  We revisit Parker's conjecture of current singularity formation in 3D
line-tied plasmas using a recently developed numerical method, variational
integration for ideal magnetohydrodynamics in Lagrangian labeling. With the
frozen-in equation built-in, the method is free of artificial reconnection, and
hence it is arguably an optimal tool for studying current singularity
formation. Using this method, the formation of current singularity has
previously been confirmed in the Hahm--Kulsrud--Taylor problem in 2D. In this
paper, we extend this problem to 3D line-tied geometry. The linear solution,
which is singular in 2D, is found to be smooth for arbitrary system length.
However, with finite amplitude, the linear solution can become pathological
when the system is sufficiently long. The nonlinear solutions turn out to be
smooth for short systems. Nonetheless, the scaling of peak current density
versus system length suggests that the nonlinear solution may become singular
at finite length. With the results in hand, we can neither confirm nor rule out
this possibility conclusively, since we cannot obtain solutions with system
length near the extrapolated critical value.
