Nowadays most magnetic lenses used to capture and to focus pions and muons utilize azimuthal magnetic fields generated by large axial currents, like horns or lithium rods (or even a Z-pinch at GSI). Capture and focusing angle is proportional to the product of the current and length of the lens. State-of-the-art for these lenses is no more than 750 kA and 70 cm. A meter long, multi-MA, magnetized axial discharges were generated by the early days of fusion. Lenses based of such devices can increase the capture angle of pions, e.g., by more than a factor of 2. Electron beam cooling is presently achieved in storage rings by having charged particles interact with a co-moving electron beam. In these devices, typical parameters are electron beam currents of about 1 A, an interaction length of about 1 meter, and interaction time of about 30 msec. Multi-MA electron beams can be used for single-pass final stage cooling in a number of machines. Calculations for some applications, as well as other advantages indicate that these schemes deserve further more serious consideration