Adding query string to current page URL without refreshing for Ajax Accordion

I have a page with an ajax accordion control on it. When the user goes to the page all the panes are closed. As soon as the user selects a pane I want to add or update the url to have the current pane id as part of the query string.

The scenario that I'm trying to account for is that when the users go to my page and select a pane there are data files they can download. If the user isn't already logged in it takes them to the login page. When I redirect them I want it to display the correct pane open so they can click on the data file again and get the data.

Thank you