Langmuir wave energy density in plasma frequency – time plane. Langmuir waves produced by the electron beam with parameters as in Figs. 3, 4 but with a magnetic flux tube that undergoes increased expansion at a critical height Eq. (13). Left panels: the critical height is r_c = 2 × 10¹⁰ cm. The severity of the extra expansion increases from top to bottom. Right panels: the critical height is r_c = 4 × 10¹⁰ cm. The severity of the extra expansion increases from top to bottom as Z_c = 10¹,10³,10⁵.