Structures and methods enable emergency or rapid shutdown of an energized no-insulation (NI) superconducting magnet, without damage due to thermal effects of a quench. A resistive bypass wire is coupled between electrical terminals of the magnet coil, and does not pass significant current during normal magnet operation. When rapid shutdown is required, the bypass wire is cooled below its critical temperature, adding a superconducting current path in parallel with the magnet coil. A portion of the coil is then heated above its critical temperature, interrupting current flow through the coil. Hot spots near the coil leads are mitigated through the use of a conductive structure, such as copper cladding, that carries away excess heat due to the quench. This heat may be deposited in a resistive matrix, such as a steel plate, over a duration of seconds and without compromising other magnet design parameters.