Confinement Time & Scaling

In a tandem mirror the ion confinement time rises roughly exponentially with the plug-to-cell potential, which is why the plug is decisive.

What sets the confinement time

For central-cell ions, the confinement time in a tandem mirror scales with the electrostatic barrier they must climb. To first order it depends on how many collisions are needed to scatter an ion into the loss cone and give it enough energy to surmount the potential peak. The result is that τ grows steeply — roughly exponentially — with the ratio (φ_p − φ_c) / T_i.

This is the leverage of the tandem-mirror concept: a modest increase in the confining potential yields a large increase in confinement time, which is what lets an open-ended machine reach fusion-relevant τ. It is also the vulnerability — confinement is only as good as the potential the plug can actually sustain.

Coupling to the gates

Because τ depends so sensitively on the plug, the plug's field (26.49 T), density, and stability all feed directly into whether the power balance closes. The steepness that gives the concept its promise is the same steepness that makes the unproven plug regime so consequential.

The exponential sensitivity cuts both ways: it is why a well-built plug confines so well, and why a plug that falls short of its design potential loses confinement far faster than a linear intuition would suggest. Small shortfalls in the achievable potential — from stress limits, instabilities, or heating efficiency — translate into large shortfalls in τ, which is why the plug gates dominate the machine's prospects.

• τ grows ~exponentially with (φ_p−φ_c)/T_i
• Small potential gains → large confinement gains
• Enables fusion-relevant τ in an open machine
• Makes the plug regime decisive for the power balance