You can use client-side code to achieve this. With jQuery for example.
Check out this post :
http://stackoverflow.com/questions/4545311/download-a-file-by-jquery-ajax
There is a jQuery plugin that makes the download very easy:
$.fileDownload('some/file.pdf')
.done(function () { alert('File download a success!'); })
.fail(function () { alert('File download failed!'); });
Then you can clear the textbox
$('#textboxId').val("");
All this happens on the client side so the user stays on the same page