A new concept for superconducting Toroidal Field (TF) magnet construction is presented in this paper. It is termed the "Demountable Externally Anchored Low Stress" (DEALS) magnet system. In contrast to continuous wound conventional superconducting coils, each magnet coil is made from several straight coil segments to form a polygon which can be joined and disjoined to Improve reactor maintenance accessibility or to replace failed coil segments if necessary. In this paper, we present a design example of a DEALS magnet system for a UWMAK IX size reactor. The overall magnet system is described, followed by a detailed analysis of the major heat loads in order to assess the refrigeration requirements for the concept. Despite the increased heat loads caused by high current power leads (200,000 amps) and the coil warm reinforcement support system, our analysis shows that at most, only about one percent (^20 Mw) of the plant electrical output >2,000 Mw) is needed to operate the magnet cryogenic system. The advantages and the drawbacks of the DEALS magnet system are also discussed. The advantages include: capability to replace failed coils, increased accessibility to the blanket shield assembly, reduced reliability requirements for the magnet, much lower stress in conductor, easier application of improved high field brittle superconductors like Nb,Sn, improved magnet safety features, etc. The drawbacks are the increased refigeration requirements and the necessity of a movable coil support system. A comparison with a conventional magnet system is made. We conclude that the benefits of the DEALS approach far outweigh its penalties, and that the DEALS concept is the most practical, economical way to construct TF magnet systems for Tokamak reactors. -NOTICE-Tfcit irpott MS pirptni ai an account of work Vofuorad by the Uaited Stales Gowtnmei... Netthet the United Sutes not the United Sutet Eaergy Reaearch and Development Adrwiwtnlion. nor any of the* employee*, aoi iny of thed tontracton, M*contffc*3n, or their employee*. make* any warranty, e«pre» oi implied, oi a»umet any knl fctbttly or ntpoiutbmy tot tn« tccuncy, campkieixx ot uvroL.es of any information, ippantin. pioduct oi proceu d*do*d. or repreicnls that in use would not, infringe printely owned rights. '