What the Economist article seem to fail to mention: "In the accelerator-on-a-chip experiments, electrons are first accelerated to near light-speed in a conventional accelerator. Then they are focused into a tiny, half-micron-high channel within a glass chip just half a millimeter long."
From the Economist article: "Dr Byer did still rely on an old-school accelerator to feed moderately high-speed electrons into his device in the first place. But lasers could do that job too, as the German team, led by Peter Hommelhoff, of the Friedrich Alexander University in Erlangen, and John Breuer, from the Max Planck Institute of Quantum Optics in Garching, demonstrate in a second paper, just published in Physical Review Letters."
"The electrons fed into it were first sped up using a midsized standard accelerator, so when they arrived at the glass accelerator they were already travelling at 99.86% of the speed of light, or 60m electron-volts..."
And again, in the complete nonsensical quest of describing particle energies by many nines in 99.999999..% of the speed of light, the proper math falls down, 99.86% c is ~10 MeV, 60 MeV is about 99.996% c, but IT'S COMPLETELY MEANINGLESS!
Nevertheless...
Here's a handy online-tool to calculate the speed of a particle accellerated in a electric field (enter 60000 kV to get the values for the 60 MeV electron):
Or calculate it yourself: E = E₀ / √( 1 - β²) with E₀ being the rest-energy of the particle (511 keV in the case of the electron) and β being the velocity relative to the speed of light.
At 99.86% of the speed of light, an electron will have a total (rest-mass + acquired energy by accelleration) energy of about 10 MeV:
(in python, energies in keV)
>>> 511. / math.sqrt( 1 - .9986 ** 2 )
9660.374008193809
Take into account, though, that accelerating electrons into near light speeds is not too difficult anyway. They are thousands of times lighter than protons, for instance, which is what the LHC works with most of the time.
Actually the reverse is true. Protons emit less synchrotron radiation, making it easier to make accelerators in a ring shape. Electrons eventually radiate as much energy as it takes to accelerate them, creating a barrier.
I don't believe that this is a major problem for the technology. I can imagine that the level of flux (amount of electrons coming through the device and being accelerated) is rather low at the moment however.
