I am obviously missing many details; the term displacement current is not
used very frequently in my teaching. But let me share an idea triggered by
a message. The displacement current was presented as something needed for
the sake of continuity. Here is a situation in which it may be viewed as
"existing without being part of a closed loop".
Think of a metallic box A, in a vacuum, facing another box B. The boxes
are suspended by nylon threads and form a capacitor. Box A has a very
strong source of beta particles inside. A collimated beam of these
relativistic electrons is emitted from A and absorbed by B. We see that
A becomes more and more positive while B becomes more and more negative.
The real current (the beam) and the displacement current exist in the
same cylindrical segment. Where is the current loop? Assume that A and B
were initially in contact and that the half life is very long. An atomic
generator of the linearly growing d.o.p., if you wish.
Ludwik Kowalski