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- W2076178885 abstract "The phenomenon of bunching which takes place in a velocity modulated electron beam can be described in purely kinematical terms if space charge effects are negligible. However, the non-uniform distribution of charge in the bunched beam gives rise to a field which opposes the bunching process so that the kinematic solution may be validly applied only for a limited length of drift space. An accurate solution of the bunching process requires the integration of the dynamical and field equations. These reduce to a linear homogeneous system under the assumption of ``small signal'' conditions. The device of a high frequency ``surface charge'' is employed in formulating the boundary conditions at the surface of the beam. In the non-relativistic approximation the dynamical and field equations yield solutions which are classified as non-solenoidal or solenoidal accordingly as the motion produces or does not produce a high frequency charge density within the beam. There exists a non-solenoidal type of motion which generates no field outside the beam. The actual physical problem is solved by taking a suitable linear combination of both solutions. Under conditions met with in practice, a large part of the actual solution may be of the solenoidal type. The high frequency component of beam current appears as a sum of a volume current and a ``surface current,'' the latter term arising from the longitudinal motion of the high frequency ``surface charge.'' Again, under conditions met with in practice, a large part of the high frequency component of beam current may occur in the form of ``surface current.'' The theory contains three debunching wave numbers: one identical with that which occurs in Webster's debunching theory for a beam of unlimited cross section, and two which depend upon the transverse dimensions of the beam and drift tube, the current density, frequency, and beam velocity." @default.
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- W2076178885 date "1946-12-01" @default.
- W2076178885 modified "2023-09-23" @default.
- W2076178885 title "Theory of Small Signal Bunching in a Parallel Electron Beam of Rectangular Cross Section" @default.
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- W2076178885 doi "https://doi.org/10.1063/1.1707671" @default.
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