Let's consider the various parameters you gave.
First, from the title, you want a vertical.
Any particular reason? That might, or might not,
be a good choice since you already have a tower.
Any particular bands you want to operate? That
makes a big difference.
How much space around the antenna do you have
to work with?
These are my parameters:
No room for ground radials
No room
at all, or "not as far as I'd like"?
What about elevated radials?
For ground-mounted verticals, there are trade-offs.
You certainly can use a quarter wave vertical with
just a ground rod at the base, although often it
won't be as efficient compared to one with a good
set of ground radials. But that's a trade-off that
you need to make, based on your operating
preferences: there is no "right" or "wrong" choice.
If you do put a vertical at the top of the tower, it
may still require radials, which would be wires
sloping down at an angle to some sort of tie-off
point (which might be at ground level or elevated).
Do you have room to run those out 60' or so from
the base of the tower?
And that trade-off between performance and other
factors (size, complexity, cost, or whatever) will
continuously crop up in this discussion.
Have: 47' Rohn 25 tower
Are you assuming the antenna will go on top
of the tower? If so, does it need to be vertical?
How far can it hang out horizontally from the
top of the tower?
Mounting an HF vertical on top of a tower isn't
always the best approach, especially on the lower
bands where propagation is more via the ionosphere
rather than line-of-sight (like VHF).
But a horizontal dipole, beam, or quad can work well
on top of the tower, especially with a rotator so you
can aim it in the desired direction.
The tower can also be used to support wire antennas,
which may be more practical on the lower bands like
40m or 80m.
Have: full legal amplifier
That's going to rule out some of the shorter options,
as the traps are prone to overheating (some are only
rated for a few hundred watts). And the operating
mode becomes important: many antennas have a
lower power rating for CW, FM, or digital modes than
they do for SSB, because the lower average power
means less heating.
Would like to be able to work the community, as well as DX
That brings up a number of options...
How far out do you consider your "community"
to extend? In many cases, more local work these
days uses VHF/UHF, rather than HF. A ~ 4' to 10'
vertical on top of the tower should work well,
although your coverage area will depend on your
local topography and what repeaters you have
available. That's what I would plan to use for
distances up to 10-20 miles on simplex, or out
to 40-50 miles (and in some cases much further)
using repeaters.
For distances out so several hundred miles,
NVIS (high-angle) propagation on 40m through
160m is likely to give the best coverage. The
choice of bands will depend on the current
ionospheric conditions, and you likely will need
to change bands to maintain 24 hour coverage.
Now, a vertical antenna is a relatively poor choice
for this coverage, as it tends to have a null overhead,
which is where you want maximum radiation. A
wire dipole, even at a relatively low height, will
generally work better (besides being much simpler
and cheaper, and not needing ground radials).
You might need several of them connected to the
same feedpoint to cover multiple bands.
Ionospheric propagation on the higher bands will
generally have
minimum distance of 500 miles or
more, unless stations are relatively close (but there
may be exceptions).
So, yes, there are vertical antennas that claim multi-band
operation with no ground radials, but they are often
limited in their power handling. (Some versions are
intentionally lossy to improve the SWR, but that means
that they are dissipating much of your power as heat
rather than radiated RF.) And, in order to cover (or at
least
claim to cover) all HF bands in one antenna with
useful radiation patterns can require a fair bit of complexity,
or large physical size.
Part of the problem also is that the same antenna
polarization or other characteristics may not be optimum
for all the HF bands.
A common solution would be to choose a combination of
antennas, rather than just one. A common approach is to
use a rotatable beam antenna for 20m through 10m (with
or without 17m and 12m, depending on your preferences).
Or you might find that just a 20m antenna is sufficient for
working longer distances most of the time - again, that is
a personal decision, but there are many options in that
category. Then 40m and 80m (and possibly 160m, 60m,
and/or 30m if desired) would use inverted vee dipoles
using the tower as a center support. That gives you both
the local coverage on the lower bands (although not just
limited - could cover a couple thousand miles or more),
and DX / longer distances on the higher ones. For local
work, you can stick a VHF/UHF FM antenna on top of the
tower as well.
That's a common and simple solution with good all-band
coverage. But, other than the VHF/UHF antenna, none
of them are verticals. That's why it is important to
understand the reason for that specification.
If you want to stick with a vertical, then something like
the DX COMMANDER, or a home-buit version, might be
a reasonable choice. This is really just a bunch of
quarter wave wires for each band of interest running up
to a pair of cross-arms, with coax attached at the
base. Because there are no traps or loading coils
(although you might need to add a coil for 80m),
there isn't much to limit the power handling capacity.
Yes, you would have better performance with a better
ground system, but if all you can manage is a ground
rod or two at the base of the tower that you use to
support the wires, that maybe adequate for your
needs. There are other variants on that same approach,
depending on what bands you want to include.
So one reason that you don't find a lot of antennas that
met your original criteria is that making a single vertical
that covers all the HF bands with a useful radiation pattern
is pretty complex. I have one up in the attic that is rated
to cover 40m through 10m (a Cushcraft R7 I think) and,
while, yes, I can set it up by myself, it can be rather
complex to adjust, easy to detune if there is anything
near the feedpoint, has narrow operating bandwidth,
and... well, the fact that it is in a bucket up in the attic,
rather than set up and in use, may give you an idea of
how well I like using it.
In another case, a multiband vertical claimed to "work"
on 80m was measured to be 1% efficient. That means,
with 1 kW input, you'd get about 10 watts radiated. But
only briefly: the remaining 990 watts turned into heat
would quickly melt the antenna.
But, if you still want one antenna with good performance
over all or most of the HF range, there are some options.
Like
this, or
this, or
this, or
this.
But they might not be in your price range.