Magnetic Mirror Ratio

The mirror ratio — peak field over central-cell field — sets how tightly the machine reflects ions and how wide the loss cone is.

A single geometric number

The mirror ratio R is the ratio of the maximum field an ion encounters to the field where it starts. In the burner, the peak is the 26.49 T plug and the throat is 17 T, both far above the low central-cell field. A larger R means a stronger reflecting force and a narrower loss cone.

The loss cone

An ion is confined if the sine of its pitch angle exceeds 1/sqrt(R). Ions inside that cone in velocity space escape. So R directly sets the fraction of a Maxwellian that leaks:

import math
# mirror ratio from design-point fields
B_throat = 17.0   # tesla
B_peak   = 26.49  # tesla
B_cell   = 3.0    # tesla, illustrative central-cell field
R_throat = B_throat / B_cell
R_peak   = B_peak / B_cell
loss_cone_half_angle = math.degrees(math.asin(1/math.sqrt(R_peak)))
print(round(R_throat,2), round(R_peak,2), round(loss_cone_half_angle,1))

A higher mirror ratio alone still leaks too fast to burn — that is the classic single-mirror problem. The tandem design closes the gap with the ambipolar potential, so the mirror ratio and the electrostatic well share the confinement job.

• Large R narrows the loss cone but cannot eliminate it
• The plug potential does what the magnetic mirror alone cannot
• R also sets the flux-tube expansion into the expander

Note the central-cell field above is illustrative; the load-bearing frozen numbers are the 26.49 T peak and 17 T throat. The mirror ratio is derived from those and the chosen central-cell field.

In practice the mirror ratio is a shared budget: raise it and the magnetic mirror carries more of the confinement, lower it and the ambipolar potential must carry more. The design study picks the split that keeps both the magnets and the required plug heating within reach.