Download and open PDF file using Ajax

$.ajax({
  url: '<URL_TO_FILE>',
  success: function(data) {
    var blob=new Blob([data]);
    var link=document.createElement('a');
    link.href=window.URL.createObjectURL(blob);
    link.download="<FILENAME_TO_SAVE_WITH_EXTENSION>";
    link.click();
  }
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

$.ajax({
  url: '<URL_TO_FILE>',
  success: download.bind(true, "<FILENAME_TO_SAVE_WITH_EXTENSION>", "<FILE_MIME_TYPE>")
});