Hello Gordon,

I would actually say that those holes are not from moles or voles.  A mole hole is a small pile of dirt with a straight vertical shaft going down and they make tunnels that are typically seen above ground as little mounded lines just under the surface of the grass and top layer of soil.

Voles actually don't build underground tunnels but rather create above ground tunnels.  They do however, use other animals holes to feed so there could be voles eating your potatoes.  

Shrews will use mole tunnels for feeding, but don't build their own.

Here's a bit more reading for you on these animals and some of their habits.

https://extension.psu.edu/moles

https://extension.umn.edu/planting-and-growing-guides/vole-damage

https://extension.psu.edu/voles

It's possible these are chipmunk or mice but it would be good if you could try to find out the animal making the holes.  That will have an impact on how you solve the issue.  You could try setting some traps to see if that helps you identify what it is.  You can use any kind of trap you like that's appropriate for a small rodent and doesn't have to involve killing the animal.

Were the potatoes being eaten from underground? That's what it sounds like.  Voles or mice will eat potato tubers underground.

https://ask2.extension.org/kb/faq.php?id=667612

I have never heard of "thumpers" but certainly reviews can help to determine how effective they are and help you determine if they are worth trying.  I would say though that determining the animal would be a helpful step in addressing the issue.

I hope this helps!

Best,