Quote from _CrimsonInferno_ >>

Does anybody know if the beam stays in existence and is hazardous for any duration? It seems odd that the spell is concentration if all you're doing is shooting another relatively low-damage ray each round while you're concentrating. The description also doesn't say the beam disappears, it just says you make a new one. Any thoughts?

 If you think about it, this spell is very powerful.  What other spell allows you to do 60d8 of damage on one spell slot?

As far as your other concern.  In the spell description the spell says:  "A beam of brilliant light flashes out from your hand in a 5-foot-wide, 60-foot-long line."

By definition, a "flash" is a sudden brief burst of bright light or a sudden glint from a reflective surface.  It does not imply a continuous beam that persists.  So by the language used, I would say that the beams disappear after an instant.  

It’s a straight line like a sun ray, but if I were DMing I’ would probably allow it to bounce or ricochet off of mirrors  or certain surfaces.

My aasimar divine soul sorcerer is about to get this spell in Rime of the Frostmaiden and my DM is letting him cast it out of his eyes. Laser eyes rock!

I think it implies that the beams go away immediately after emitting. Otherwise each one would set up an area of effect like dawn or moonbeam and creatures  would have to make saves upon entering said area, but the RAW doesn’t say any of that. 

One fun thing about Sunbeam when used by sorcerers, is they can use this with Quickened Spell:

1. Use Quickened Spell to cast Sunbeam as a Bonus Action.
2. Use your Action to create a new line of radiance on that same turn.
3. ???
4. Profit!

Best of all, each time you use your action to create a new line of radiance, you can cast Silvery Barbs on a creature that succeeds on their saving throw, forcing them to reroll it.