If you handle the file downloading yourself in server side code by writing chunk by chunk to the response stream, then you'll know when the file had finished downloading. You would simply have to connect the FileStream to the response stream, send data chunk by chunk, and redirecting after complete. This can be inside your popup window.
Response.ContentType = "application/octet-stream";
Response.AppendHeader("content-disposition", "attachment; filename=bob.mp3");
Response.AppendHeader("content-length", "123456789");
Make sure you check Response.IsClientConnected when writing out to the response stream.
or
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File Download in ASP.NET and Tracking the Status of Success/Failure of Download[
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