Inspiron 17 7000 (7778/7779) power-connector d=4.4mm, not d=7.3mm

Hello,

After I fell from my mountain-bike in 2007 I can't use my hands anymore. Luckily I use only Dell laptops and till now Dell used always the same laptop power connector. So my friends build an adapter on my electric wheelchair. So far, so good.

This year my good old XPS 17 had to be renew after 6 years of work. I wanted to try touch-screen and bought the Inspiron 17 7000 (7778/7779). Great laptop but I can't use the power cord on my wheelchair; the old 19,6V 7.3mm-connector is to big. After 3 hours the battery is empty or I am bound the whole day to the wall with a power cable :(

I have 10x adapters with the 7.3mm-connector in my house so I can charge everywhere without to take my adapter with me. Now they are obsolete.

On internet it's difficult to select the right connector. Does anyone know how to call the 4.4mm-connector; slimeline-? ultrabook-connector?

Does anyone know how to fix this problem? I could make a 7.3-to-4.4-adaptor-cable. I could make it my self by taking the contra-connector from my old XPS laptop but the I need a new 4.4mm-connector...but how do I now that I order the right connector?

Thanks for your reply!