First, you don't "SEND" session variable. If you have a session started then they exist for all pages in the session - so they aren't sent: you just use them.
For AJAX, you can send any values you wish when executing the XMLHttpRequest send() function. Since your using jQUery, you'll need to use their method. I prefer straight javaScript.
How yous send values, which are essentially part of the URL, depends on how you invoke the send - they're retrieved on the other side in the $_GET or $_POST arrays, or $_REQUEST, which access both.
Here for "real" AJAX:
AJAX Introduction[
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You can find their jScript tutorial, as well, if you need it.