{"id":799,"date":"2025-07-20T03:40:11","date_gmt":"2025-07-20T03:40:11","guid":{"rendered":"https:\/\/synchrotron-light.net\/wp\/?page_id=799"},"modified":"2025-07-20T05:12:17","modified_gmt":"2025-07-20T05:12:17","slug":"chapter-10-non-photon-analogues-of-synchrotron-radiation","status":"publish","type":"page","link":"https:\/\/synchrotron-light.net\/wp\/?page_id=799","title":{"rendered":"Chapter 10: Non-photon analogues of synchrotron radiation"},"content":{"rendered":"<p>Below is a set of python codes associated with Chapter 10 of Daniele Pelliccia and David M. Paganin, &#8220;Synchrotron Light: A Physics Journey from Laboratory to Cosmos&#8221; (Oxford University Press, 2025).<\/p>\n<p>In order to run any of these python codes, you will need to include the following header.<\/p>\n<pre class=\"theme:obsidian lang:python decode:true\">import numpy as np \r\nimport matplotlib.pyplot as plt\r\n\r\nsynchrotron_style = {\r\n    'font.family': 'FreeSerif',\r\n    'font.size': 30,\r\n    'axes.linewidth': 2.0,\r\n    'axes.edgecolor': 'black',\r\n    'grid.color': '#5b5b5b',\r\n    'grid.linewidth': 1.2,\r\n}<\/pre>\n<h2 id=\"The-basics:-plotting-a-radial-field\">Angular dependence of classical-electrodynamics dead cone<\/h2>\n<p>See Fig. 10.24.<\/p>\n<pre class=\"theme:obsidian lang:python decode:true\">alpha = np.linspace(0,2,100)\r\nfunc = alpha**2 \/ (1 + alpha**2)**6\r\n\r\nwith plt.style.context(('seaborn-v0_8-whitegrid')):\r\n    plt.rcParams.update(synchrotron_style)\r\n    fig = plt.figure(figsize=(12,12))\r\n    plt.plot(alpha, func, lw = 6)\r\n    \r\n    plt.xticks([0, 1\/np.sqrt(5), 2\/np.sqrt(5), 3\/np.sqrt(5), 4\/np.sqrt(5)], [\"\", \"\", \"\", \"\", \"\"], fontsize = 26)\r\n    plt.yticks([0, 0.035, 0.071], [\"0\", \"0.035\", \"0.07\"], fontsize = 34)\r\n    plt.ylim(-0.0001,0.071)\r\n    plt.tight_layout()<\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-801\" src=\"https:\/\/synchrotron-light.net\/wp\/wp-content\/uploads\/2025\/07\/shynchrotron-light-10.24-1024x1024.png\" alt=\"\" width=\"700\" height=\"699\" \/><\/p>\n<h2>Dead cone for gravitational waves<\/h2>\n<p>See Fig. 10.28.<\/p>\n<pre class=\"theme:obsidian lang:python decode:true\">theta = np.linspace(-np.pi, np.pi, 360)\r\nbeta_ = [0.9, 0.99, 0.999, 0.9999]\r\n\r\nwith plt.style.context(('seaborn-v0_8-whitegrid')):\r\n    # plt.rcParams.update(synchrotron_style)\r\n    fig = plt.figure(figsize=(16,8.2))\r\n    \r\n    for b in beta_:\r\n        gamma = (1. - b**2)**(-0.5)\r\n        pgw = np.sin(theta)**4 \/ (1.0 - b*np.cos(theta))**2 \r\n        plt.plot(theta, pgw, lw = 4, label = \"$\\\\beta=$\"+str(b))\r\n        plt.legend(fontsize = 30, frameon=True, framealpha=1)\r\n        plt.xticks(fontsize = 26)\r\n        plt.yticks(fontsize = 26)\r\n\r\n        plt.xlabel('$\\\\theta$ (rad)', fontsize=30, labelpad=10)\r\n        plt.title(\"$\\\\gamma^{-2} p_{gw} (\\\\theta)$\", fontsize=30)\r\n        plt.tight_layout()\r\n\r\nplt.show()<\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-803\" src=\"https:\/\/synchrotron-light.net\/wp\/wp-content\/uploads\/2025\/07\/shynchrotron-light-10.28-1024x522.png\" alt=\"\" width=\"700\" height=\"357\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Below is a set of python codes associated with Chapter 10 of Daniele Pelliccia and David M. Paganin, &#8220;Synchrotron Light: A Physics Journey from Laboratory to Cosmos&#8221; (Oxford University Press, 2025). In order to run any of these python codes, you will need to include the following header. import numpy as np import matplotlib.pyplot as [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":79,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-799","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/799","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=799"}],"version-history":[{"count":2,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/799\/revisions"}],"predecessor-version":[{"id":814,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/799\/revisions\/814"}],"up":[{"embeddable":true,"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=\/wp\/v2\/pages\/79"}],"wp:attachment":[{"href":"https:\/\/synchrotron-light.net\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}