Magnetic Mirror Fusion Confinement

Magnetic Bottle

Mirror ratio R = B_max/B_min 5.0

Particle speed v₀ 1.0

Injection rate 6/s

Confinement

Loss-cone half-angle θ_c

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Trapped

Escaped

Confinement fraction

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Active particles

How it works

A magnetic mirror confines charged particles with a magnetic field that is weak in the middle and strong at both ends (two coils). As a particle drifts toward a coil, its perpendicular (gyration) speed v⊥ grows while its parallel speed v∥ shrinks, because two quantities are conserved along the way:

Magnetic moment (adiabatic invariant): μ = m v⊥² / (2B)  ≈ constant
Kinetic energy:                        v∥² + v⊥² = v₀² = constant
Mirror force along the field line:     m dv∥/dt = −μ dB/dz

If v∥ reaches zero before the particle reaches the coil (B = B_max), it turns around — trapped, bouncing forever between the two mirror points. If the particle's pitch angle θ (between v and B) is too small — too much of its speed is parallel to the field — v∥ never reaches zero and the particle escapes through the throat. This escape region is the loss cone:

sin²θ_c = B_min / B_max = 1 / R
θ_c = asin(1/√R)

Mirror ratio R — how much stronger the field is at the coils than at the midplane. A larger R shrinks the loss cone and traps a larger fraction of particles.
Particle speed v₀ — sets the bounce period; the loss-cone angle itself does not depend on speed.
Injection rate / Inject Bunch — particles are launched from the midplane with an isotropic (3D-random) direction, exactly as thermal particles would arrive from a plasma source.

Real-world relevance: this is the original confinement scheme tried for fusion (e.g. the 1950s–80s mirror machines, and today's tandem-mirror and Z-pinch-adjacent research); its fundamental leak — the loss cone — is the reason most modern reactors (tokamaks, stellarators) instead close the field lines into a torus with no ends to lose particles through.

Trapped (bouncing) Escaping (loss cone)

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