Fusion by channel
Collected at the cups and belt
Assumptions, removed one at a time
Where the drive goes
State
Gain against size
The four assumptions
| For | Against |
|---|
| No neutrals | Taken as given by Hedditch 2015. | Charge exchange is 10⁶ to 10⁷ times likelier than a Coulomb scatter. |
| Neutralised core | EMC2 2014: a cusp held fast electrons far better at high β. | Sydney 2019 reported no potential well. POPS found neutralisation too weak. |
| Plugged cusps | Hedditch 2015: electric and magnetic trapping together. RF plugs cut cusp ion loss by 95% at Nagoya. | Rider 1995: electron loss intolerable for every fuel except perhaps D–T. |
| Forgiving well | Hedditch 2015. Nebel and Barnes 1998. | Rider and Nevins 1995: keeping ions beam-like costs more than fusion returns. |
Burn the deuterium. Leave the tritium sealed.
Every fuel at 1 kW of fusion
Water is the thickness that brings the surface to 1 µSv/h, counting neutron removal only, so read it as a minimum. p–¹¹B is taken at one neutron per 100,000 reactions, an estimate.
The field has an axis of symmetry, so each ion keeps its canonical angular momentum. That one invariant fixes the ring current that makes the rings untouchable. No simulation is needed, and device size drops out.
Pφ = m r vφ + qψ ⇒ Icrit = S · Bρ / μ₀
Orbit integrator, live
Electric kicks are Störmer–Verlet, the map you get by discretising the action. The magnetic step is an exact rotation. Both fields come from the gradients of the same interpolated φ and ψ that define the energy.
Where least action helps
| Strong | Symmetry gives the shield current exactly. Above it the integrator found no ring strike in 4,800 bounces; just below, strikes return. |
| Strong | Discretise the action, not the equations, and long-run errors stay bounded. Whole-device 6D tokamak codes are now built this way. |
| Medium | Relaxed states: minimise energy at fixed helicity and the end state follows without tracking turbulence. This cusp has no closed flux to relax. |
| Weak | A hidden gain regime. These methods integrate the same Vlasov–Maxwell physics more faithfully; they add no terms. The transport stack on your slides assumes near-Maxwellian plasma on nested flux surfaces, so it is silent on a beam-like cusp device. I found no collisional, structure-preserving model of this geometry. |
Your cage is this cell at a higher harmonic. Its holes are the cusps, and the more of them the symmetry forces, the higher the power of r the field must start from at the centre.
| Core field | Quiet core | Exact shield |
|---|
| 2 rings | r¹ | 7% | 224 kA·turn |
| 4 rings, currents 1 : −0.74 | r³ | 33% | 235 kA·turn |
| 6 rings, 1 : −0.70 : 0.61 | r⁵ | 44% | 452 kA·turn |
| Cube cage, 6 coils | r³ | 33% | none |
| Icosahedral cage like your render, 12 or 32 coils | r⁵ | 44% | none |
Quiet core is the share of the cage radius where the field is under a tenth of its edge value. Shield current is per ring, for D⁺ at 25 kV. A polyhedron has no axis, so nothing conserves Pφ and no current makes its coils untouchable. Coaxial rings reach the same harmonic and keep the shield: no ring strike in 4,000 bounces above the threshold, for every stack.
What the harmonic buys at these settings
Standing waves
| Strong | Harmonic order sets the quiet core, as above. |
| Strong | Resonant breathing of the ion cloud is real: Los Alamos drove it and saw the resonance. It needs a harmonic well, and this one is not. On the bench an ion started at half radius bounces in 117 ns and one from the wall in 198 ns, so no single tone between 5 and 8.5 MHz keeps them in step. A harmonic well takes a uniform electron cloud, which is the neutralised-core assumption again. |
| Medium | Standing RF fields have plugged cusps. Nagoya cut ion loss through a line cusp by up to 95% and lengthened confinement tenfold, with megawatt oscillators. It is untried on 100 keV electrons in a cell this size. |
| Weak | The pattern as cause. Chladni and Faraday figures are the nodal lines of a driven resonator. They move matter to the nodes and leave the tunnelling rate alone. Any gain has to arrive as density, energy or lifetime, which are the rows above. |
Cavitation
| In the plasma | A bubble is a liquid wall falling in on a little gas, and the liquid's inertia does the squeezing. A plasma has no wall and nothing to tear. |
| Caviton | The nearest true analogue. Radio waves near the plasma frequency push plasma out of their own antinodes; the hollows trap the wave and collapse to a few Debye lengths (Zakharov 1972, seen in the lab from 1974). The energy lands in electrons, and the hollow is a drop in density, so fusion falls there. |
| Breathing cloud | Ions in a harmonic well fall to the centre together and rebound, as the bubble wall does. That is the Los Alamos resonance above, and it dephases in this well. |
| Plasma in the bubble | Turn it inside out: make the cavity in a liquid or solid and put the plasma inside. General Fusion closes a lithium liner on a magnetised plasma and reported 0.72 keV and tenfold density in June 2026. First Light in Oxford began from pistol-shrimp cavity collapse. Both are pulsed machines that fill a hall. |
| Measured | A single bubble reaches about 20,000 K at the surface of its plasma, thousands of times short of what D–D needs, with no fusion products seen. The 2002 Oak Ridge fusion claim was not reproduced. |
Gravity
Gravity only adds up, which is how 10⁵⁷ nuclei hold a star shut. A mass current does make a field, as your figure shows, at G/c² = 7×10⁻²⁸ m/kg: the last row is 1,000 turns with the flow started in one second. Where it counts here is buoyancy: it layers the tank, could turn the loop without a pump, and pulls a bubble off centre.
Self-similarity
| Strong | Gain is your triangle. Each bounce returns a fraction g of the ion's cost and loses the ion with chance p, so Q = g + g(1−p) + g(1−p)² + … = g/p. |
| Strong | Smaller cells win, on paper. In the oscillating-sphere theory power per cell rises as 1/a, so one volume cut into N³ cells gives N⁴ the power, until voltage hold-off and the Debye length stop it. That is the published form of the fractal instinct. |
| Medium | Cascaded collapse. A plasma focus concentrates through a chain of instabilities, sheath to filaments to a plasmoid tens of microns across, each step denser than the last. |
| Weak | Fractal electrodes or cage shapes as a source of gain. The one fractal every hot plasma already has is its turbulent cascade, and that is the main way tokamaks lose heat. |
Bench tests
25 kV with a storage capacitor behind it can kill. Above about 15 kV the rings make X-rays that pass glass ports. A 100 W CO₂ beam blinds and ignites. Neutron dose scales with success. In the UK, work with X-ray apparatus falls under IRR17.
Sources