Using jQuery AJAX to download a binary file

Just use XHR directly. This example is taken from MDN:

var oReq = new XMLHttpRequest();
oReq.open("GET", "/myfile.png", true);
oReq.responseType = "arraybuffer";

oReq.onload = function(oEvent) {
  var arrayBuffer = oReq.response;

  // if you want to access the bytes:
  var byteArray = new Uint8Array(arrayBuffer);
  // ...

  // If you want to use the image in your DOM:
  var blob = new Blob([arrayBuffer], {type: "image/png"});
  var url = URL.createObjectURL(blob);
  someImageElement.src = url;

  // whatever...
};

oReq.send();