Download file through an ajax call php

I have a button and onclick it will call an ajax function.

Here is my ajax function

function csv(){

    ajaxRequest = ajax();//ajax() is function that has all the XML HTTP Requests

    postdata = "data=" + document.getElementById("id").value;

    ajaxRequest.onreadystatechange = function(){
        var ajaxDisplay = document.getElementById('ajaxDiv');
        if(ajaxRequest.readyState == 4 && ajaxRequest.status==200){
            ajaxDisplay.innerHTML = ajaxRequest.responseText;           
        }
    }

    ajaxRequest.open("POST","csv.php",false);
    ajaxRequest.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded');
    ajaxRequest.send(postdata);
}

I create the csv file based on the user input. After it's created I want it to prompt download or force download(preferably force). I am using the following script at the end of the php file to download the file. If I run this script in a separate file it works fine.

$fileName = 'file.csv';
$downloadFileName = 'newfile.csv';

if (file_exists($fileName)) {
    header('Content-Description: File Transfer');
    header('Content-Type: text/csv');
    header('Content-Disposition: attachment; filename='.$downloadFileName);
    ob_clean();
    flush();
    readfile($fileName);
    exit;
}
echo "done";

But If I run it at the end of csv.php it outputs the contents of the file.csv into the page(into the ajaxDiv) instead of downloading.

Is there a way to force download the file at the end of csv.php?

AJAX isn't for downloading files. Pop up a new window with the download link as its address, or do document.location = ....