This Letter is devoted to the still open problem of the evolution of a
three-dimensional coronal flux tube embedded in a low-beta ideal plas
ma and having its footpoints twisted by slow photospheric motions. Suc
h a process has been simulated with a recently developed magnetohydrod
ynamic code. In the particular calculation reported here, the system o
ccupies a large cubic box. The field is initially potential, being gen
erated by an underlying horizontal dipole, and it is twisted by two vo
rtices located on the lower face {z = 0} of the box, on both sides of
the neutral line. In a first phase, the field roughly evolves quasi-st
atically through a sequence of force-free configurations. Thus, it ent
ers a dynamical phase during which it suffers a very fast expansion, c
losely approaching after some finite time a semiopen configuration. Th
e energy increases monotonically during all the evolution, and it tend
s to a limit, which is equal to about 80% of the energy of the totally
open field associated with B-z.