Abstract
In our earlier work, we showed that a low-energy state of an electron beam exists in a nonuniform channel between two virtual cathodes in a magnetron with diffraction output, which consists of three uniform sections with increasing radius. A uniform axial magnetic field fills the interaction space. This led to magnetron operation with >90% efficiency when combined with a magnetic mirror field at the output end. In this present paper, we show that a low-energy state of an electron beam can be realized in a uniform channel in which an increasing magnetic field is used in order to create a magnetic mirror at the output end. We consider two cases, one where the injected beam current slightly exceeds the space-charge-limiting current and the other where the injected beam current greatly exceeds the space-charge-limiting current. On the time scale of relevance to planned experiments (∼30 ns), when the injected current slightly exceeds the space-charge-limiting current a stationary virtual cathode forms and when the injected current greatly exceeds the space-charge-limiting current the virtual cathode oscillates back and forth.
Highlights
In our earlier work using the MAGIC particle-in-cell (PIC) code [1], we showed that a low-energy state of an electron beam exists in a nonuniform channel between two virtual cathodes (VCs) in a magnetron with diffraction output (MDO), which consists of three uniform sections (Figure 1) with increasing radius
ICEPIC simulations show that when Ib only slightly exceeds Ilim, a stationary VC appears with the low-energy state of electrons in the two-stream electron beam between the VC and the magnetic mirror
An explosive emission cathode is used to generate a thin-walled tubular beam and a magnetic mirror field described by H (z) =
Summary
In our earlier work using the MAGIC particle-in-cell (PIC) code [1], we showed that a low-energy state of an electron beam exists in a nonuniform channel between two virtual cathodes (VCs) in a magnetron with diffraction output (MDO), which consists of three uniform sections (Figure 1) with increasing radius [2,3]. The first VC (VC1) occurs when the electron beam with radius R0 = 1 cm propagates from a tubular cathode along a strong longitudinal magnetic field into a tube with radius R1 = 1.5 cm, exceeding the space-charge-limited current in the larger radius tube with radius R2 = 2.11 cm. The formation of a potential well with voltage U = 0, which is analogous to the low-energy state of electrons, is very useful to achieve high electronic efficiency in an MDO This led to the operation of an MDO with efficiency >90% in PIC simulations, a record for a high power microwave (HPM) source [4]. This earlier result motivated us to consider whether such a low-energy state of electrons can occur in a uniform channel.
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