Effect of hydromagnetic waves in a dipole field on the longitudinal invariant

Hydromagnetic wave violation of the longitudinal invariant of a particle trapped in a mirror magnetic field is investigated quantitatively. It is shown that the passage of hydromagnetic waves across the region of mirroring leads to a diffusion of the individual-particle mirror points. If the relative wave amplitude ΔB/B is maintained throughout the mirror field, particles released in the field will soon diffuse out through the mirror and be lost. Application to thermonuclear devices is obvious. Confining our attention principally to the charged particles trapped in the geomagnetic field, it is shown that high-energy (105-ev) electrons in the outer Van Allen radiation zone are caused to diffuse along the lines of force with a characteristic time of 4 months by hydromagnetic waves of 1 cps and an amplitude of 10−4 gauss. Hydromagnetic diffusion appears to be more important than collisions in determining the electron lifetime and distribution in the outer Van Allen radiation zone. Different wave distributions along the lines of force can give radically different particle distributions. It is shown that, if the hydromagnetic disturbances extend throughout the geomagnetic field, then, rather than yielding particle acceleration, they result in a net loss of particle energy. But if we assume a region of hydromagnetic disturbance localized inside the geomagnetic field, limited particle acceleration may result.