Force Download

Unfortunately, this is not a matter that you can control yourself. Even if the pdf links have this download attribute, the browser settings determine what happens – you can force a download – but the pdf file will open anyway in the browser.

// with file-extension
function force_pdf_link_to_download() { 
?>
<script type="text/javascript">
window.addEventListener("DOMContentLoaded", function () { 
(function($){
      $('a[href$=".pdf"]').each(function() {
         pdfName = $(this).attr('href').match(/\/([^\/?#]+)[^\/]*$/)[1];
         $(this).attr('download', pdfName ).attr('target', '_blank'); 
      });
})(jQuery);
});   
</script>
<?php 
}
add_action('wp_footer', 'force_pdf_link_to_download');

it is not possible to add a download attribute to a link with no value – even if you try that –
texteditor will correct it to: download="" so the script above will insert download="filename.pdf"

Even an entry in the htaccess file does not have to be followed by the browser:

<FilesMatch "\.(?i:pdf)$">
ForceType application/octet-stream
Header set Content-Disposition attachment
</FilesMatch>

so what could be reached is that the file downloads on click – but it will open in browser tab too.

Perhaps a more skilled programmer than me can force this behaviour – but I think it will be futile, especially since it is supposed to be browser independent.