To ATP TDi
Cut the pampas grass back to about 2 feet. Use an herbicide containing glyphosate, Roundup is one. Spray the exposed cuts, following manufacturers guidelines. It may take several applications and several weeks to kill the clump completely.
A faster way would be to cut the plant down to the ground. Chop and cut into the clump exposing roots. Spray roots with an herbicide containing glyphosate. Again this may take several applications.
Do dispose of or burn any root you chop away, they could make new plants.
Hope this helps.
Reine