A character from the third Red Dwarf novel, Backwards, introduced shortly after Ace Rimmer is introduced.

Spoiler Alert

I was really confused by the whole thing because beta Rimmer is only a character in the novels and this was entirely skipped in the episode Dimension Jump when Ace is introduced to the TV show. So, if you plan to read the book and prefer suprises, stop now because it's pretty impossible to tell you who beta Rimmer is without spoiling a good portion of the book. You've been warned.

Ace goes to a bar and picks a fight with a young man (the only guy in the place), with the secret motive of raising the boy's confidence so he would take and pass his flight exam the following day. Ace lets the boy win, and ends up getting a black eye and having his St. Christopher's medallion inadvertantly taken from him during the scuffle. The accidental theft of his medallion later saves his life.

For the past several days, Rimmer had been preparing to pilot an expirimental craft capable of breaking the light speed barrier. Since it has never been done before, nobody really knows what would happen when the drive is engaged. The day after the barroom fight, three days prior to take-off, the craft returns. Before it's even left. It is scorched and scarred, and inside they find the body of Ace Rimmer burnt to a crisp inside, his medallion melted to the control panel and the conclusion is that faster than light speeds mean time travel (and high temperatures). Despite the fact that Ace would die, two conclusions are drawn. The first is that causality means Ace is destined to make the jump and can't not jump. The second is as Ace put, "I'm a test pilot in the Space Corps. It's my job to do it." (What a guy!) Therefore, the launch schedule remains unchanged, although Ace and Spanners Lister do try to work out what went wrong.

Two things tip them off as to not what happened, but who it happened to. First, the date recorded in the wreckage's black box was three days prior to launch. If it had come from the future, the date should be a future date. The second was that the medallion Ace had lost wound up melted to the controls. So it appears to Ace and Spanners that this is not a future Ace, but instead, an alternate version of Ace from a parallel universe who simply left three days prior to the time Ace is scheduled to leave. (As you can tell it's already getting confusing.) While the team tried to work out what went wrong with the alternate Rimmer's ship so that Ace could make the jump successfully, Ace suggests they refer to the dead Rimmer as "beta Rimmer" so as to avoid any further confusion.

Well I won't say what happens to Ace because this isn't a writeup on the Ace Rimmer, just an alternate version of him. Just read Backwards by Rob Grant. You'll like it.