Cusp Guns for Helical-Waveguide Gyro-TWTs of a High-Gain High-Power W-Band Amplifier Cascade

  • V. N. Manuilov
  • S. V. Samsonov
  • S. V. Mishakin
  • A. V. Klimov
  • K. A. Leshcheva


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.


Vacuum electron device Gyrotron traveling-wave amplifier Electron-optics Axis-encircling electron beams Cusp guns Large-orbit gyrotrons 

1 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, B0, 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 B0 = 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

As it is quite common in gun design for many varieties of gyrotron-type devices, a configuration of the main solenoid is usually determined by the optimum electron-wave interaction, assembly peculiarities, and the type of magnet (DC liquid-cooled, superconducting, permanent etc.) used. In this paper, as in most of the other similar works, we design the cusp guns using only one additional counter-running coil (from here onwards called the cathode coil) creating a reverse of the axial B-field near the cathode (Fig. 1). In addition, we base our designs here on the use of superconducting coils (both main and cathode coils) having somewhat different geometries as compared to cases discussed in references [18, 20, 21] where liquid-cooled normal-conducting coils has been implemented.
Fig. 1

Schematic views of magneto- and electro-static systems along with normalized Bz-profiles for low-power (a) and high-power (b) gyro-TWTs; Bmax for the cathode coil is 0.086 (a) and 0.026 (b) of Bmax for the main coil

For preliminary estimations, the analytical model of a step-function reverse (ideal cusp) of the magnetic field is used [13, 22]. After the cusp plane, the magnetic field axial profile is assumed to be adiabatic. The corresponding expressions are based on the energy conservation law, the Busch theorem, and the transverse adiabatic invariant conservation law (see [22] for details). The emitting current density was assumed to be as high as 5 A/cm2 while the cathode surface electric field threshold was defined as 70 kV/cm and the preliminary value of the emitter ring width, ΔRem, with respect to its mean radius, Rem, was taken to be proportional to the admissible perpendicular velocity spread, ΔRem/Rem = 3.5⋅δv (factor of 3.5 appeared due to the ratio between max-min and the rms values for the rectangular-shaped distribution function). The use of these data in the analytical model of an ideal cusp enabled us to find a magnetic compression ratio, emitter radius and width, cathode-anode distance, preliminary position of the gun with respect to the main coil center, and some other parameters. Then, the numerical optimization of the EOS was carried out to find the optimum gun geometry, position, and currents of the coil that produced the desired beam properties. Let us note that the optimization procedure is essentially more complicated than optimization of conventional gyrotron magnetron-injection guns (MIG) [23] because in addition to ensuring sufficiently high pitch-factor and adequate velocity spread, it also involves providing small deviation of the particle’s guiding centers from the axis (see details below). Most numerical simulations were carried out by the 2D EPOS code [23, 24]. The final gun designs were also checked by the 3D Particle Tracking Solver of CST Studio Suite [25]. Using two independent codes increases the reliability of the gun design. The given and required parameters for both EOS are summarized in Table 1.
Table 1

Design parameters of the Electron-Optical Systems







Voltage, U0(kV)



Magnetic field, B0(T)



Max. emitting current density, Jem(A/cm2)


Electric field threshold, Eth(kV/cm)



Beam current, Ibeam(A)



Pitch-factor, α


Max. perp. velocity spread, δv (%)



Max. beam radius, Rib (mm)



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, Bcath, 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 = (ωpc)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.

Further optimization of the cathode and anode shapes allowed us to fulfill the condition when the particle trajectories became parallel to the guiding magnetic field line after the entrance to the transportation channel (magnetic confinement condition) and thus to provide small beam ripples (Fig. 2). The simulations show that average guiding center of the particles in the interaction region is as small as 0.06 mm, while its maximum value does not exceed 0.12 mm which is 2.5 times less than the Larmor radius. Thus the maximum radial coordinate of a perfectly aligned beam in the operating B-field region amounts to Rb = 0.42 mm which is safely less than the admissible value specified above. Special attention was also paid to the maximum value of the electric field, Emax, on the electrode surfaces. In the optimized gun version, Emax does not exceed 68 kV/cm, which is quite suitable for the gyrotron vacuum conditions.
Fig. 2

Electrodes geometry, particles trajectories, and profile of the guiding magnetic field for the low-current EOS. Perpendicular velocities distribution function at z = 250 mm is shown as an insert with the vertical blue lines corresponding to the minimum and maximum values

Small variations of the cathode coil current result in quite a considerable change in the magnetic field at the emitter making it possible to adjust the particles’ pitch-factor within the range of 1.2…1.5 without significant change in the velocity spread which remains very moderate and satisfies the desired limit of 3% with a rather large margin (Table 2). Let us note that the difference between the maximum and minimum simulated values of the perpendicular velocities (see Fig. 2 insert) divided by its average value is usually 3–4 times larger than the relative rms deviation used here as a measure of the velocity spread. The numerical simulation by the CST Particle Tracking Solver resulted in reasonably close beam parameters (Table 2).
Table 2

Simulated (by codes EPOS and CST) beam parameters for EOS1 at various beam current and magnitude of magnetic field at z = 0

Bcath, mT

Ibeam = 1 mA

Ibeam = 0.5 A













− 8.8









− 9.6









− 10.4









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 Rem. The range of Rem = 10…20 mm was considered. Two combinations of accelerating voltage U0 and beam current I0 corresponding to about the same beam power of 1200…1300 kW were examined: U0 = 80 kV with Ibeam = 16 A and U0 = 100 kV with Ibeam = 13 A. In all cases the cathode current density was assumed to be the same, i.e., not higher than 7 A/cm2. It is important to note that the requirements for the velocity spread in this case are less stringent, δv< 10%. Choosing larger values of Rem 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 (B0/Bcath> 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 ΔRem/Rem. 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 Rem = 12.8 mm. Corresponding preliminary parameters of the gun were as follows: Rem = 12.8 mm, Bcath = − 2.6 mT, F = 70, ΔRem = 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.

As a result of many parameter optimization, it was found that for a flat emitter in the form of a cone shape, like for the previous gun (Fig. 2), suitable beam parameters could be obtained only for the beam current of less than 10 A. For higher currents, even for large gradients of the magnetic field, the space-charge forces were so strong that it was impossible to focus the beam and ensure uniform radii of the particles crossing the plane of the magnetic cusp, thus different parts of the beam acquired perpendicular velocities of considerably different values. In addition, the resonance mechanism [23], also increasing the velocity spread due to the regular intersections of electron trajectories took place. As a result, the velocity spread as well as the radial deviation substantially exceeded the admissible levels. Considerably, better focusing of the electron beam was achieved when the shape of the emitter was changed from the flat one to a concave arc (Fig. 3). Using this configuration and optimizing the neighboring element geometry as well as the cathode coil’s current and position with respect to the main coil’s and emitter’s position (Table 3), the final version of the gun was obtained (Fig. 3). According to the 2D EPOS and 3D CST modeling, this EOS allows one to produce an electron beam with the main parameters listed in Table 4 which marginally satisfy the requirements listed in Table 1. It is important to note that for both regimes listed in Table 4, there are no particles reflected from the magnetic mirror—maximum v of 0.515c is smaller than that of the total velocity of 0.545c (see Fig. 3 insert). Let us also note that our optimization with the main goal of minimizing the velocity spread for maximum beam current has resulted in a configuration where the axial B-field at the emitter turns out to be positive (see Table 4) instead of negative as is usually the case for a typical cusp gun. As a result, the generated electron beam has changed its topology from an axis-encircling to an MIG-like configuration but with the guiding center radii just a few percent larger than that of the Larmor radii. Due to this fact, the beam has effectively larger cross section and therefore smaller density which evidently helps to diminish the negative influence of its space charge. The maximum simulated radial position of the particles in the interaction region amounts to 0.88 mm while the minimum radius of the designed circuit is 1.16 mm; so in spite of enlarged beam cross section, its alignment ensuring 100% transport seems technically feasible. In the optimum gun configuration, the emitting current density should be about 7 A/cm2 which seems to be a reasonable value for long-life (104–105 h) operation in the pulsed mode with duty factors of 20–30% when using the dispenser cathodes and appropriate technologies for its manufacture (see, e.g., [26] and websites of various industrial companies dealing with the cathode production for vacuum tubes).
Fig. 3

Electrodes geometry, particles trajectories, and profile of the guiding magnetic field for the high-current EOS. Perpendicular velocities distribution function at z = 220 mm is shown as an insert with the vertical blue lines corresponding to the minimum and maximum values

Table 3

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


Emitting surface curvature

15…100 mm

Angles of conical surfaces under and above the emitter


Emitting current density

5…7 A/cm2

Cathode voltage

80…100 kV

Beam power

1.2…1.3 MW

Cathode B-field

−5…2 mT

Table 4

Simulated (by codes EPOS and CST) beam parameters for EOS2 at various beam current and magnitude of magnetic field at z = 0

Bcath, mT

Ibeam = 1 mA

Ibeam = 13 A































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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. N. Manuilov
    • 1
    • 2
  • S. V. Samsonov
    • 1
  • S. V. Mishakin
    • 1
  • A. V. Klimov
    • 1
    • 2
  • K. A. Leshcheva
    • 1
    • 2
  1. 1.Institute of Applied PhysicsRussian Academy of SciencesNizhny NovgorodRussia
  2. 2.Nizhny Novgorod State UniversityNizhny NovgorodRussia

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