I am trying to find a short story that was in a hardback short story collection which I recall reading in the late 50s to early 60s.

It involves a group of children -- boys, as I recall -- on a sort of field trip.

They are genius adepts with awesome skills although this is not immediately apparent.

The story is not juvenile science fiction, however. 

The story had a sort of Cordwainer Smith meets Philip K. Dick not to mention Gene Wolfe flavor but before their heydays. 

It really had that scary future other timely ambiance with little exposition.

Unusual for the time.

Their conversation includes one saying he is going to be President of the World next week.

They go to an arena centered on an ovoid force field wherein they see a group of spear carrying warriors before a fire standing before a shaman or, magician or wizard who is chanting and gesturing. 

It was a portal in time apparently.

One of the boys is bored and through some sort of psionic exercise adds his powers to the shaman and collapses the forcefield.

Which leaves warriors and shaman there in the arena. 

Havoc ensues. 

After that, I seem to recall that things are resolved and the boys are on their way home.

It may be that the reference to being President of the World was made then.

These were super children not without attitudes and a real deal prehistoric to dark ages era shaman possibly with real powers. 

And one of them was going to be President of the World next week.

That's the best of my recollections. 

It was something that especially stayed with me, not unlike *Horrer Howce* by Margaret St. Clair or "Go for Baroque" by Jody Scott or "Alpha Ralpha Boulevard" -- there were edge and craft to it and that far weird future ambiance.

I hope it exists and someone has read it. If I dreamt this fifty years ago, I will be most bemused.