What you are referring to is the 'return wire':
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From the website: faqlight.carpassion.info:
The importance of spacing for return wire on D2 bulb
If the return wire (on the bulb) electrically hits headlight reflector, you can risk your ballast. The igniting mechanism in ballasts are relatively frigile and start voltage can decrease from the rated 23kV. That means that it will not be aurn wire and the metal. (Notice that even plastic reflectors are considered an electrical conductor. They are chromed.) You can get away with a close distance if area is very small. But it might give unpredictable results. Its the same with lighting froime.
How do I fix a broken return wire insulator?
HID bulb return wire is covered with a thin ceramic tube and is therefor brittle. HID bulbs are frigile, they cannot be handled as much as halogen bulbs. The most common reason for broken insulator is after using HID bulbs in a halogen housing. It may sound awkward, what is really the difference you may wonder. Fact is that halogen headlights have a much smaller diameter hole compared to an OEM headlight. An OEM headlight typically has an opening of about 25mm (1 inch). So if you buy HID equipment and insulator is broken about 30% of way from the base, well then seller has not been aware that bulb must be HANDLED WITH CARE when inserting/removing.
Life of bulb will be reduced if insulator broken. The intention of the insulator is to stop high voltage arcs during startup directly from inner wire to return wire. Such archs will eventually kill bulb. Rapairing it is probably not worth the effort. There is not really any material that will stop high voltage from arcing besides ceramic. If you are able to place special rinsed clay onto wire, then burn it a 1000C oven, it be great for wire but not HID bulb. Return wire could be cut, a new insulator could be attached (not available on the marked), then return wire could be welded back together. This would require a small scale welder - not very common tool to have.
Conclusion: Broken return wire equals defective bulb
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Sorry chief but it seems that you need a new bulb or else you'll risk the ballasts and any other high voltage damage that can occur from this.
Bunthy