Instead of requireing admin.php you just can use WP built-in ajax functionality, even if it’s not ajax in this case.
Add a hook
add_action('wp_ajax_my_plugin_function', 'my_plugin_function_callback');
Create your output function (callback)
function my_plugin_function_callback() {
// do stuff
}
Call it this way
instead of:
file : url + '/box.php',
you should be able to use the global ajaxurl:
file: ajaxurl + '?action=my_plugin_function&optional=data ...
Maybe add a nonce for security reasons, but that’s up to you 🙂