Feeding the Burning Plasma

Abstract

A burning plasma consumes only part of the fuel that passes through it. The fueling system must continuously choose how much deuterium and tritium to inject, where to deposit it, how to shape density, how to recover unburned isotopes, and how to stop the reaction without leaving an uncertain inventory in walls and pumps. I combine edge gas injection, high-field-side cryogenic pellet injection, impurity seeding, disruption-mitigation payloads, exhaust recovery, and mass accountancy into one architecture. Pellet penetration and reliability are as important as nominal throughput. Every valve, reservoir, transfer line, and diagnostic receives a confinement and accountancy role because tritium is both scarce fuel and regulated radioactive material.

Fuel moves through the plasma faster than the plant

In a magnetic-confinement plant, only a fraction of injected deuterium and tritium fuses before particles leave the confined plasma. The exhaust system returns most fuel to processing. The fuel cycle is therefore a high-throughput loop surrounding a much smaller burn rate.

For fusion power $P_f$, the reaction rate is

$$\dot N_f=\frac{P_f}{E_f}.$$

At $P_f=1\ \mathrm{GW}$ and $E_f=17.6\ \mathrm{MeV}=2.82\times10^{-12}\ \mathrm{J}$,

$$\dot N_f\approx3.55\times10^{20}\ \mathrm{s^{-1}}.$$

This corresponds to roughly $1.5\ \mathrm{mg/s}$ of deuterium-tritium fuel burned, or about $130\ \mathrm{g/day}$. Circulating inventory can be far larger because burnup per pass is limited and processing equipment contains material.

Edge gas is useful but shallow

Gas valves provide fast, adjustable fueling and are valuable during startup, edge-density control, wall conditioning, and selected operating phases. Neutral atoms entering from the boundary ionize and become tied to magnetic field lines. In a large, hot plasma, much of this source remains near the edge.

Increasing gas flow can raise divertor and pumping load without efficiently raising core density. The edge response also depends on recycling from the wall. A commanded valve flow is not identical to the source reaching the confined fuel.

Gas injection remains one actuator among several. Its lines need short response, known volume, isotope-compatible materials, double isolation, purge capability, and leak detection. The control system distinguishes a valve command, measured line flow, vessel response, and recovered exhaust.

Pellets carry fuel inward

Cryogenic pellets of frozen hydrogen isotopes can cross the plasma edge before ablation deposits their material. Injection from the high-field side can exploit drift and geometry to improve core deposition. Pellet size, speed, composition, launch angle, guide-tube curvature, and plasma state determine penetration.

A pellet’s kinetic energy is modest,

$$E_k=\frac{1}{2}mv^2,$$

but its thermal and mechanical fragility is severe. A $5\ \mathrm{mg}$ pellet at $1{,}000\ \mathrm{m/s}$ carries $2.5\ \mathrm{kJ}$. It must survive fabrication, acceleration, bends, vibration, and injection with controlled shape.

The pellet plant includes isotope metering, freezing, extrusion or forming, cutting, acceleration, guide tubes, trajectory measurement, missed-pellet capture, and tritium confinement. Reliability is calculated per pellet. If steady operation needs several injections per second, a failure rate that seems small per shot can create frequent plant interruptions.

Actuator	Best use	Limitation
Gas injection	Fast edge control and startup	Weak core penetration in large hot plasmas
Cryogenic pellets	Core fueling and density-profile control	Factory and guide reliability, discrete perturbations
Neutral beams	Heating, current, torque, and some particles	High electrical demand and complex beamline
Impurity seeding	Exhaust radiation and detachment	Core dilution and contamination risk
Mitigation pellets or gas	Rapid abnormal-event response	Delivery must outrun disruption evolution

Fuel ratio is a profile

Maximum deuterium-tritium reaction rate favors similar local densities, but the plant controls sources at the boundary and observes composition indirectly. Isotope transport, neutral beams, pellets, recycling, and preferential pumping can create radial and temporal variation.

For fixed total fuel ion density $n_f=n_D+n_T$, the reaction source is proportional to

$$n_Dn_T=f_D(1-f_D)n_f^2,$$

where $f_D=n_D/n_f$. The product reaches its maximum at $f_D=0.5$. A $60:40$ mixture retains $96\%$ of the maximum product, which provides some operating tolerance. Accurate ratio control still matters to performance and tritium use.

Spectroscopy, neutron diagnostics, gas analysis, calibrated injection, and exhaust composition together estimate the isotope state. No single measurement closes the inventory.

Walls participate in fueling

Plasma-facing surfaces absorb fuel during one phase and release it during another. Retention depends on material, temperature, damage, implantation, codeposition, dust, and prior exposure. A hot wall can release inventory after plasma termination; a cool deposit can hide tritium from process measurements.

I divide the fuel balance into measured and inferred stores:

$$M_{\mathrm{injected}}+M_{\mathrm{bred}} =M_{\mathrm{burned}}+M_{\mathrm{exhaust}}+M_{\mathrm{process}}+M_{\mathrm{stored}}+M_{\mathrm{wall}}+M_{\mathrm{loss}}.$$

Each term carries uncertainty. If the residual exceeds its limit, operation stops until the discrepancy is understood. Accountancy is an online control function, not a monthly administrative reconciliation.

Impurities are injected on purpose

The divertor may need seeded neon, argon, nitrogen, or other species to radiate exhaust power over a larger surface. The injection system meters small flows with high dynamic range and spatial control. Too little radiation leaves an excessive target load. Too much cools or dilutes the core.

Fueling and impurity seeding share the density and exhaust budget. Their controllers need a coordinated objective:

$$J=w_1(P_{\mathrm{target}}-P^*)^2+w_2(n_e-n^*)^2+w_3(Z_{\mathrm{eff}}-Z^*)^2,$$

subject to stability and actuator constraints. The expression is schematic, but it makes the coupled task explicit.

Termination needs dedicated payloads

Routine shutdown reduces heating and fueling while controlling current and density. An incipient disruption may demand rapid delivery of radiating material to spread thermal energy and raise plasma density enough to suppress runaway electrons. Massive gas injection, shattered pellets, or other projectiles are candidates.

The mitigation system is physically a fueling system with a different safety classification. It needs independent stored payloads, rapid diagnostics, verified line readiness, and a response time shorter than the developing event. A failed routine pellet should not disable emergency injection.

PrepareMeter and form clean isotopes

Control composition, purity, pressure, and cryogenic state.

DeliverPlace particles at useful depth

Coordinate gas, pellets, beams, impurities, and mitigation payloads.

RecoverPump and separate exhaust

Return unburned fuel while removing helium and contamination.

AccountReconcile every inventory

Bound material in storage, process equipment, walls, dust, and waste.

Availability is built pellet by pellet

Parallel injectors permit maintenance and fault recovery. Isolation valves allow a guide tube or forming unit to be removed without venting the torus. Diagnostic sections identify pellet speed and integrity before it reaches the machine. Misfires flow into a confined recovery volume rather than an inaccessible plant space.

MeasureEstimate density and isotope profiles InjectSelect gas, pellet, beam, or impurity ObserveConfirm deposition and plasma response RecycleRecover exhaust and reconcile mass

Fuel determines density, but density alone does not create a burning state. External systems must initiate the plasma, raise its temperature, drive non-inductive current, and retain enough control authority after alpha heating becomes dominant.