Studies of the nonlinear evolution of the electron‐density profile in crossed‐field devices indicate the classical Brillouin profile to be inadequate for the explanation of the operation of such devices. Instead, the existence of a density plateau at the edge of the electron sheath is found to be essential in the operation of such a device. Such a plateau placed at the edge of a classical Brillouin profile creates a double‐box profile. The operational theory for crossed‐field devices based on this double‐box density profile is presented. It is shown that this profile generates an operating voltage range that agrees quite well with the actual voltage operating range of such devices, except for high magnetic fields.
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