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When there is a strong electric field, electrons can be removed from a metal after overcoming its work function through corona discharge in air.

But why can't the electron be removed (ignoring thermionic emission) when the metal is in vacuum? Is it possible to apply an extremely large potential difference, causing electrons to be ripped out of the metal?

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Yes, they also jump through a vacuum, but there's no corona because there are no air molecules to collide with.

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  • $\begingroup$ Then why do X-Ray tubes require a filament current? Given the high potential difference between the cathode and anode, wouldn't a filament current be irrelevant since thermionic emission is not required? $\endgroup$ – Michael Nov 4 '16 at 19:19
  • $\begingroup$ @Michael, ...to notably increase the current. $\endgroup$ – Digiproc Nov 4 '16 at 19:42
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Yes, it is indeed possible to remove electrons from a metal by high applied electric fields. The phenomenon is called field electron emission or Fowler-Nordheim tunneling and becomes noticeable for field strengths around $10^9 V/m$. Electrons are hindered to leave a metal by a surface energy barrier called work function that is on the order of several eV. Thus at room temperature only a very small fraction of conduction electrons can overcome this barrier. If you apply a positive electric field to the surface of a metal the step-like shape of the potential barrier due to the work function becomes triangular with a base thickness that narrows with the applied field strength. If this barrier is thin enough, the electrons in the metal can pass it by the quantum mechanical tunnel effect without any energy increase. This leads to an electron emission current which increases rapidly with applied voltage.

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