It's not quite as simple as that I'm afraid - if you want to kill the roots, you will have to expose the woody parts, drill or cut into them and apply SBK, a brushwood killer. The alternative is to dig them all out, or pay someone else to take them out. Even then, depending which variety of C. alba you've got, if they've been there a long time and there are lots of them (not sure quite what you mean by a 'plantation', sort of implies a massive field full of them), the roots will be fairly extensive.

There are worse things to have a plantation of! If you cut it back and let the young stems come up you should get great winter colour (that most people long for in their gardens)