Electron Beam Focusing with Periodic Permanent Magnet Fields

Two-plane focusing of high-space-charge sheet electron beams using periodically cusped magnetic fields

“…Constructive interference between the two oscillations creates large amplitude, or completely unconfined, orbits which lead to beam loss to the transport channel. This situation is similar to the case for round beams in permanent periodic magnet ͑PPM͒ focusing treated by Mendel et al 21 In Ref. 21, the radial equation of motion for edge electrons in a round beam was recast in the form of Matthieu's equation.…”

“…This situation is similar to the case for round beams in permanent periodic magnet ͑PPM͒ focusing treated by Mendel et al 21 In Ref. 21, the radial equation of motion for edge electrons in a round beam was recast in the form of Matthieu's equation. Tabulated solutions for Matthieu's equation showed the existence of a series of passbands and stopbands as the PPM period was increased corresponding to transport of the beam through the focusing stack or loss of the beam to the channel walls.…”

Stability Analysis for Electron Beam Transport in Double-Periodic Permanent Magnet Focusing Structure

“…Stability of the solutions of the paraxial ray equation (1) is determined in the line of Mathieu-Hill stability [1], [6]. For the double periodic case, the equation of motion conforms to Hill's differential equation, which is solved using cascaded matrix approach.…”

“…The common form of a PPM structure consists of an array of axially charged ring magnets kept alternately at reverse polarities that are separated by soft-iron pole pieces (Figure 1a). This arrangement usually provides periodic sinusoidal magnetic field at the axis of the structure, if the ratio of the gap between the ferrules (g) and the magnetic periodicity (L) maintained around the value of 1/3 that cancels out the third harmonic Fourier component in the axial magnetic field [1]. However, in high power klystrons and coupled-cavity traveling-wave tubes (CCTWTs), the operating regime of parameters sometimes demands a longer period, for which the stable beam transport is achieved using a special type of focusing arrangement (Figure1b), known as double periodic permanent magnet focusing structure [2]- [4].…”

Three-dimensional W-band klystrino simulation

“…For optimum focusing the rms field value should equal the BRIL-LOUIN field for the beam where the magnetic focusing force just compensates space-charge-and centrifugal force [1]. According to our beam parameters the BRILLOUIN field is ½ mT, requiring an amplitude ¼ ¾ mT.…”