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A novel insertion device for electron storage rings called the MAX-Wiggler has been constructed at MAX-lab. The MAX-Wiggler is a cold bore superconducting wiggler magnet with 47 3.5-T poles and a period length of 61 mm aimed for the production of X-rays at the 1.5-GeV electron storage ring MAX-II at MAX-lab. The MAX-Wiggler consists of 98 racetrack coils connected in series in the superconducting magnet and the total stored magnetic energy at the nominal maximum field strength of 3.5 T is 48 kJ. This paper describes the quench analysis of the magnet. Several protection schemes have been evaluated, such as an external dump resistor and safety switch or subdivision of the series of coils into sections with shunt resistors or silicon diodes in parallel to each group of coils in a section. It has been found that the most suitable protection scheme, in order to prevent the superconducting coils from getting overheated, is subdivision with a shunt path containing silicon diodes operating at liquid helium temperatures. The MAX-Wiggler has been commissioned and it has survived the quenches occurring during the initial training of the superconducting coils.