Warp drives are purely speculative and involve exotic negative matter, horrendous amounts of energy and possibly need FTL particles to steer the thing. There is no way magnetic fields could be used to generate this.
This paper which is further discussed in
this paper proposes ways of getting around the horrendous energy requirements outlined in
this paper. The "trick" is to change the warp bubble so that it's exterior radius is microscopic yet the interior radius is large enough to accommodate your vehicle (essentially making a warp bubble that's bigger on the inside than on the out). Apparently this would greatly shrink the amount of energy needed to manageable levels. They don't outline how exactly a shell could be build around a ship in such a fashion nor how the ship could leave.
However neither of these approaches fixes the other problems of a warp bubble such as requiring the construction of an exotic matter shell, superluminal signalling to steer/control the bubble and the huge amount of radiation a warp drive subjects you to. There are some interesting (but technical) objections in
this paper that apparently show that a warp drive would only be capable of very low velocities as well as highlighting other problems.
So without exotic matter that may
not even exist we are stuck to trying to make slower than light vehicles. To make an interstellar vehicle would be fantastically complex though requiring horrific amounts of energy (even if we used an antimatter rocket we would need potentially thousands-millions of tonnes for a high fraction of
c.) as well as a thorough understanding of ecology so as to make a stable environment in a closed system to keep the occupants alive.