You can obtain Portable Firefox here:
http://portableapps.com/

http://portableapps.com/news
Firefox releases and Firefox Beta versions, but not Aurora which is like a second stage alpha development version.

"...but not Aurora which is like a second stage alpha development version. "

Sad but true.

Anyway it seems to be possible to tune a beta-fire into an alpha-burning-fire.

But it does not to be downloadable from anywhere.

Thanks for the answer anyway. I'll post if I find portable alpha-fire.

replacing the \App\firefox folder inside the portable firefox folder with the contents of the .zip package of aurora available from ftp://ftp.mozilla.org/pub/mozilla.org/firefox/nightly/latest-mozilla-aurora/ (or any other firefox version for that matter) works for me.

Note that the Aurora builds are updated daily, so you would need to repeat this daily to stay up to date.
otherwise you only get the current snapshot and you may be unlucky in some cases.
The beta channel would be better suited for this.

updating it through the internal auto-update feature will even work in the portable version!

I set "app.update.channel" to "aurora" in about:config in portable.beta.

But nothing happened.

You can't modify the app.update.channel pref via about:config.
That value is hard coded in the defaults\pref\channel-prefs.js file and you need to modify that file yourself to change the update channel.
If you have replaced the current Firefox version by the Aurora files then this should already has happened, but updating in general may have been disabled in the portable version.

the portable versions support updating: http://portableapps.com/forums/support/firefox_portable/faq#1