Not FOSS, and more an issue tracker than helpdesk software (although a lot of people who implement it as an issue tracker end up dumping their existing helpdesk software and moving on to Jira).

So you haven't used it for 5 years? Give it another go sometime, it's been under heavy development. Still not quite a "Helpdesk" though. And it's not Open Source

One of my little fuzzy sociopaths would fit the role perfectly. One dose of catnip and she goes off like an overcharged food mixer! Are they hiring?