The betatron effect in collapsing magnetic traps

We consider the question of how the betatron effect affects the particle acceleration in a magnetic trap with a rapidly decreasing length. We show that the additional increase in energy caused by the betatron acceleration as the trap contracts is exactly offset by the decrease in the time of particle confinement in the trap, because the loss cone becomes larger during the contraction. As a result, the particle energy at the time of escape from the trap remains the same as that in a collapsing trap without contraction. We estimate the Alfvén-pumping efficiency in a collapsing trap in connection with the problem of particle acceleration in solar flares. The additional energy acquired by particles from magnetic-field oscillations is shown to be negligible. We discuss the possible observational manifestations of the betatron effect in solar flares.