{
  "id": "hpc-027-bicone-angular-sweep",
  "type": "test",
  "title": "HPC-027 \u2014 Bicone Angular Sweep, 35\u00b0 Optimal at 3,428\u00d7 EM Concentration",
  "status": "confirmed",
  "project": "hpc_simulation_campaigns",
  "date_published": "2026-03-27",
  "date_updated": "2026-05-12",
  "tags": [
    "hpc-027",
    "bicone",
    "fdtd",
    "96-cubed",
    "em-concentration",
    "patent-data",
    "geometric-amplification"
  ],
  "author": "Jonathan Shelton",
  "log_subtype": "experiment_complete",
  "url": "https://prometheusresearch.tech/research/tests/hpc-027-bicone-angular-sweep.html",
  "source_markdown_url": "https://prometheusresearch.tech/research/_src/tests/hpc-027-bicone-angular-sweep.md.txt",
  "json_url": "https://prometheusresearch.tech/api/entries/hpc-027-bicone-angular-sweep.json",
  "summary_excerpt": "HPC-027 swept bicone half-angles from 10\u00b0 to 60\u00b0 in 5\u00b0 steps under 96\u00b3 FDTD. The result: 35\u00b0 half-angle gives 3,428\u00d7 peak EM concentration, with the 30\u00b0\u201340\u00b0 range all giving over 2,000\u00d7.\nWhy 35\u00b0. The bicone waist is where standing-wave nodes from both cones overlap. The optimal half-angle places tho...",
  "frontmatter": {
    "id": "hpc-027-bicone-angular-sweep",
    "type": "test",
    "title": "HPC-027 \u2014 Bicone Angular Sweep, 35\u00b0 Optimal at 3,428\u00d7 EM Concentration",
    "date_published": "2026-03-27",
    "date_updated": "2026-05-12",
    "project": "hpc_simulation_campaigns",
    "status": "confirmed",
    "log_subtype": "experiment_complete",
    "tags": [
      "hpc-027",
      "bicone",
      "fdtd",
      "96-cubed",
      "em-concentration",
      "patent-data",
      "geometric-amplification"
    ],
    "author": "Jonathan Shelton",
    "predicts": [
      "bicone-shape-concentrates-em"
    ],
    "data_supporting": [],
    "data_refuting": [],
    "see_also": [
      "hpc-039-heptagonal-resonance"
    ],
    "attachments": [
      {
        "path": "downloads/scripts/HPC-027_bicone_apex_sweep.py.txt",
        "role": "script",
        "description": "96\u00b3 FDTD bicone sweep, half-angles 10\u00b0 to 60\u00b0 in 5\u00b0 steps"
      }
    ]
  },
  "body_markdown": "\n## Author notes\n\nHPC-027 swept the half-angle of a bicone resonant cavity from 10\u00b0 to 60\u00b0\nin 5\u00b0 steps under 96\u00b3 FDTD simulation. The hypothesis (cipher-predicted)\nwas that bicone geometry should concentrate incident EM via the\ndouble-pinch focusing of the apex region, with an optimal angle somewhere\nin the 30\u201345\u00b0 range determined by the standing-wave geometry of the\ntwo cones meeting at the central waist.\n\n**Setup.**\n- Grid: 96\u00b3 cells, FDTD with PML boundaries.\n- Cavity: two cones meeting apex-to-apex at the central plane, each with\n  half-angle \u03b8 \u2208 {10\u00b0, 15\u00b0, 20\u00b0, 25\u00b0, 30\u00b0, 35\u00b0, 40\u00b0, 45\u00b0, 50\u00b0, 55\u00b0, 60\u00b0}.\n- Source: plane-wave incident on one cone's base, broadband pulse\n  10 GHz \u2013 8 THz.\n- Measurement: peak EM concentration at the apex region (central plane),\n  normalized to incident plane-wave intensity at the entrance.\n\n**Result.**\n\n| Half-angle | Peak EM concentration |\n|---|---|\n| 10\u00b0 | ~120\u00d7 |\n| 15\u00b0 | ~380\u00d7 |\n| 20\u00b0 | ~720\u00d7 |\n| 25\u00b0 | 1,150\u00d7 |\n| 30\u00b0 | 2,180\u00d7 |\n| **35\u00b0** | **3,428\u00d7** |\n| 40\u00b0 | 2,950\u00d7 |\n| 45\u00b0 | 2,140\u00d7 |\n| 50\u00b0 | 1,420\u00d7 |\n| 55\u00b0 | 760\u00d7 |\n| 60\u00b0 | 410\u00d7 |\n\n**Headline finding:** 35\u00b0 is the optimal half-angle, with peak EM\nconcentration of **3,428\u00d7 incident intensity**. The 30\u201340\u00b0 range gives\n>2,000\u00d7 \u2014 a broad optimum, not a sharp resonance, which is consistent\nwith geometric (not chromatic) concentration.\n\n**Why 35\u00b0 specifically.** The bicone's central waist is where the two\ncones' standing-wave nodes overlap. The optimal half-angle is the one\nthat places the first standing-wave node of each cone exactly at the\nwaist plane \u2014 a geometric constraint, not a frequency-tuned one. 35\u00b0\nis roughly the solution of a transcendental equation involving the\nratio of cone height to base radius; the FDTD result confirms the\ngeometric prediction.\n\n**Sphere control:** a spherical cavity of equivalent volume showed\npeak concentration of ~840\u00d7, well below the bicone optimum. The\nresult is geometry-driven, not just cavity-volume-driven.\n\n**Patent significance.** This result underlies two of the framework's\nprovisional patents (TPU + Generator, filed 2026-03-29). The 35\u00b0\noptimum with broadband response gives a geometric EM concentrator\nwith no chromatic tuning, no metamaterial requirements, no exotic\nfabrication \u2014 just shape. The patent application calls out the 35\u00b0\nhalf-angle and the 30\u201340\u00b0 tolerance range explicitly.\n\n**Reproducibility.** The full FDTD driver is attached. To reproduce:\ndownload `HPC-027_bicone_apex_sweep.py.txt`, rename to .py, run with\nNumPy + the project's FDTD engine (`engine_4d.py.txt` works after\nrenaming). 96\u00b3 run takes ~4 hours on a single Hetzner box. The result\nshould match the table above to within ~3% (small grid-resolution\nvariance is expected).\n\n**What this is and is not.**\n- IS: a geometry-only mechanism producing 3,428\u00d7 broadband EM\n  concentration with a broad geometric optimum.\n- IS NOT: a magic energy source. Energy is concentrated, not created.\n  The waist sees 3,428\u00d7 intensity *because* the surrounding cone\n  volume has correspondingly less. Conservation holds.\n- IS: directly patentable as a geometric EM concentrator design pattern.\n- IS NOT: optimal across all cavity shapes. HPC-032 ran the Archimedean-solid\n  sweep and HPC-039 ran the {7}-fold-cavity test \u2014 both are separate\n  geometries with their own optima.\n\n## Summary\n\nHPC-027 swept bicone half-angles from 10\u00b0 to 60\u00b0 in 5\u00b0 steps under 96\u00b3\nFDTD. The result: **35\u00b0 half-angle gives 3,428\u00d7 peak EM concentration**,\nwith the 30\u00b0\u201340\u00b0 range all giving over 2,000\u00d7.\n\n**Why 35\u00b0.** The bicone waist is where standing-wave nodes from both\ncones overlap. The optimal half-angle places those nodes exactly at\nthe waist plane \u2014 a geometric constraint solved by the cone geometry,\nnot a frequency-tuned resonance. The result is broadband (not narrow-band),\nwhich is consistent with shape-driven (not chromatic) concentration.\n\n**Sphere control:** equivalent-volume spherical cavity gave ~840\u00d7,\nwell below the bicone optimum. The result is shape-driven.\n\n**Patent context.** This test underlies the TPU (Thermal Photonic\nUnit) provisional patent filed 2026-03-29. A geometric EM concentrator\nproducing >3,000\u00d7 concentration broadband with no metamaterial\nrequirements is patentable as a manufacturing-process design pattern.\n\n**Status: confirmed.** Result reproduced across multiple grid\nresolutions (64\u00b3 \u2192 96\u00b3 \u2192 128\u00b3, all within ~3%). The 35\u00b0 optimum is\nrobust. Full FDTD driver attached for independent verification.\n",
  "body_html": "<h2>Author notes</h2>\n<p>HPC-027 swept the half-angle of a bicone resonant cavity from 10\u00b0 to 60\u00b0 in 5\u00b0 steps under 96\u00b3 FDTD simulation. The hypothesis (cipher-predicted) was that bicone geometry should concentrate incident EM via the double-pinch focusing of the apex region, with an optimal angle somewhere in the 30\u201345\u00b0 range determined by the standing-wave geometry of the two cones meeting at the central waist.</p>\n<p><strong>Setup.</strong></p>\n<ul>\n<li>Grid: 96\u00b3 cells, FDTD with PML boundaries.</li>\n<li>Cavity: two cones meeting apex-to-apex at the central plane, each with</li>\n<p>half-angle \u03b8 \u2208 {10\u00b0, 15\u00b0, 20\u00b0, 25\u00b0, 30\u00b0, 35\u00b0, 40\u00b0, 45\u00b0, 50\u00b0, 55\u00b0, 60\u00b0}.</p>\n<li>Source: plane-wave incident on one cone's base, broadband pulse</li>\n<p>10 GHz \u2013 8 THz.</p>\n<li>Measurement: peak EM concentration at the apex region (central plane),</li>\n<p>normalized to incident plane-wave intensity at the entrance.</p>\n</ul>\n<p><strong>Result.</strong></p>\n<table class=\"entry-table\">\n<thead><tr>\n<th>Half-angle</th>\n<th>Peak EM concentration</th>\n</tr></thead>\n<tbody>\n<tr>\n<td>10\u00b0</td>\n<td>~120\u00d7</td>\n</tr>\n<tr>\n<td>15\u00b0</td>\n<td>~380\u00d7</td>\n</tr>\n<tr>\n<td>20\u00b0</td>\n<td>~720\u00d7</td>\n</tr>\n<tr>\n<td>25\u00b0</td>\n<td>1,150\u00d7</td>\n</tr>\n<tr>\n<td>30\u00b0</td>\n<td>2,180\u00d7</td>\n</tr>\n<tr>\n<td><strong>35\u00b0</strong></td>\n<td><strong>3,428\u00d7</strong></td>\n</tr>\n<tr>\n<td>40\u00b0</td>\n<td>2,950\u00d7</td>\n</tr>\n<tr>\n<td>45\u00b0</td>\n<td>2,140\u00d7</td>\n</tr>\n<tr>\n<td>50\u00b0</td>\n<td>1,420\u00d7</td>\n</tr>\n<tr>\n<td>55\u00b0</td>\n<td>760\u00d7</td>\n</tr>\n<tr>\n<td>60\u00b0</td>\n<td>410\u00d7</td>\n</tr>\n</tbody></table>\n<p><strong>Headline finding:</strong> 35\u00b0 is the optimal half-angle, with peak EM concentration of <strong>3,428\u00d7 incident intensity</strong>. The 30\u201340\u00b0 range gives >2,000\u00d7 \u2014 a broad optimum, not a sharp resonance, which is consistent with geometric (not chromatic) concentration.</p>\n<p><strong>Why 35\u00b0 specifically.</strong> The bicone's central waist is where the two cones' standing-wave nodes overlap. The optimal half-angle is the one that places the first standing-wave node of each cone exactly at the waist plane \u2014 a geometric constraint, not a frequency-tuned one. 35\u00b0 is roughly the solution of a transcendental equation involving the ratio of cone height to base radius; the FDTD result confirms the geometric prediction.</p>\n<p><strong>Sphere control:</strong> a spherical cavity of equivalent volume showed peak concentration of ~840\u00d7, well below the bicone optimum. The result is geometry-driven, not just cavity-volume-driven.</p>\n<p><strong>Patent significance.</strong> This result underlies two of the framework's provisional patents (TPU + Generator, filed 2026-03-29). The 35\u00b0 optimum with broadband response gives a geometric EM concentrator with no chromatic tuning, no metamaterial requirements, no exotic fabrication \u2014 just shape. The patent application calls out the 35\u00b0 half-angle and the 30\u201340\u00b0 tolerance range explicitly.</p>\n<p><strong>Reproducibility.</strong> The full FDTD driver is attached. To reproduce: download <code>HPC-027_bicone_apex_sweep.py.txt</code>, rename to .py, run with NumPy + the project's FDTD engine (<code>engine_4d.py.txt</code> works after renaming). 96\u00b3 run takes ~4 hours on a single Hetzner box. The result should match the table above to within ~3% (small grid-resolution variance is expected).</p>\n<p><strong>What this is and is not.</strong></p>\n<ul>\n<li>IS: a geometry-only mechanism producing 3,428\u00d7 broadband EM</li>\n<p>concentration with a broad geometric optimum.</p>\n<li>IS NOT: a magic energy source. Energy is concentrated, not created.</li>\n<p>The waist sees 3,428\u00d7 intensity *because* the surrounding cone volume has correspondingly less. Conservation holds.</p>\n<li>IS: directly patentable as a geometric EM concentrator design pattern.</li>\n<li>IS NOT: optimal across all cavity shapes. HPC-032 ran the Archimedean-solid</li>\n<p>sweep and HPC-039 ran the {7}-fold-cavity test \u2014 both are separate geometries with their own optima.</p>\n</ul>\n<h2>Summary</h2>\n<p>HPC-027 swept bicone half-angles from 10\u00b0 to 60\u00b0 in 5\u00b0 steps under 96\u00b3 FDTD. The result: <strong>35\u00b0 half-angle gives 3,428\u00d7 peak EM concentration</strong>, with the 30\u00b0\u201340\u00b0 range all giving over 2,000\u00d7.</p>\n<p><strong>Why 35\u00b0.</strong> The bicone waist is where standing-wave nodes from both cones overlap. The optimal half-angle places those nodes exactly at the waist plane \u2014 a geometric constraint solved by the cone geometry, not a frequency-tuned resonance. The result is broadband (not narrow-band), which is consistent with shape-driven (not chromatic) concentration.</p>\n<p><strong>Sphere control:</strong> equivalent-volume spherical cavity gave ~840\u00d7, well below the bicone optimum. The result is shape-driven.</p>\n<p><strong>Patent context.</strong> This test underlies the TPU (Thermal Photonic Unit) provisional patent filed 2026-03-29. A geometric EM concentrator producing >3,000\u00d7 concentration broadband with no metamaterial requirements is patentable as a manufacturing-process design pattern.</p>\n<p><strong>Status: confirmed.</strong> Result reproduced across multiple grid resolutions (64\u00b3 \u2192 96\u00b3 \u2192 128\u00b3, all within ~3%). The 35\u00b0 optimum is robust. Full FDTD driver attached for independent verification.</p>",
  "see_also": [
    "hpc-039-heptagonal-resonance"
  ],
  "cited_by": [
    "factor3-concentrator-hypothesis",
    "hpc-024-angular-deficit",
    "hpc-028-frequency-selectivity",
    "hpc-031-prescriptive-materials-prereg",
    "hpc-032-sphere-family-archimedean",
    "hpc-039-heptagonal-resonance",
    "paper-6-status-2026-05",
    "plasma-phasing-geometric-nudging"
  ],
  "attachments": [
    {
      "path": "downloads/scripts/HPC-027_bicone_apex_sweep.py.txt",
      "role": "script",
      "description": "96\u00b3 FDTD bicone sweep, half-angles 10\u00b0 to 60\u00b0 in 5\u00b0 steps"
    }
  ],
  "schema_version": "1.0",
  "generated_at": "2026-05-12T03:27:18.533879Z"
}