You'll need 100% pure O2 through a non-rebeather mask like the O2ptimask for CH, at 15 l/minute, minimum.
You can get an O2ptimask through clusterheadaches.com store, not available here.
I don't think site admin here would mind a link, if it brings you relief:
http://www.clusterheadaches.com/ccp8/index.php?app=ecom&ns=prodshow
&ref=clustero2kit
The trick with these things is having enough O2 in the bag, 3 liters or more and making sure you don't re-breathe any exhaled breath.
Some are using O2 demand valves pushing well over 15l/min and having success where before they did not.
O2 Concentrators can't support the purity required or as Kim says, the flow required rate.
Pete Batcheler also has some O2 breathing techniques (hyperventilation technique) that may help, he's the O2 expert there.
If your GP recommends a concentrator, he's not read up on O2 in CH at all and you may have trouble getting prescribed O2 from that GP. A referral to a Neurologist should be able to prescribe O2 for CH.