Semi-analytic analysis of the Alfvén wings of TRAPPIST-1 b with line cuts along the φ-direction that display the magnetic field components B_r, B_ϑ, and B_ϑ (from top to bottom). The blue line represents the field component extracted from the simulation results and the red line shows the same components calculated with the Alfvén wing polarization relations (Eqs. (8) and (9)) and the simulated plasma velocity. The panels a, c, and e show a cut through the inwardly traveling Alfvén wing at r = 16 R_*. The panels b, d, and f show a cut through the outwardly traveling wave structures at r = 40 R_*.