The Loss Cone
The loss cone is the range of velocity angles a mirror cannot reflect; collisions continually scatter particles into it, driving end losses.
A hole in velocity space
At each point in a mirror, particles are confined only if the angle between their velocity and the field exceeds a critical value set by the mirror ratio: sin2θc = 1/R. Particles within θc of the field line lie in the loss cone and stream out the end. Larger mirror ratio R shrinks the cone but never closes it.
Collisions are the problem. Even a perfectly confined ion is scattered by Coulomb collisions and can be knocked into the loss cone, after which it escapes on a transit time. This scatter-into-loss-cone process sets the intrinsic end-loss rate of a mirror and, without plugging, is far too fast for a power plant.
How the tandem mirror plugs it
The electrostatic potential built by the end plugs raises the effective barrier for ions leaving the central cell, so an ion must be scattered into the loss cone and have enough energy to climb the potential. This dramatically slows end loss — the central mechanism that makes the tandem mirror viable.
The size of the loss cone also governs how sensitive confinement is to the mirror ratio: because it depends on 1/R, pushing R higher yields diminishing returns, so beyond a point the electrostatic plug — not a stronger magnetic pinch — is the only economical way to further close the leak. That is the structural reason the tandem mirror exists.
- Loss cone half-angle: sin2θc = 1/R
- Collisions scatter ions into the cone
- Simple mirror leaks far too fast
- Plug potential adds an energy barrier on top