how to set value of autocomplete field and trigger search event with jquery
Looking in misc/autocomplete.js, there's a function called populatePopup() (Drupal.jsAC.prototype.populatePopup). Since that function is bundled into the jSAC object, we can't call it directly. Instead, let's simulate the event that calls it which is found in the onkeyup() function.

&lt;script&gt;
/**
 *  Fill an input field and then display the autocomplete popup.
 *
 *  @param $field
 *    This is a jQuery field reference -- e.g. $('#my-input-field')
 *  @param searchVal
 *    The text to place into the input field
 */
function ShowAutoComplete($field, searchVal) {
  var e = $.Event('keyup'); // Create an event to trigger
  e.which = 32; // Add the keyCode (32 is a space, but it shouldn't matter)

  // Set the field value, focus on the field, then trigger the event
  $field.val(searchVal).focus().trigger(e);
}
&lt;/script&gt;


FYI, I used this post as a reference to figure out how to fire the keyup event.