Cusp Guns for Helical-Waveguide Gyro-TWTs of a High-Gain High-Power W-Band Amplifier Cascade
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Abstract
The evaluation, design, and simulations of two different electron guns generating the beams for W-band second cyclotron harmonic gyro-TWTs forming a high-gain powerful amplifier cascade are presented. The optimum configurations of the systems creating nearly axis-encircling electron beams having velocity pitch-factor up to 1.5, voltage/current of 40 kV/0.5 A, and 100 kV/13 A with acceptable velocity spreads have been found and are presented.
Keywords
Vacuum electron device Gyrotron traveling-wave amplifier Electron-optics Axis-encircling electron beams Cusp guns Large-orbit gyrotrons1 Introduction
The gyrotron-traveling wave tube (gyro-TWT) is known as a broad-frequency-band variety of gyrotron-type amplifiers having potential for production of the highest average or continuous-wave (CW) power in the millimeter wavelength range [1, 2, 3] and therefore it is attractive as a microwave source for a number of applications such as radars and telecommunication [1, 4]. Recently, a cascade of two gyro-TWTs operating at the second cyclotron harmonic and ensuring the highest pulsed and average power in the W-band frequency range (90…100 GHz) was proposed and modeled by detailed 3D PIC simulations [5, 6, 7]. The theoretical analysis of the beam-wave interaction [5, 6] along with the thermal and RF breakdown evaluation [7] showed that the cascade is capable of producing 350-kW pulsed and 50-kW average power, respectively, with about 8 GHz bandwidth when driven by a tens of mW input RF source. It was optimized so that the first-in-cascade tube should be driven by a relatively low-energetic electron beam having the axial magnetic field inside the interaction region, B_{0}, of 1.82 T, particles’ energy of 40 keV, beam current of 0.5 A, pitch-factor α = v_{⊥}/v_{||} (v_{⊥} and v_{||} are the perpendicular and axial particles’ velocities, respectively) of 1.2–1.4, maximum radius of 0.45 mm (two times less than the sub-cut-off drift channel radius) and the relative perpendicular velocity spread, δv_{⊥} = Δv_{⊥}/\( {\overline{\mathrm{v}}}_{\perp } \), of less than 3% where Δv_{⊥} is the standard (rms) deviation of v_{⊥} from its average value \( {\overline{\mathrm{v}}}_{\perp } \). The second tube of the cascade was designed to be driven by an electron beam with much higher power having the particles’ energy in the range of 80–100 keV and beam current of 16–13 A, but with less stringent requirements on the radial and velocity spreads: at the pitch-factor of 1.3–1.4, the electrons’ radial coordinate and the perpendicular velocity spread should be less than 0.9 mm and 10%, respectively, for B_{0} = 1.96 T.
This paper is focused on the evaluation, design, and simulations of two different electron-optical systems (EOS) or electron guns generating the beams according to parameters listed above. An evaluation of the Larmor radii for these two cases, namely 0.3 mm (for 40 keV) and 0.46 mm (for 100 keV), along with the radial restrictions of 0.45 and 0.9 mm, inevitably leads to the configuration of a nearly axis-encircling beam having spread in the guiding center radii less than the Larmor radius which, in turn, entails the use of a cusp gun as the most appropriate type of EOS [8, 9, 10, 11, 12, 13]. The cusp guns have been quite actively developed in the last few decades as the electron beam source for large-orbit gyrotrons [14, 15, 16], gyro-TWTs, and gyro-BWOs operating at the second cyclotron harmonic [17, 18, 19, 20, 21]. Whereas a cusp gun for the first gyro-TWT with 40 keV/0.5 A beam seems to be relatively simple to design because similar systems were experimentally realized for Ka-band [17, 18, 19] and W-band [20] gyro-TWTs, a gun for a powerful 100 kV/13 A tube appears to be more challenging. The nearest analogues discussed in references [17, 18] have almost half the power (70 kV/10 A) and are used for Ka-band gyro-TWTs operating at almost three times lower static magnetic fields. However, a direct scaling of the system inversely proportional to the magnitude of the static B-field inevitably runs into some fundamental and technological limitations, which include limitations imposed by the electro-static breakdown and the achievable emission density of the cathode.
2 General Approach and Technique
Design parameters of the Electron-Optical Systems
Parameter | Value | ||
---|---|---|---|
EOS1 | EOS2 | ||
Given | Voltage, U_{0}(kV) | 40 | 80–100 |
Magnetic field, B_{0}(T) | 1.82 | 1.96 | |
Max. emitting current density, J_{em}(A/cm^{2}) | 5–7 | ||
Electric field threshold, E_{th}(kV/cm) | 70 | ||
Required | Beam current, I_{beam}(A) | 0.5 | 16–13 |
Pitch-factor, α | 1.2–1.5 | ||
Max. perp. velocity spread, δv_{⊥} (%) | 3 | 10 | |
Max. beam radius, R_{ib} (mm) | 0.45 | 0.9 |
3 Gun for the Low-Power Gyro-TWT (EOS1)
As it can be evaluated using the approach discussed above, the axial magnetic field at the emitter, B_{cath}, is negative and amounts to only 10 mT. As a result, even for very moderate value of the beam current of 0.5 A the square ratio of plasma frequency to cyclotron frequency, F = (ω_{p}/ω_{c})^{2}, exceeds 3 which indicates quite a strong influence of the space-charge forces. Our experience shows that in order to diminish the perturbation of the beam parameters by the space-charge forces, one should provide a relatively high gradient of the magnetic field at the beginning of the transportation channel in such a manner so that F becomes less than 0.1 at the distance equal to the radius of transportation channel from its entrance. This consideration was taken into account during optimization of the magnetic system by adjusting the cathode coil position.
Simulated (by codes EPOS and CST) beam parameters for EOS1 at various beam current and magnitude of magnetic field at z = 0
B_{cath}, mT | I_{beam} = 1 mA | I_{beam} = 0.5 A | ||||||
---|---|---|---|---|---|---|---|---|
α | δv_{⊥}(%) | α | δv_{⊥}(%) | |||||
EPOS | CST | EPOS | CST | EPOS | CST | EPOS | CST | |
− 8.8 | 1.22 | 1.22 | 1.37 | 1.43 | 1.19 | 1.17 | 1.51 | 1.12 |
− 9.6 | 1.34 | 1.33 | 1.43 | 1.51 | 1.30 | 1.29 | 1.20 | 1.14 |
− 10.4 | 1.49 | 1.48 | 1.49 | 1.57 | 1.44 | 1.44 | 1.11 | 1.26 |
4 Gun for the High-Power Gyro-TWT (EOS2)
The magnetic system for the second tube significantly differs from that discussed above by a considerably shorter main coil and a larger diameter of the cathode coil (Fig. 1). It is also important that this EOS should provide the beam with considerably larger current and current density. Therefore, one could expect significantly larger influence of the space-charge forces on the beam quality. Consequently, the most important parameter influencing the beam quality becomes the strength of the magnetic confinement F.
The first step in the gun design was the estimation of the gun parameters, including F, corresponding to different emitter radii R_{em}. The range of R_{em} = 10…20 mm was considered. Two combinations of accelerating voltage U_{0} and beam current I_{0} corresponding to about the same beam power of 1200…1300 kW were examined: U_{0} = 80 kV with I_{beam} = 16 A and U_{0} = 100 kV with I_{beam} = 13 A. In all cases the cathode current density was assumed to be the same, i.e., not higher than 7 A/cm^{2}. It is important to note that the requirements for the velocity spread in this case are less stringent, δv_{⊥}< 10%. Choosing larger values of R_{em} results in a simpler manufacturing procedure for the cathode assembly, but, at the same time, leads to a very low absolute value of the magnetic field at the cathode (less than 1 mT, which becomes comparable within an order of magnitude of the Earth’s magnetic field). At such a high magnetic compression ratio (B_{0}/B_{cath}> 2000), the gun starts to be sensitive to any small perturbations caused by external magnetic fields, misalignment, thermal velocities of electrons, and some other factors. Moreover, for this gun, the F parameter exceeds 200 (as compared to F = 3 for the EOS1), which causes large velocity spread due to the space-charge forces. On the other hand, a small emitter radius reduces the influence of the listed above factors, but causes the increase of velocity spread proportional to the ratio of ΔR_{em}/R_{em}. Finally, after consideration of some gun variants and first runs of the trajectory analysis procedure, it became clear that the best chance of getting suitable beam parameters was to use an electron gun with an intermediate radius R_{em} = 12.8 mm. Corresponding preliminary parameters of the gun were as follows: R_{em} = 12.8 mm, B_{cath} = − 2.6 mT, F = 70, ΔR_{em} = 2.4 mm. The trajectory analysis has also shown that a combination of the higher voltage and smaller current, 100 kV/13 A, gives better beam quality due to the reduction of the space-charge density in the formation region.
Further numerical simulations were aimed at finding the cathode coil current and position as well as the shape of electrodes providing moderate velocity spread, small deviation of the guiding centers from the axis, and pitch-factor within the range of 1.3…1.5. The position of the cathode coil was optimized to ensure large enough (at least 1.5–3.0 T/m) gradient of the axial magnetic field, ∇B, and at the same time small (less than 1%) perturbation of the magnetic field distribution in the interaction space caused by this coil (the gyro-TWT interaction circuit is positioned at the homogeneous (within 2% margin) part of the B-field). It is important to note that both too small and too large values of ∇B are not suitable for formation of an e-beam with the desired parameters. In the first case, the region after the entrance to the transportation channel with a weak magnetic confinement, where practically the only force acting on the beam is the space-charge force, becomes unacceptably long. In the opposite case, it is very difficult to provide the magnetic tracking of the particles, i.e., the situation when particles’ trajectories are parallel to the guiding magnetic field lines after the plane where F becomes less than 0.1, which leads to a large ripple of the beam’s shape and, consequently, to large deviation of the guiding centers from the axis.
Main parameters of EOS2 and ranges of their optimization
Axial distance between cathode and main coils | 180…250 mm |
Cathode-anode gap | 30…45 mm |
Emitter mean radius | 10…20 mm |
Emitting surface angle to z axis | 45…90° |
Emitting surface curvature | 15…100 mm |
Angles of conical surfaces under and above the emitter | 30…90° |
Emitting current density | 5…7 A/cm^{2} |
Cathode voltage | 80…100 kV |
Beam power | 1.2…1.3 MW |
Cathode B-field | −5…2 mT |
Simulated (by codes EPOS and CST) beam parameters for EOS2 at various beam current and magnitude of magnetic field at z = 0
B_{cath}, mT | I_{beam} = 1 mA | I_{beam} = 13 A | ||||||
---|---|---|---|---|---|---|---|---|
α | δv_{⊥}(%) | α | δv_{⊥}(%) | |||||
EPOS | CST | EPOS | CST | EPOS | CST | EPOS | CST | |
0.98 | 1.05 | 1.03 | 2.7 | 3.3 | 1.23 | 1.25 | 8.9 | 9.7 |
0.59 | 1.24 | 1.22 | 2.7 | 3.7 | 1.49 | 1.52 | 7.4 | 9.1 |
5 Conclusion
Preliminary analytical estimations and further numerical optimization have proved that cusp guns enable one to form nearly axis-encircling helical electron beams suitable for utilization in the high-power high-gain cascade gyro-TWTs operating at the second cyclotron harmonic with frequency of about 95 GHz. Two electron-optical systems for a moderate-power (40 kV/0.5 A) and a high-power (100 kV/13 A) tubes were designed and optimized. It was found that in order to realize appropriate beam properties it is preferably to use the principle of magnetic confinement behind the axial coordinate where the plasma frequency is smaller than the cyclotron frequency. For a fixed electron beam power, it is better to use maximum admissible accelerating voltage to diminish the influence of the space-charge forces on the beam quality. Investigation of the high-power cusp gun shows that for the accelerating voltage of 100 kV and B-field in the operating region of about 2 T, the beam current limit lies in the range of 10–15 A up to which the gun can generate a beam with marginally acceptable parameters (pitch-factor, radius, and velocity spread) for use in second-harmonic gyro-TWTs, large-orbit gyrotrons, and other similar gyro-devices.
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