Let me add a little to Owen's excellent explanation.

We can mathematically separate any two currents into a "common mode" (or
even mode) current and a "differential mode" (or odd mode) current. If
the two currents are equal in magnitude and opposite in direction, the
common mode component is zero; if they're equal in magnitude and in the
same direction, the differential mode component is zero.

This mathematical trickery is very useful in analyzing transmission
lines, because superposition allows us to treat the effects of the two
mode currents separately and sum the results. In a transmission line,
the differential mode current is sometimes appropriately called the
"transmission line" current, and the common mode current the "antenna"
current. This is because the differential mode current conforms to all
the transmission line rules -- that is, it behaves as though it and it
alone is being carried by the transmission line, and its properties can
be found by applying normal transmission line equations and analysis. No
radiation results from the transmission line currents. (In practice, a
very small amount of radiation results from the differential current on
a non-coax line, but if it's significant, a poor choice of transmission
line was made.) And the common mode current behaves just like any other
current on a single conductor (or identical currents on two parallel
conductors) - it creates a radiating field. The conductor carrying the
current is, by any definition, an antenna. So if we want to eliminate
feedline radiation we need to eliminate (or, practically speaking,
reduce to a small value) the common mode current.

To do this analysis with a symmetrical line such as twinlead or open
wire line, we use the currents on the two conductors as the two currents
to separate into common and differential mode components. We can do
exactly the same thing with coax, using the current on the inner
conductor as one of the currents to be separated, and the vector total
current on the inside and outside of the shield to be the other. If we
do this, we find that the two types of line behave identically: If the
common mode current is zero, the line won't radiate (and can be
considered balanced). If it isn't, the line will. Equations and analysis
are identical. Either type of line can be balanced or unbalanced.

Coaxial lines do, however, have an interesting characteristic not shared
by other kinds -- the differential and common mode components aren't
simply a mathematical convenience, but are actually physically separate.
If we do the analysis described above, we find that the common mode
current equals the current on the outside of the shield and the
differential current equals the current on the inside. As Owen pointed
out, the differential current is solely on the inside of the shield and
the common mode current solely on the outside. While this makes the
effects of each mode current easier to visualize and sometimes to
measure, the net effects of common mode and differential currents are
exactly the same for coaxial and non-coaxial lines.

Roy Lewallen, W7EL

Owen Duffy wrote:
"Tam/WB2TT" wrote in
:

...
The choke suppresses the common mode signal. There will still be
current flowing on the shield which will have the same magnitude as
the current flowing in the center conductor. You are not throwing away
...

This might just be really loose language, but assuming fully effective
skin effect (which is a reasonable assumption for most practical coaxial
cables at HF):

The current flowing on the outside of the inner conductor is accompanied
by a current equal in magnitude and opposite in direction flowing on the
inside of the outer conductor.

Skin effect isolates the inner of the outer conductor from the outer of
the outer conductor, but current on the inner of the outer conductor may
contribute to current on the outer of the outer conductor depending on
the treatment of the shield at the ends of the cable.

So, a choke formed by coiling the coaxial cable or placing ferrite
sleeves on the cable affects the impedance in the current path of the
outer of the outer conductor and does not directly affect what is
happening inside the coax.

Mind you, this concept is not universally accepted by hams.

In the case of coax, so-called common mode current flows only on the
outside of the outer conductor, and differential mode current flows only
on the inside of the outer conductor and outside of the inner conductor.

Owen