Make while loop for get_category_children (jquery/idtabs)

I’m trying to integrate idtabs into a menu; https://www.sunsean.com/idTabs/

I wonder if I can make a loop for the childs of every category/parent and load it into a div:

<ul class="idTabs">
  <li><a href="#jquery">jQuery</a>
</li>

  <li><a href="#official">Tabs 3</a>
</li>

</ul>

<div id="jquery">If you haven't checked out ...</div>

<div id="official">idTabs is only a simple ...</div>

SO in this case jquery should be “$cat” and every cat should also be as an id in de div that needs to be the submenu.

Can someone help me out with this ?