confused about copying a partition

[Dave Stevens]

I have a working spinning disk install of ubuntu, configured to do
various useful things. I'd like to move that functionality to a usb
stick. If it worked I'd be able to put together a system that would
boot identically to the current one, but cheaper, less power needed,
various advantages.

It seems as if I might be able to copy the existing partition (29GB) to
the target usb (32GB) and have a working bootable USB setup ready to
go. The purpose of the exercise is to gather air pollution measurements.

I can't seem to find what I need to do this, the usual assumption is
that I want to install a new ubuntu instance, but I don't and in any
case know how to do this already.

So is there a source of directions about how to clone the whole source 
partition to the destination USB stick.

Suggestions appreciated,

D