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The stability of magnet conductors can be characterized by their minimum quench energies (MQE), i.e. the minimum energy pulse of small extent and short duration needed to initiate a quench. The MQE of a considerable number of prototype strands for the superconducting LHC magnets have been measured at BNL within the framework of the US-CERN accelerator collaboration. The main interest of this work was to study the effect of different strand designs, copper to superconductor ratios (Cu/Se) and the source of the niobium-titanium alloy on MQE. Although MQE varied significantly between the strands, the measurements revealed that except for Cu/Se ratio, these above stated parameters do not affect MQE in a consistent way. Numerical simulations indicate that these tests made with a restricted helium volume and heat exchange surface were quasi-adiabatic in nature, and hence the influence of the cooling even in superfluid helium was minimal.