{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Piège de Penning\n", "\n", "_À partir du sujet de 2021_\n", "\n", "En physique, les pièges à ions sont des dispositifs permettant de stocker des particules chargées pendant une longue durée, notamment dans le but de mesurer leurs propriétés avec précision.\n", "\n", "Il n'est pas possible de réaliser un piège à ions uniquement avec un champ électrique statique : en effet, un tel piège nécéssiterait d'avoir un maximum ou minimum du potentiel électrique - ce qui est impossible car son Laplacien est nul.\n", "\n", "Le piège de Penning est un dispositif permettant de stocker des particules chargées, grâce à la combinaison d'un champ magnétique uniforme et d'un champ électrique quadripolaire constant. Nous proposons d'en simuler le comportement. \n", "\n", "On considère un ion béryllium $Be^+$ dont on notera $q$ la chage. On note $B$ l'amplitude du champ magnétique, uniforme, et dirigé selon $z$. Le champ electrostatique dipolaire dérive du potentiel suivant :\n", "\n", "$$ \n", "V = \\frac{Q}{2} \\left(x^2 +y^2 - 2z^2\\right)\n", "$$\n", "\n", "Le champ électrique vaut donc :\n", "\n", "$$\n", "\\vec E = -Q\\left( x\\vec{u}_x + y\\vec{u}_y -2z\\vec{u}_z \\right)\n", "$$\n", "\n", "La force est donnée par :\n", "\n", "$$\n", "\\vec{F} = q\\left(\\vec{E} + \\vec{v}\\wedge\\vec{B}\\right)\n", "$$\n", "\n", "où le symbol $\\wedge$ représente le produit vectoriel.\n", "\n", "Valeurs numériques : " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "keep" ] }, "outputs": [], "source": [ "proton_mass = 1.67E-27\n", "m = 9*proton_mass\n", "q = e = 1.6E-19\n", "\n", "# Valeurs par défaut\n", "B = 2 # Tesla\n", "Q = -300/1E-2**2 # 300V/cm^2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Ecrire une fonction python qui renvoie l'accélération $\\vec{F}/m$ en fonction de $\\vec{r}$ la position et $\\vec{v}$ la vitesse représentée par des tableaux numpy. On pourra utiliser la fonction ``np.cross`` pour calculer la produit vectoriel" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "u_x = np.array([1, 0, 0])\n", "u_y = np.array([0, 1, 0])\n", "u_z = np.array([0, 0, 1])\n", "\n", "def acceleration(r, v, Q, B):\n", " return q*(-Q*r*np.array([1, 1, -2]) + np.cross(v, B*u_z))/m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Ecrire une fonction qui à partir d'une condition initiale $r_0$, $v_0$ renvoie la position et la vitesse pour un ensemble de valeur (croissante) $t_i$\n", "\n", " def trajectoire(r_0, v_0, t_array, Q, B):\n", " ....\n", " return x, y, z, vx, vy, vz\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "def fun(t, y, Q, B):\n", " r = y[:3]\n", " v = y[3:6]\n", " acc = acceleration(r, v, Q, B)\n", " return np.concatenate([v, acc])\n", "\n", "def trajectoire(r_0, v_0, t_array, Q, B):\n", " y0 = np.concatenate([r_0, v_0])\n", " res = solve_ivp(fun, [0, t_array[-1]], y0, method='RK45', t_eval=t_array, args=(Q,B))\n", " x, y, z, vx, vy, vz = res.y\n", " return x, y, z, vx, vy, vz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Dans un champ magnétique uniforme (sans champ électrique), un particule à une trajectoire circulaire dans le plan orthogonal au champ. Vérifier ceci en calculant la tractoire d'une particule ayant initialement une vitesse de 100 m/s dans ce plan.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "t_array = np.linspace(0, 1E-6)\n", "\n", "x, y, z, vx, vy, vz = trajectoire(0*u_x, 100*u_x, t_array, Q=0, B=B)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(x, y)\n", "ax.set_aspect(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. On considère maintenant une particule dans le champ magnétique et électrique. Paramètre initiaux : $\\vec{r} = (0, 100~\\mathrm{\\mu m}, 0)$ et $\\vec{v} = (500~\\mathrm{m/s}, 100~\\mathrm{m/s}, 1~\\mathrm{m/s})$. On calculera pendant $5~\\mathrm{\\mu s}$ en échantillonant sur au moins 2000 points. Tracer la trajectoire dans le plan $x, y$ puis en 3D.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t_array = np.linspace(0, 5E-6, 2001)\n", "\n", "R = 100e-6\n", "vx0 = 500\n", "vy0 = 100\n", "vz0 = 1\n", "x, y, z, vx, vy, vz = trajectoire(R*u_x, vx0*u_x + vy0*u_y + vz0*u_z, t_array, Q=Q, B=B)\n", "\n", "fig = plt.figure()\n", "ax = fig.subplots(1, 1)\n", "\n", "ax.plot(x, y)\n", "ax.set_aspect(1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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