From 5650a806347044d6a24f8a2830fd3aaf56952029 Mon Sep 17 00:00:00 2001 From: Clement Moissard Date: Fri, 15 Jul 2022 17:25:09 +0100 Subject: [PATCH] Jupyter Notebooks from a course on Laser Plasma Interaction and High Energy Density Plasma --- hack/LIHEDP_notebooks/Airy.ipynb | 1316 +++++++++++++++++ .../LIHEDP_notebooks/Assignment_answers.ipynb | 658 +++++++++ hack/LIHEDP_notebooks/E_Fermi.ipynb | 252 ++++ .../Inverse_Bremsstrahlung.ipynb | 100 ++ hack/LIHEDP_notebooks/Res_absorption.ipynb | 148 ++ .../Saha_first_impressions.ipynb | 516 +++++++ .../Temperature-Density_answer.png | Bin 0 -> 103881 bytes hack/LIHEDP_notebooks/Thomas_Fermi.ipynb | 430 ++++++ hack/LIHEDP_notebooks/critical density.ipynb | 140 ++ 9 files changed, 3560 insertions(+) create mode 100644 hack/LIHEDP_notebooks/Airy.ipynb create mode 100644 hack/LIHEDP_notebooks/Assignment_answers.ipynb create mode 100644 hack/LIHEDP_notebooks/E_Fermi.ipynb create mode 100644 hack/LIHEDP_notebooks/Inverse_Bremsstrahlung.ipynb create mode 100644 hack/LIHEDP_notebooks/Res_absorption.ipynb create mode 100644 hack/LIHEDP_notebooks/Saha_first_impressions.ipynb create mode 100644 hack/LIHEDP_notebooks/Temperature-Density_answer.png create mode 100644 hack/LIHEDP_notebooks/Thomas_Fermi.ipynb create mode 100644 hack/LIHEDP_notebooks/critical density.ipynb diff --git a/hack/LIHEDP_notebooks/Airy.ipynb b/hack/LIHEDP_notebooks/Airy.ipynb new file mode 100644 index 0000000..530bd8e --- /dev/null +++ b/hack/LIHEDP_notebooks/Airy.ipynb @@ -0,0 +1,1316 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Import useful modules" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy import constants as sc\n", + "from scipy import special as ssp\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def sciprint(a):\n", + " print(f\"{a:0.2g}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Stokes equation & the Airy functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Airy functions (maths)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Stokes equation is most commonly written:\n", + "\n", + "$$\n", + "y'' - xy = 0\n", + "$$\n", + "\n", + "and has for solutions: \n", + "\n", + "$$\n", + "y(x) = \\alpha A_i(x) + \\beta B_i(x)\n", + "$$\n", + "\n", + "where $A_i(x)$ and $B_i(x)$ are the Airy functions, and $a$ and $b$ are constants that we can find by using the boundary conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import special\n", + "x = np.linspace(-15, 5, 201)\n", + "ai, aip, bi, bip = special.airy(x)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(x, ai, 'r', label='Ai(x)')\n", + "plt.plot(x, bi, 'b--', label='Bi(x)')\n", + "plt.ylim(-0.5, 1.0)\n", + "plt.xlabel(\"x\", fontsize=18)\n", + "plt.ylabel(\"Airy functions\", fontsize=18)\n", + "plt.grid()\n", + "plt.legend(loc='upper left')\n", + "\n", + "\n", + "plt.axvline(-1, color=\"black\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note:** The maximum of $A_i(x)$ can be found at $x = -1$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The electric field (physics)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have\n", + "$$\n", + "\\boxed{\n", + "\\frac{d^2 E_0}{dx^2} + k_0^2 \\left( \\frac{x}{L} \\right) E_0 = 0\n", + "}\n", + "$$\n", + "\n", + "which can rewrite in the common form of the Stokes equation:\n", + "$$\n", + "\\boxed{\n", + "\\frac{d^2 E_0}{d \\xi^2} - \\xi E_0 = 0 \\ \\ \\ \\text{ with } \\xi = - k_0^{2/3} L^{-1/3} x\n", + "}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Therefore, we have\n", + "\n", + "$$\n", + "\\boxed{\n", + "E_0 = \\alpha A_i(\\xi) + \\beta B_i(\\xi)\n", + "}\n", + "$$\n", + "or, more directly:\n", + "$$\n", + "\\boxed{\n", + "E_0 = \\alpha A_i(- k_0^{2/3} L^{-1/3} x) + \\beta B_i(- k_0^{2/3} L^{-1/3} x)\n", + "}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Let us see what this looks like" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "#free space\n", + "lambda_0 = 0.2\n", + "L = 5\n", + "\n", + "k0 = 2*sc.pi / lambda_0\n", + "\n", + "xmax = L\n", + "xmin = -5\n", + "N = int(20*(xmax-xmin)*k0) #number of points (this formula gives you enough points per period)\n", + "x = np.linspace(xmax, xmin, N)\n", + "\n", + "xi = -k0**(2/3)*L**(-1/3)*x \n", + "Ai, _, Bi, _ = ssp.airy(xi)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n", + "ax.plot(x/L, Bi, 'b--', label='Bi(x)')\n", + "ax.set_ylim([-0.5, 1.0])\n", + "ax.set_xlim([xmax/L, xmin/L])\n", + "\n", + "plt.axvline(L**1/3 * k0**(-2/3) / L, color=\"black\")\n", + "\n", + "plt.axvline(0, color=\"firebrick\")\n", + "plt.text(-0.05, 0.6, 'critical surface, where ne=nc', color=\"firebrick\")\n", + "\n", + "plt.xlabel(\"x/L\", fontsize=18)\n", + "plt.legend(loc='upper left')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note:** The maximum of $A_i(\\xi)$ can be found at $\\xi_{max} = -1$.\n", + "\n", + "This corresponds to $-k_0^{2/3} L^{-1/3} x_{max} = 1$, _i.e._ $\\boxed{x_{max} = L^{1/3} k_0^{-2/3}}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Finding $\\alpha$ and $\\beta$: Boundary conditions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Finding $\\beta$: avoiding non-physical results" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n", + "ax.plot(x/L, Bi, 'b--', label='Bi(x)')\n", + "# ax.set_ylim([-0.5, 1.0])\n", + "ax.set_xlim([xmax/L, xmin/L])\n", + "\n", + "plt.xlabel(\"x/L\", fontsize=18)\n", + "plt.legend(loc='upper left')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly, we should have: $\\beta = 0$.\n", + "\n", + "Otherwise the electric field would go to infinity around the critical density.\n", + "\n", + "This leaves us with:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x/L, Ai, 'r', label='Ai(x)')\n", + "ax.set_ylim([-0.5, 1.0])\n", + "ax.set_xlim([xmax/L, xmin/L])\n", + "\n", + "plt.xlabel(\"x/L\", fontsize=18)\n", + "plt.legend(loc='upper left')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Finding $\\alpha$: the boundary with free space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember how we got here: $n_e = n_C \\left(1 -\\frac{x}{L} \\right)$\n", + "\n", + "From this, we can define \"free space\" as $x \\geq L$.\n", + "\n", + "Therefore, we need to match a free wave with our Airy solution, at $x = L$.\n", + "\n", + "We can define our free wave as:\n", + "\n", + "$$E_0(x \\geq L) = \\tilde{E_0}_{FS} e^{-i (k_0 x + \\phi)}$$\n", + "\n", + "We will just consider the real part of this:\n", + "\n", + "$$E_0(x \\geq L) = \\tilde{E_0}_{FS} \\cos\\left( k_0 x + \\phi \\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want:\n", + "\n", + "$$\n", + "\\tilde{E_0}_{FS} \\cos\\left( k_0 L + \\phi \\right) = \\alpha A_i(- k_0^{2/3} L^{-1/3} L)\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xmax = 2*L\n", + "xmin = -5\n", + "N = int(20*(xmax-xmin)*k0) #number of points (this formula gives you enough points per period)\n", + "x = np.linspace(xmax, xmin, N)\n", + "\n", + "x_under_L = np.array([xj for xj in x if xj < L])\n", + "x_over_L = np.array([xj for xj in x if xj >= L])\n", + "\n", + "xi = -k0**(2/3)*L**(-1/3)*x_under_L\n", + "Ai, _, Bi, _ = ssp.airy(xi)\n", + "\n", + "#Free wave\n", + "E0_FS = 1\n", + "phi = 0\n", + "E0 = E0_FS*np.cos(k0*x_over_L + phi)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x_over_L/L, E0, label='Wave in free space')\n", + "ax.plot(x_under_L/L, Ai, 'r', label='Ai(x)')\n", + "ax.set_ylim([-0.5, 1.0])\n", + "ax.set_xlim([xmax/L, xmin/L])\n", + "\n", + "plt.xlabel(\"x/L\", fontsize=18)\n", + "plt.legend(loc='upper left')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to match these two, we would need to match both phase and amplitude.\n", + "For the sake of this lecture, we will declar ourselves satisfy with just amplitude." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "application/javascript": [ + "/* Put everything inside the global mpl namespace */\n", + "window.mpl = {};\n", + "\n", + "\n", + "mpl.get_websocket_type = function() {\n", + " if (typeof(WebSocket) !== 'undefined') {\n", + " return WebSocket;\n", + " } else if (typeof(MozWebSocket) !== 'undefined') {\n", + " return MozWebSocket;\n", + " } else {\n", + " alert('Your browser does not have WebSocket support. ' +\n", + " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", + " 'Firefox 4 and 5 are also supported but you ' +\n", + " 'have to enable WebSockets in about:config.');\n", + " };\n", + "}\n", + "\n", + "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", + " this.id = figure_id;\n", + "\n", + " this.ws = websocket;\n", + "\n", + " this.supports_binary = (this.ws.binaryType != undefined);\n", + "\n", + " if (!this.supports_binary) {\n", + " var warnings = document.getElementById(\"mpl-warnings\");\n", + " if (warnings) {\n", + " warnings.style.display = 'block';\n", + " warnings.textContent = (\n", + " \"This browser does not support binary websocket messages. \" +\n", + " \"Performance may be slow.\");\n", + " }\n", + " }\n", + "\n", + " this.imageObj = new Image();\n", + "\n", + " this.context = undefined;\n", + " this.message = undefined;\n", + " this.canvas = undefined;\n", + " this.rubberband_canvas = undefined;\n", + " this.rubberband_context = undefined;\n", + " this.format_dropdown = undefined;\n", + "\n", + " this.image_mode = 'full';\n", + "\n", + " this.root = $('
');\n", + " this._root_extra_style(this.root)\n", + " this.root.attr('style', 'display: inline-block');\n", + "\n", + " $(parent_element).append(this.root);\n", + "\n", + " this._init_header(this);\n", + " this._init_canvas(this);\n", + " this._init_toolbar(this);\n", + "\n", + " var fig = this;\n", + "\n", + " this.waiting = false;\n", + "\n", + " this.ws.onopen = function () {\n", + " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", + " fig.send_message(\"send_image_mode\", {});\n", + " if (mpl.ratio != 1) {\n", + " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", + " }\n", + " fig.send_message(\"refresh\", {});\n", + " }\n", + "\n", + " this.imageObj.onload = function() {\n", + " if (fig.image_mode == 'full') {\n", + " // Full images could contain transparency (where diff images\n", + " // almost always do), so we need to clear the canvas so that\n", + " // there is no ghosting.\n", + " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", + " }\n", + " fig.context.drawImage(fig.imageObj, 0, 0);\n", + " };\n", + "\n", + " this.imageObj.onunload = function() {\n", + " fig.ws.close();\n", + " }\n", + "\n", + " this.ws.onmessage = this._make_on_message_function(this);\n", + "\n", + " this.ondownload = ondownload;\n", + "}\n", + "\n", + "mpl.figure.prototype._init_header = function() {\n", + " var titlebar = $(\n", + " '
');\n", + " var titletext = $(\n", + " '
');\n", + " titlebar.append(titletext)\n", + " this.root.append(titlebar);\n", + " this.header = titletext[0];\n", + "}\n", + "\n", + "\n", + "\n", + "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "\n", + "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", + "\n", + "}\n", + "\n", + "mpl.figure.prototype._init_canvas = function() {\n", + " var fig = this;\n", + "\n", + " var canvas_div = $('
');\n", + "\n", + " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", + "\n", + " function canvas_keyboard_event(event) {\n", + " return fig.key_event(event, event['data']);\n", + " }\n", + "\n", + " canvas_div.keydown('key_press', canvas_keyboard_event);\n", + " canvas_div.keyup('key_release', canvas_keyboard_event);\n", + " this.canvas_div = canvas_div\n", + " this._canvas_extra_style(canvas_div)\n", + " this.root.append(canvas_div);\n", + "\n", + " var canvas = $('');\n", + " canvas.addClass('mpl-canvas');\n", + " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", + "\n", + " this.canvas = canvas[0];\n", + " this.context = canvas[0].getContext(\"2d\");\n", + "\n", + " var backingStore = this.context.backingStorePixelRatio ||\n", + "\tthis.context.webkitBackingStorePixelRatio ||\n", + "\tthis.context.mozBackingStorePixelRatio ||\n", + "\tthis.context.msBackingStorePixelRatio ||\n", + "\tthis.context.oBackingStorePixelRatio ||\n", + "\tthis.context.backingStorePixelRatio || 1;\n", + "\n", + " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", + "\n", + " var rubberband = $('');\n", + " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", + "\n", + " var pass_mouse_events = true;\n", + "\n", + " canvas_div.resizable({\n", + " start: function(event, ui) {\n", + " pass_mouse_events = false;\n", + " },\n", + " resize: function(event, ui) {\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " stop: function(event, ui) {\n", + " pass_mouse_events = true;\n", + " fig.request_resize(ui.size.width, ui.size.height);\n", + " },\n", + " });\n", + "\n", + " function mouse_event_fn(event) {\n", + " if (pass_mouse_events)\n", + " return fig.mouse_event(event, event['data']);\n", + " }\n", + "\n", + " rubberband.mousedown('button_press', mouse_event_fn);\n", + " rubberband.mouseup('button_release', mouse_event_fn);\n", + " // Throttle sequential mouse events to 1 every 20ms.\n", + " rubberband.mousemove('motion_notify', mouse_event_fn);\n", + "\n", + " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", + " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", + "\n", + " canvas_div.on(\"wheel\", function (event) {\n", + " event = event.originalEvent;\n", + " event['data'] = 'scroll'\n", + " if (event.deltaY < 0) {\n", + " event.step = 1;\n", + " } else {\n", + " event.step = -1;\n", + " }\n", + " mouse_event_fn(event);\n", + " });\n", + "\n", + " canvas_div.append(canvas);\n", + " canvas_div.append(rubberband);\n", + "\n", + " this.rubberband = rubberband;\n", + " this.rubberband_canvas = rubberband[0];\n", + " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", + " this.rubberband_context.strokeStyle = \"#000000\";\n", + "\n", + " this._resize_canvas = function(width, height) {\n", + " // Keep the size of the canvas, canvas container, and rubber band\n", + " // canvas in synch.\n", + " canvas_div.css('width', width)\n", + " canvas_div.css('height', height)\n", + "\n", + " canvas.attr('width', width * mpl.ratio);\n", + " canvas.attr('height', height * mpl.ratio);\n", + " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", + "\n", + " rubberband.attr('width', width);\n", + " rubberband.attr('height', height);\n", + " }\n", + "\n", + " // Set the figure to an initial 600x600px, this will subsequently be updated\n", + " // upon first draw.\n", + " this._resize_canvas(600, 600);\n", + "\n", + " // Disable right mouse context menu.\n", + " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", + " return false;\n", + " });\n", + "\n", + " function set_focus () {\n", + " canvas.focus();\n", + " canvas_div.focus();\n", + " }\n", + "\n", + " window.setTimeout(set_focus, 100);\n", + "}\n", + "\n", + "mpl.figure.prototype._init_toolbar = function() {\n", + " var fig = this;\n", + "\n", + " var nav_element = $('
');\n", + " nav_element.attr('style', 'width: 100%');\n", + " this.root.append(nav_element);\n", + "\n", + " // Define a callback function for later on.\n", + " function toolbar_event(event) {\n", + " return fig.toolbar_button_onclick(event['data']);\n", + " }\n", + " function toolbar_mouse_event(event) {\n", + " return fig.toolbar_button_onmouseover(event['data']);\n", + " }\n", + "\n", + " for(var toolbar_ind in mpl.toolbar_items) {\n", + " var name = mpl.toolbar_items[toolbar_ind][0];\n", + " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", + " var image = mpl.toolbar_items[toolbar_ind][2];\n", + " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", + "\n", + " if (!name) {\n", + " // put a spacer in here.\n", + " continue;\n", + " }\n", + " var button = $('