Falsifiable prediction
No single magnetic confinement geometry can serve both fuels. Any shape tuned for a deuterium–tritium burning plasma near its operating temperature will miss the confinement quality an aneutronic proton–boron plasma requires. Any shape built around proton–boron leaves no admissible volume for the breeding blanket deuterium–tritium cannot run without. The two geometry classes are disjoint.
The disjointness follows from three fuel constants — the nuclear charge product, the reduced mass, and the fraction of fusion power leaving as neutrons — plus one imported premise: that the field-line pitch profile must be commanded from OUTSIDE the plasma. That premise is a stellarator result, not a fuel constant, and it is the weakest link in the chain. This page names it rather than hiding it.
The live objection, stated fairly. The pinch and compact-toroid classes — toroidal screw pinch, reversed-field pinch, field-reversed configuration — SELF-ORGANIZE the pitch profile from the plasma current rather than holding it from outside, and they run at high beta, the ratio of plasma pressure to magnetic pressure, where a tokamak runs a few percent. High beta is exactly the lever an aneutronic fuel wants, and the FRC literature says so explicitly. TAE Technologies has pursued proton-boron in a beam-driven FRC for two decades on that reasoning. If self-organization can hold the shear window at high beta, the empty region on this page narrows sharply.
Second kill route, cheaper than the first: demonstrate a self-organized configuration holding a stabilizing pitch-shear window at high beta on an aneutronic fuel. That kills the imported premise directly, without touching the fuel constants. One datapoint neither side owns: the first proton-boron fusion measured in a magnetically confined plasma was TAE’s, run in NIFS’s Large Helical Device — a stellarator.
How to kill it: run the stellarator community’s own gyrokinetic optimization toolchain at both operating points and produce one geometry that closes both power balances. Or, cheaper, on an existing shaped stellarator: scan the ion-to-electron temperature ratio at matched profiles — this page predicts the electron-scale electromagnetic transport share must fall as the ratio rises. A fuel-agnostic geometry, or a channel mix that refuses to shift, kills this page.
Settleable only by the field’s own instruments and codes. No private data required. If it dies, it dies in public.
The computed angles
The pitch of a field line is not a style choice. It is computable from the machine's published geometry:
tan(pitch) = iota × r / R (stellarator)
tan(pitch) = r / (q × R) (tokamak)
Here iota is the rotational transform and q the safety factor, both published operating quantities; R and r are the machine's major and minor radii.
W7-X (R = 5.5 m, a = 0.53 m) — its three published edge iota settings:
iota 0.8 → 4.4° iota 1.0 → 5.5° iota 1.2 → 6.6° (half-radius ≈ 2.8°)
ITER-class tokamak (R = 6.2 m, a = 2.0 m):
edge q ≈ 3 → 6.1° near-axis q ≈ 1 → 3.7°
Read the table twice. The magnitudes are similar: a few degrees either way. What differs is who commands the angle. A tokamak's pitch is set by the plasma's own current profile, self-organized, and it drags whatever shear that current happens to produce. A stellarator's pitch is set from outside, by the coil winding: W7-X carries twenty planar coils whose entire job is dialing that edge angle across a fifty percent range. External command of the angle profile is precisely the lever a proton-boron machine spends its whole budget on.
Derived standoff and fill (from the layer stack, same derivation run):
D-T coil standoff 1.5–2.2× plasma radius · p-B11 standoff 1.05–1.1×
plasma fills ~40% of the D-T cross-section · ~85% of the p-B11 cross-section
Coil count, by inverting the ripple (same derivation run):
a finite ring of N coils leaves a corrugation that decays as rho^(-N)
N = −ln(ripple) / ln(rho) rho = coil standoff / plasma radius
1% ripple, rho 1.67 → N = 8.9800 → 9 coils rho 1.10 → N = 48.3177 → 48 coils
ratio 48.3177 / 8.9800 = 5.38058
The ratio is tolerance-invariant: at 0.5%, 1% and 2% ripple it returns 5.38058 unchanged, because the ripple tolerance cancels in the quotient. It is not a chosen number. W7-X carries 50 modular coils and the class model asks for 48 at the proton-boron standoff — a check the model survived, not a prediction, since the machine long predates the arithmetic.
Large-aspect-ratio surface formula: these are class numbers, not a coil specification. Every angle above inverts back to its published iota or q exactly, so check them. The drawings on this page obey this table: the geometry parameters came out of a LabForge derivation run over the published anchors, and features the run could not derive are labeled illustration in the part cards.
The article
THE FUEL DRAWS THE MACHINE
By Cory Graves
Look at a soap bubble. Nobody designed it. Surface tension pushes the same in every direction, and the sphere is simply what that force permits. A star works the same way. Gravity is isotropic, so the star is round. Shapes are not chosen. They are consequences.
For seventy years, fusion engineering has run this logic backwards. We pick a machine first, a tokamak or a stellarator, then spend decades persuading the plasma to live in it. The plasma objects constantly. Turbulence, eruptions at the edge, heat leaking through channels we did not invite. What if the objection is the message? What if the shape was never ours to pick?
Start from first principles and see where the fuel itself leads.
Every fusion fuel must climb a Coulomb barrier before it can burn, and that barrier is computable from two constants of the fuel alone: the nuclear charge product and the reduced mass. The Gamow energy is E_G = 2 mu c^2 (pi alpha Z1 Z2)^2. Run the four candidate fuels through it. Deuterium-deuterium comes out near 0.99 MeV. Deuterium-tritium, 1.18. Deuterium-helium-3, 4.73. Proton-boron-11, 22.58. That single line of algebra orders the fuels by how hot they must run, and proton-boron must run roughly nineteen times harder than deuterium-tritium. No experiment needed yet. Two constants did that.
Next, ask where each fuel's energy exits. Deuterium-tritium releases 17.6 MeV per reaction and hands 14.1 of it to a neutron. Four fifths of the machine's power leaves as particles no magnetic field can touch. Proton-boron releases everything as charged alpha particles. This is not a detail. It is a step function across the fuel list, and it decides what the machine must be made of.
Third, the radiation tax. Bremsstrahlung power scales as Z_eff times electron density squared times the square root of electron temperature. Boron carries charge five, so a proton-boron plasma radiates roughly thirty-nine times more than deuterium-tritium at equal ion density, and over a hundred times once the temperature penalty is included. Confinement quality is not optional for this fuel. It is the entire game.
Now the topology, and here mathematics closes a door. A confining magnetic field must lie along the plasma surface, because any field line that crosses the surface is an exit ramp. The hairy ball theorem says a smooth field combed along a sphere must vanish somewhere, and a vanishing point in a confining field is a hole. You cannot build a magnetic bubble. The torus is the only closed surface that combs flat. Every magnetic fusion machine is a donut by theorem, not by tradition. The sphere endpoint exists, but it belongs to a different force: lasers crushing a target inertially, or gravity building a star.
Put the pieces together and two machines fall out, drawn by their fuels.
Deuterium-tritium draws a fortress. Its neutrons demand a meter of lithium blanket to breed the tritium it burns, dense shielding to protect the magnets, and a vast vessel to hold it all. The plasma ends up the smallest thing in its own machine. Structure dominates because the fuel's energy exits in a form only bulk matter can catch.
Proton-boron draws a sculpture. No neutrons worth catching, so no blanket, no shield, almost no structure. What it demands instead is confinement quality, and the lever for that is geometry itself: coils shaped so the field-line pitch changes with radius. The tearing turbulence that leaks electron heat grows fastest where that variation sits near zero, weakens as the variation rises, and returns in a second band if it is pushed too far. The requirement is a window, not a knob, and it must be held from outside: a tokamak's self-organized current profile lands where it lands, while an externally shaped coil set can place the profile inside the window and keep it there. That mechanism chain is measured on the W7-X stellarator and published for anyone to check. The entire engineering budget goes into the winding shape. The geometry is not a cage around the physics. It is the physics.
And the drawings on this page are no longer an artist's guess. We ran the geometry as a derivation. The field-line pitch computes from published machine radii and the rotational transform, spanning 4.4 to 6.6 degrees at the edge across the anchoring stellarator's published settings, and every value inverts back to its input exactly. The coil standoff follows from the layer stack: roughly 1.7 times the plasma radius for deuterium-tritium once the blanket and shield are paid for, and barely 1.1 for proton-boron. The plasma fills about forty percent of one machine's cross-section and about ninety percent of the other. Two independent renderings of this page once disagreed with each other; both were checked against the derived table, and each kept only the features the derivation supports. The fuel draws the machine, literally: the picture obeys the numbers.
One force, two fuels, two machines that cannot trade places. A proton-boron plasma starves in the fortress. A deuterium-tritium plasma has nowhere to breed in the sculpture. The force picks the topology. The fuel picks the geometry within it.
That is a falsifiable claim, and this page carries its own kill condition. Press the red button. Run your community's own optimization codes at both operating points and produce one geometry that serves both fuels, and this page dies in public. We think it survives. The fuel constants say so.
Every number here traces to published physics: the Gamow formula, the bremsstrahlung scaling, the reaction kinetics, one topology theorem, and one measured stabilization mechanism. Our engine assembled the anchors and the derivation followed. First principles, all the way down.