[jQuery] each, index to addClass

[yskel]

New to jQuery, and I have a problem that I suspect has a really simple
solution:

For a set of elements matching $(a.CustomClass), how do I add a class
to each element based on that element's index?   For instance my
document contains:

<a class='CustomClass' src='#'>test</a>
<a class='CustomClass' src='#'>test</a>
<a class='CustomClass' src='#'>test</a>

I'd like to run the jQuery script to end up with something like this:

<a class='CustomClass index_0' src='#'>test</a>
<a class='CustomClass index_1' src='#'>test</a>
<a class='CustomClass index_2' src='#'>test</a>

I've been trying to use:

$(a.CustomClass).each(function(){
    var index = $(this).index(this);
        $(this).addClass(index);
});

but it definitely is not doing what I expect.  Any help would be
greatly appreciated.