Here's the odd thing:
In this image
http://i.imgur.com/T02fdtl.jpg You can see a plasma stream going from the electrode TO the mirror. This suggests significant current is flowing from the electrode to the mirror and to the water cooling supply. This is BAD. Mirrors aren't designed to carry any current or come in contact with the plasma stream.
You need to flush the tube with clean water and run it on deionized water or even flush with alcohol and then run on mineral oil. If you wish to salvage this tube at all you need to prevent plasma flow to the mirror.
I don't know if the power supply is just inadequate, or if this tube cannot be run on AC at all, as this is highly atypical behavior, but until the mirror being in circuit situation is rectified it doesn't really matter. You're going to destroy your mirrors at this rate. (Also, that point of the wire connecting the electrode is not meant to be in contact with plasma either, and it WILL wear out too.)