Magnetic Mirror and Loss Cone

In an adiabatic guiding-center model, a charged particle moving in a slowly varying magnetic field conserves both its total kinetic energy and its magnetic moment (μ ~ v_perp² / B). As the particle approaches a region of stronger magnetic field (a "magnetic mirror"), its perpendicular kinetic energy increases while its parallel kinetic energy decreases to conserve total energy. If the parallel kinetic energy reaches zero, the particle is reflected. This defines the concept of the loss cone: particles with a pitch angle smaller than a critical value will not be reflected and will escape the trap.

experiment

To observe the adiabatic reflection of particles in a magnetic mirror, use the Interactive visualization below to adjust the initial conditions and track the particle's energy components. Follow the link to open the module: https://riano.app/module/magnetic-mirror-loss-cone.

1. Set the Mirror ratio to 4 and observe the critical pitch angle calculated by the model.
2. Change the Pitch degrees to 45 (greater than the critical angle). Note that the particle is reflected before reaching the maximum probe point, showing its energy components as "Unavailable" at the probe fraction of 1.
3. Adjust the Probe fraction to 0.5 to investigate the particle's state halfway to the mirror point. Notice how the perpendicular energy fraction increases as the probe moves deeper into the stronger field, at the expense of the parallel energy fraction.