Fig. 5

Trajectories of relativistic electrons in the (θ −ζ) phase space for S = − 0.4. The phase ζ of non-resonant electron oscillates between 0 and 2 \( \pi \) (blue line), whereas the oscillation for resonant electrons (\( v_{\parallel } \cong V_{R} \)or\( \theta \cong 0 \)) draws closed trajectories (red trajectory). The region where electrons draw closed phase trajectories is called trapping region (colored in white), and the boundary of the region is defined as separatrix of the trapping region. Resonant electrons continue to gain energy while they are trapped within the region