---
id: hpc-027-bicone-angular-sweep
type: test
title: HPC-027 — Bicone Angular Sweep, 35° Optimal at 3,428× 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: 96³ FDTD bicone sweep, half-angles 10° to 60° in 5° steps
---

## Author notes

HPC-027 swept the half-angle of a bicone resonant cavity from 10° to 60°
in 5° steps under 96³ 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 30–45° range determined by the standing-wave geometry of the
two cones meeting at the central waist.

**Setup.**
- Grid: 96³ cells, FDTD with PML boundaries.
- Cavity: two cones meeting apex-to-apex at the central plane, each with
  half-angle θ ∈ {10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°}.
- Source: plane-wave incident on one cone's base, broadband pulse
  10 GHz – 8 THz.
- Measurement: peak EM concentration at the apex region (central plane),
  normalized to incident plane-wave intensity at the entrance.

**Result.**

| Half-angle | Peak EM concentration |
|---|---|
| 10° | ~120× |
| 15° | ~380× |
| 20° | ~720× |
| 25° | 1,150× |
| 30° | 2,180× |
| **35°** | **3,428×** |
| 40° | 2,950× |
| 45° | 2,140× |
| 50° | 1,420× |
| 55° | 760× |
| 60° | 410× |

**Headline finding:** 35° is the optimal half-angle, with peak EM
concentration of **3,428× incident intensity**. The 30–40° range gives
>2,000× — a broad optimum, not a sharp resonance, which is consistent
with geometric (not chromatic) concentration.

**Why 35° specifically.** 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 — a geometric constraint, not a frequency-tuned one. 35°
is roughly the solution of a transcendental equation involving the
ratio of cone height to base radius; the FDTD result confirms the
geometric prediction.

**Sphere control:** a spherical cavity of equivalent volume showed
peak concentration of ~840×, well below the bicone optimum. The
result is geometry-driven, not just cavity-volume-driven.

**Patent significance.** This result underlies two of the framework's
provisional patents (TPU + Generator, filed 2026-03-29). The 35°
optimum with broadband response gives a geometric EM concentrator
with no chromatic tuning, no metamaterial requirements, no exotic
fabrication — just shape. The patent application calls out the 35°
half-angle and the 30–40° tolerance range explicitly.

**Reproducibility.** The full FDTD driver is attached. To reproduce:
download `HPC-027_bicone_apex_sweep.py.txt`, rename to .py, run with
NumPy + the project's FDTD engine (`engine_4d.py.txt` works after
renaming). 96³ 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).

**What this is and is not.**
- IS: a geometry-only mechanism producing 3,428× broadband EM
  concentration with a broad geometric optimum.
- IS NOT: a magic energy source. Energy is concentrated, not created.
  The waist sees 3,428× intensity *because* the surrounding cone
  volume has correspondingly less. Conservation holds.
- IS: directly patentable as a geometric EM concentrator design pattern.
- IS NOT: optimal across all cavity shapes. HPC-032 ran the Archimedean-solid
  sweep and HPC-039 ran the {7}-fold-cavity test — both are separate
  geometries with their own optima.

## Summary

HPC-027 swept bicone half-angles from 10° to 60° in 5° steps under 96³
FDTD. The result: **35° half-angle gives 3,428× peak EM concentration**,
with the 30°–40° range all giving over 2,000×.

**Why 35°.** The bicone waist is where standing-wave nodes from both
cones overlap. The optimal half-angle places those nodes exactly at
the waist plane — 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.

**Sphere control:** equivalent-volume spherical cavity gave ~840×,
well below the bicone optimum. The result is shape-driven.

**Patent context.** This test underlies the TPU (Thermal Photonic
Unit) provisional patent filed 2026-03-29. A geometric EM concentrator
producing >3,000× concentration broadband with no metamaterial
requirements is patentable as a manufacturing-process design pattern.

**Status: confirmed.** Result reproduced across multiple grid
resolutions (64³ → 96³ → 128³, all within ~3%). The 35° optimum is
robust. Full FDTD driver attached for independent verification.