76ajBTU3DdfjuGzj2Xm0ERjBTsdju+/vWvY/v27bjhhhsSalQzBzHnfhmiiKG7uxs33HADPvnkEzz//PNR9+yPFurr67Ft2za88847SElJwSOPPBJzWW0iwDMR5aDT6fDqq6/i5ZdfxsTEhJenhFSSmJ6e5qTZaWlpKCoqEuzfGB4exuTkpN9gGl84nU5cddVV2Lx5M/793/99XpPCz372M+Tm5uI//uM/AAB33303CgsLsXt3RPaMc+4XIooYzGYzkpOTcd5553EyVZZludJjPA1Ng2kl7r77bpx//vn41a9+hcOHD+PKK6+M6oCQ+QKj0YjXX38dL7/8MgYGBjhPiVDnf1/wh9ZQa31KEpOTk5iYmAhJCi6XC9/61rewceNG3HbbbfP+b9Hf34/LL78cR48eBcuyWLp0KQ4dOhSp9HzO/VJE5xg++eQT/OAHP8DRo0djv6owsWXLFtx55504//zzAQBLlizBJ598ErUmovkIvqdEZ2cn5ymxbt06yYQ+MzODyclJjI6Owu12Y8mSJSgqKgrYLOZ2u/Htb38ba9aswV133TXvSYHioosuwsMPP4yJiQk8/fTT2Lt3b6SXnHO/GNGfjLfffhsNDQ0AZj8gn3zyCW677bY51Qi1fft2fPDBBwBm+/mdTqeQLv2MQkZGBnbt2oU9e/bg448/xsaNG/G73/0O55xzDu6880589NFH8HjEWQ2mp6dDo9FAo9Fg3bp18Hg8aGpqwmeffYahoSE4HA7uuR6PB9///vexatWqmJHC0NAQzj//fKxatQrV1dVc41Kscf311+P3v/89nnvuudM2iRoyYmBZFg6HA1u2bMFdd92FLVu2YPfu3SguLsbixYvx/PPPY926dfjP//zPeK05IJxOJ6677jo0NTVBpVLhkUcewQUXXJDoZc1J8D0ljh49ynlKnHPOOQETzGNjYxgdHUV9fb3X8YFvrW8wGPDRRx9haGgI5eXl+K//+q+YRQpjY2MYGxvD2rVrYTabsW7dOrz66qsxd3tyOp2oqamBy+VCV1dXNLwz5lzEAEJIsC9CCCG9vb2kvr6eeDwe4nA4SGFhIWloaCB//OMfSXt7O7n66qtJR0cHfTpxu92EZVkihL6+PjIyMiL4PRmJgcPhIG+//Ta5/vrrSXV1NbnuuuvI66+/TgwGA7FYLMRisZCenh7yj3/8g0xPT3OPCX319fWRrVu3ksWLF5MNGzaQZ555Jm7vY+vWreTdd9+Ny2vdcMMN5M4774zW5ULtw7h/Bf1me3s7ueGGG8iOHTvItddeSwgh5J133iFr164lfX195MYbbyTr168nCxcuJG63m1gsFr937Ha7icfjIYQQotPpyBNPPEFWrlxJNmzYQF588cWABDIf8MgjjxAARKvVJnopUYPL5SIHDhwg3/ve90h1dTW5+uqrye23305uuOGGkKRgNpvJjTfeSG688Ubi8XiITqcjn332WVzW3dfXR0pLS8n09HTMX8vj8ZC6ujrS2dkZrUsmnAh8v4J+02QykV/84hfknHPOISkpKeT//u//yDPPPEO+8Y1veL2r8fFxQgghjz32GKmvryd33303aWpq8nv3NpuNWCwW4vF4yEcffUS+8pWvkN7eXu77ZrM5jN9pYjA4OEg2b95MysrKTiti4MPtdpP777+flJSUkPr6erJr1y7y4osvEq1WK0gKt9xyC/nOd77D3QjiBbPZTNauXUv27dsX89dqa2sjixcvJrfeems0L5twIvD9CvUEDhMTE+Tw4cPE5XKRq666inz1q18lr7zyCjl+/Dix2+3c844dO0Z++tOfkg0bNpD169eTW2+9lXR3dwv+NhYuXEja29sJIYQcOHCAfPWrXyU1NTXkl7/8JXE4HFJ/uXHFjh07SFNTEykvLz9ticHlcpFrr72WGI1G4vF4yMcff0xuvfVWUltbS3bs2EH++Mc/komJCTIzM0PuvPNOcs011xC32x3XNTqdTrJ582byi1/8Iq6vG2UknAh8v0QTAx8mk4k8++yzZNu2beS+++4LeIdob28n99xzD3nnnXcIIcSLQF588UWyceNGQshsDqOuro588MEH5NChQ2TTpk1kdHQ05G8zUXj11VfJzTffTAghpzUxBILH4yFHjhwhd955J6mvryerVq0i27dvjzspsCxLrr76arJ79+64vm4MkHAi8P0Kixj48P0wsCwr+AGhuYSRkRFy1VVXkZ07d5JXX32VEELIHXfcQb75zW8SQmbvUrfccgt56aWXxLx8zHDhhReS6upqv69XX32VrF+/nhiNRkLImUkMfHg8HvLaa68l5Bh48OBBAoDU1NSQuro6UldXR/bv3x/3dUQBCScC36+IGx98SzUMw3CPUXUkwzBwOBz4y1/+gieffBI7d+7EN7/5Ta7B6eDBg/jv//5v7nrT09OwWq1c1SQRwphA7lLHjx9HX18f6urqAMzKgteuXYtDhw4lfARdIqBQKLB169aEvPa55547e3eTEX2EYI6oYHh4mGzfvp1kZGSQv/71r17f6+npISUlJdy/dTodqampIQMDA9F6+ZjiTI8YZEQFCY8QfL/i0uRQXFyMm266CTt37sR9992H8847DwcOHAAAfPjhh1yjk8PhwIEDB1BUVISysjL5biBDRoIQtx7qCy+8kHMA/utf/8p5Gp577rl477330Nvbi87OTrz99tu49tprASTuGCEF/f39iV6CDBlRR0LMFS6++GLu/8vLy1FSUoJLL70URUVFuPvuu7khI/Hs2pyruOOOO/DGG29ApVJhyZIleO6552JiDS9DBh9zysFpZGQkomnMpyPeffddXHDBBUhKSsKdd94JAFyiVsZpgzkXFs+pW3JxcbGcV/DB5s2buaams88+G8PDwwlekYwzAXOKGADM+ZxCIvHss8/iS1/6UqKXIeMMwJwjhjMRmzZtwurVq/2+XnvtNe45Dz74IJKSkvCNb3wjgSuNHd555x0sX74cVVVVeOihhxK9nDMecyrHIEMYv//97/G73/0OBw4ckDwQdz7A4/Fg2bJleO+991BSUoLGxka8+OKLMfdVmEOYc2GyHDHMcbzzzjt4+OGH8frrr5+WpAAAhw4dQlVVFSorK6FSqbBr1y6vaElG/HHGE8Phw4dRW1sLu90Oi8WC6upqtLa2JnpZHG666SaYzWZcdNFFqK+vx/e+971ELynqGBkZQWlpKffvkpISjIyMJHBFMubukIg4obGxEVu3bsVPfvIT2Gw2XHXVVVi9enWil8Whu7s70UuQcQYiVI7hjADDMCoAhwHYAZxDCBHnjnqagGGYLQAeB6AE8DQhJK7ZP4ZhNgC4lxBy8al/3wUAhJCfx3MdMj7HGX+UOIU8AOkAMgCImkJ6uoBhGCWAXwP4EoBVAL7GMEy8s36HASxlGGbxKZLeBeD1OK9BBg8yMczidwB+CuDPAM40WeF6AN2EkF5CiBPASwC2xXMBhBA3gJsA/BVAO4C/EELa4rkGGd4443MMDMN8E4CLEPLCqbvnRwzDXEAI+Vui1xYnFAMY4v17GMBZ8V4EIeQtAG/F+3VlCOOMJwZCyB8A/OHU/3uQgE0hQ8Zcg3yUkDECoJT375JTj8k4gyETgww58SfDD2f8UeJMByHEzTAMTfwpATwrJ/5kyDoGGTJk+EE+SsiQIcMPMjHIkCHDDzIxyJAhww8yMciQIcMPMjHIkCHDDzIxyJAhww8yMciQIcMPMjHIkCHDD/8f5EkKCaSFNnsAAAAASUVORK5CYII=\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "if 0:\n", + " n_start = 500\n", + " n_end = 3000\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111, projection = '3d')\n", + " ax.scatter(p_x[n_start:n_end],p_y[n_start:n_end],p_z[n_start:n_end],c = 'r')\n", + " ax.set_xlabel('x')\n", + " ax.set_ylabel('y')\n", + " ax.set_zlabel('z')\n", + " plt.show()\n", + "\n", + "if 1:\n", + "\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111, projection = '3d')\n", + " ax.scatter(p_x,p_y,p_z,c = 'r')\n", + " ax.set_xlabel('x')\n", + " ax.set_ylabel('y')\n", + " ax.set_zlabel('z')\n", + " plt.show()\n", + " \n", + "if 1:\n", + " plt.plot(p_x, p_y, 'o', color='black');\n" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'list' object has no attribute 'shape'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mmpl_toolkits\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmplot3d\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mAxes3D\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;31m#print(positions[1:2](0))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpositions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0mfig\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'shape'" + ] + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "#print(positions[1:2](0))\n", + "print(np.array(positions.shape))\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "ax.scatter(positions[:][0], positions[:][1], positions[:][2], zdir='z', c= 'red')\n", + "ax.set_xlabel('x')\n", + "ax.set_ylabel('y')\n", + "ax.set_zlabel('z')\n", + "plt.savefig(\"demo.png\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 6aef90d2bb9998370b22b0b91d1e23cea5f286f6 Mon Sep 17 00:00:00 2001 From: polymurph Date: Fri, 7 Oct 2022 20:53:15 +0200 Subject: [PATCH 3/3] work on trajectory calculation --- quadrupole/trajectory.py | 57 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 57 insertions(+) create mode 100644 quadrupole/trajectory.py diff --git a/quadrupole/trajectory.py b/quadrupole/trajectory.py new file mode 100644 index 0000000..fdcda53 --- /dev/null +++ b/quadrupole/trajectory.py @@ -0,0 +1,57 @@ +import numpy as np +from scipy import constants as cs +import matplotlib.pyplot as plt + +def amuToKg(amu): + return amu * 1.66054e-27 + +def get_a(U,m,omega,r0): + return 4*cs.e*U/(m*omeag**2*r0**2) + +def get_q(V,m,omega,r0): + return 2*cs.e*V/(m*omeag**2*r0**2) + +def get_U(a,m,omega,r0): + return a * m * omega**2 * r0**2 / (4*cs.e) + +def get_V(q,m,omega,r0): + return q * m * omega**2 * r0**2 / (2*cs.e) + +amu_mass = 100 + +mass = amuToKg(amu_mass) + +a = 0 +q = 0.7 + +f = 100e6 +omega = 2*np.pi*f +r0 = 0.007 + +U = get_U(a,mass,omega,r0) +V = get_V(q,mass,omega,r0) + +print(mass) +print(U) +print(V) + + +N = 1000 + +t_start = 0 +t_stop = 1e0 + +t = np.linspace(t_start, t_stop, N) + + +func = -q/r0**2*mass*(t**2*U*0.5+V*np.sin(omega*t)/omega**2) + +x = func +y = -func + +plt.close('all') +plt.plot(x,y,'ro') +plt.show() + + +