Beam Axial Velocity Research Articles

Studies of a high-efficiency, long-pulse relativistic backward wave oscillator

A high-efficiency long-pulse relativistic backward wave oscillator (RBWO) operating in the C band is described. The electrodynamical structure of the RBWO consists of a resonance reflector, a slow-wave structure (SWS), an extractor, and a coaxial collector. To achieve high electron beam-electromagnetic wave interaction efficiency, a SWS for the RBWO is designed comprising of two structural segments with different corrugations that enables the gradually decreased electron beam axial velocity to better match the spatially constant electromagnetic wave phase velocity of the operating mode of the RBWO. To suppress electron emission and plasma formation on the inner surface of the electrodynamical structure, which is caused by a strong RF electric field, the RF electric field magnitude is optimized in computer simulations to be less than 700 kV/cm. A coaxial collector is designed to slow down the expansion of the collector plasma. The design of the RBWO is optimized in numerical simulations and its operation is validated in practical microwave-generation experiments. An output power of 3.3 GW is obtained in a practical experiment with a 796-kV, 10.3-kA electron beam guided by an external magnetic field of 2.2 T. The RBWO efficiency and microwave pulse width are measured in the experiment and found to be about 40% and 100 ns, respectively.

Nonlinear behavior of a vibrating axially moving small‐size beam under an electrostatic force

AbstractSmall size (micro/nano)‐scale beams constitute important building blocks of microelectromechanical systems (MEMS)/nanoelectromechanical systems (NEMS). Emerging roll‐based, high rate, manufacturing processes can make these small size‐beams vibrate, while they are axially moving. In this paper, an analytical‐numerical study on the nonlinear transverse vibration of the representative case of axially moving micro‐beam under an electrostatic force is conducted. The analytical model is realized by employing Hamilton's principle together with Galerkin discretization. The method of multiple time‐scales and Runge‐Kutta based numerical scheme are utilized to investigate the nonlinear dynamic behavior of the micro‐beam. Results are obtained for the influence of axial beam velocity and modified couple stress theory length scale parameter (i) on the values of pull‐in instability voltage of the small‐size beam, and (ii) on the small‐size beam nonlinear softening/hardening characteristics. The effect of axial load on the frequency response is investigated.

Design studies of the Ku-band, wide-band Gyro-TWT amplifier

This paper reports a Ku-band, wide band Gyrotron-Traveling-wave-tube(Gyro-TWT) that is currently being developed at Kwangwoon University. The Gyro-TWT has a two stage linear tapered interaction circuit to obtain a wide operating bandwidth. The linearly-tapered interaction circuit and nonlinearly-tapered magnetic field gives the Gyro-TWT a wide operating bandwidth. The Gyro-TWT bandwidth is 23%. The 2d-Particle-in-cell(PIC) and MAGIC2d code simulation results are 17.3 dB and 24.34 kW, respectively for the maximum saturated output power. A double anode MIG was simulated with E-Gun code. The results were 0.7 for the transvers to the axial beam velocity ratio (=alpha) and a 2.3% axial velocity spread at 50 kV and 4 A. A magnetic field profile simulation was performed by using the Poisson code to obtain the grazing magnetic field of the entire interaction circuit with Poisson code.

Numerical Simulations of Nonlinear Dynamics of Electron Cyclotron Maser with a Straight Beam

An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered, and the nonlinear equation of beam-wave interaction is presented. With the numerical methods, the nonlinear dynamics of the ADECM is investigated. It is shown that the saturated interaction efficiency of the ADECM approaches 90% and the interaction length for the saturated efficiency spans about 5–20 cm. The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.

Influence of self-fields on electrostatic waves in a relativistic electron beam with axial magnetic field

An analysis of electrostatic eigenmodes of a cylindrical metallic waveguide completely filled with a magnetized relativistic electron beam is presented. Self-fields are taken into account by considering a rotating electron beam. For the equilibrium configuration when this rotational motion is not too large, one can see a non-relativistic electron beam in the beam frame moving with the axial beam velocity. Therefore, electrostatic approximation can be assumed which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes in the beam frame. The resulting dispersion relation (DR) for the electrostatic waves that is Lorentz transformed back to the laboratory frame reveals the relativistic effects as electromagnetic fields of the wave. The resulting DR reduces to the previously found results in the absence of self-fields as well as in the non-relativistic limit. A numerical analysis is performed to study the dispersion characteristics of the space-charge and cyclotron modes. It was found that increasing the axial velocity lowers the asymptotic frequencies at infinite wave numbers for both electrostatic modes and the cutoff frequencies of the cyclotron modes. The effect of self-fields on the DR of the cyclotron modes is large and shifts the dispersion curves to lower frequencies without changing their shape appreciably.

An Iron-Free Magnetron-Injection-Gun for a 28GHz, 200kW Gyroklystron Amplifier

A design study of a double-anode magnetron-injection-gun is performed to incorporate the electron gun into a high power 28GHz gyroklystron amplifier operating at 70kV and 8.2A. The electron gun is designed to be used in a tapered magnetic field in the cathode region produced from an iron-free superconducting magnet. An electron trajectory code predicts a beam axial velocity spread of 5.9% at α = 1.5, 70kV, 8.2A and 10.4kG, which is a high quality electron beam suitable for the high gain, high efficiency, five-cavity gyroklystron amplifier. The successful design of the high quality electron gun is attributed to a longer gap between the modulating anode and the grounded anode compared with the case of the first 28GHz electron gun built with an iron enclosed electromagnet.

Efficiency scaling law for the two-stream amplifier

The mechanism of conversion from the kinetic energy of electron beams to electromagnetic wave energy is investigated in the two-stream amplifier. It is shown that the optimal efficiency of the amplifier scales according to ΔV/V for relativistic electron beams and (ΔV/V)2 for nonrelativistic electron beams, where ΔV is the axial velocity difference in the two beams and V is the mean axial beam velocity. This scaling law not only explains intrinsically low efficiencies (≲5%) observed in numerous nonrelativistic two-stream amplifier experiments, but also predicts that the optimal efficiency of a relativistic two-stream amplifier is typically greater than that of a nonrelativistic two-stream amplifier by one order of magnitude.

Experimental investigation of a broadband dielectric-loaded gyro-TWT amplifier

The bandwidth of a gyrotron travelling wave amplifier has been broadened by incorporating a dielectric-loaded interaction waveguide to reduce the circuit's dispersion. This proof-of-principle experiment was designed for the X-band frequency range and operates in the fundamental mode of a rectangular waveguide loaded with dielectric Macor. The amplifier is zero-drive stable and demonstrates a peak output power of 55 kW, 11% efficiency, 27 dB saturated gain with an unprecedented untapered gyro-TWT constant-drive bandwidth of 11% and a saturated bandwidth of 14%. Its performance can be further enhanced by reducing the beam's axial velocity spread as shown by previous simulation studies.

Effects of beam velocity spread on two-stage tapered gyro-TWT amplifier

The recent successful operation of a two-stage K/sub a/-band gyro-TWT amplifier at the Naval Research Laboratory has demonstrated its viability as a source of broadband high-power millimeter waves. However, it has been observed experimentally that sharp gain reductions occur at certain frequencies. In this paper, an analytical theory is presented which describes the effect of electron beam quality on the device's instantaneous bandwidth. It is shown that these observed gain dips are due to electron phase-mixing, resulting from finite beam velocity spreads, in the frequency-dependent sever. In addition, the theory demonstrates that the velocity-spread induced dips can be shifted or reduced by adjusting the magnetic field profile, circuit length, and beam axial velocity, consistent with experimental observations.

Nonlinear theory of a folded waveguide gyrotron traveling-wave tube amplifier.

We have developed a three-dimensional nonlinear theory for broadband gyrotron traveling-wave amplification in an H-plane-bend folded waveguide. The H-plane-bend configuration is formed by folding a rectangular waveguide so that the orientation of the magnetic field changes along the bend in contrast to the conventional E-plane bend, where the orientation of the electric field changes. Calculations show the feasibility of amplifier operation with large instantaneous bandwidth and moderate efficiency both in the slow wave region and the reduced dispersion fast wave region. Numerical results for a cold beam show an efficiency of 26% with 11% bandwidth in the slow wave region and an efficiency of 47% with 10% bandwidth in the fast wave region. For an electron beam with 2% velocity spread and 2% guiding center spread, the slow wave efficiency drops to 6% but the bandwidth increases to 16% whereas the efficiency and bandwidth of the fast waves decrease by a small amount to 42% and 9.5%, respectively. The efficiency is more sensitive to the axial beam velocity spread in the slow wave region due to larger Doppler shift. (c) 1995 The American Physical Society

Convective growth of cyclotron harmonic waves on a bounded coaxial electron beam.

Analysis and numerical evaluations are presented for the spatial growth of small-signal modified electron Bernstein waves that stand radially and propagate axially along a beam-filled coaxial waveguide. It is shown that these waves, when coupled strongly to fields of an electromagnetic ${\mathrm{TE}}_{11}$ mode in the interior cylindrical waveguide of this configuration, can make possible an amplifier of cyclotron harmonic waves that would possess several unique properties. In particular, millimeter wavelength amplifiers based on this interaction would require neither high magnetic fields nor high electron beam voltages, and thus would not require the bulky superconducting magnets and highly insulated high voltage power supplies usually associated with fast-wave gyro devices. The analysis extends prior work on interactions of this type, including in the calculations simultaneous contributions from more than one term in the infinite series dispersion relation. Effects of finite axial beam velocity spread on the gain and bandwidth characteristics of the interactions are also calculated, thereby accounting for the irreducible velocity spreads attributable to space charge potential depression on the beam.

Design of a 50 kW, wideband Ka-band slow wave cyclotron amplifier

A two-stage slow wave cyclotron amplifier is investigated to demonstrate a high power, stable, and broad Ka-band radiation source, operating at a low beam power (/spl sim/60 kV, /spl sim/5 amps) and a low magnetic field (/spl sim/7 kG). A linear theory predicts that the second harmonic gyro-BWO is competing in the amplifier and can be stabilized by inserting a sever in the interaction circuit. A slow-time-scale non-linear code, with a sever included, predicts a saturated gain of 24-28 dB, an efficiency of 15-17%, and an instantaneous bandwidth of 15-20% at a beam axial velocity spread of 2%. A broadband RF coupler, a mode converter, and a RF vacuum window are designed by the use of a 3D electromagnetic, finite element code. Measured RF characteristics are in good agreement with predictions. >

Nonlinear theory of gyroharmonic radiation from spatiotemporally modulated electron beams.

A multimode nonlinear particle simulation code is used to find the saturated efficiency for power transfer into modes of a cylindrical waveguide carrying a spatiotemporally modulated gyrating electron beam. For A ${\mathrm{TE}}_{51}$-mode fifth harmonic 94-GHz harmonic converter using a 150-kV, 6.7-A cold beam, this code predicts a conversion efficiency of 57% when a linearly tapered guide magnetic field is used, and 70% when a nonlinear taper is used. Efficiency in the linear taper case is shown to be insensitive to beam axial velocity spread, while both cases show negligible power flow into competing modes.

Design considerations for the gyro-peniotron oscillator

The gyro-peniotron shows great promise as a source of microwave radiation. In this paper we investigate the stability and the non-linear saturated efficiency of a gyropeniotron oscillatro with an axis encircling beam operating at the TE211 and the TE311 cylindrical cavity modes. Beam and cavity parameters for stable high efficiency operation are presented from a linear theory analysis of the start-oscillation condition. Using design parameters taken from the linear analysis, the strong field non-linear emission efficiencies are studied numerically. The sensitivity of the saturated efficiency to beam axial velocity and guiding center spread is also considered. The results of our modeling indicate that high efficiency (70–90%) operation of the gyro-peniotron oscillator is possible, even with large guiding center\((\delta r_{gc_ \circ } \mathop< \limits_ \sim 0.2 - 0.4r_{L_ \circ } )\) and large axial velocity\((\delta \beta _{||} \mathop< \limits_ \sim 0.3\beta _{||_ \circ } )\) spread.

Linear and non-linear theory of the Doppler-shifted cyclotron resonance maser based on TE and TM waveguide modes

This paper presents a comprehensive theory of the cyclotron resonance maser (CRM) interaction in a circular waveguide. The kinetic theory is used to derive the dispersion relationships for both TE and TM modes. The TE mode case has been investigated by several authors, but there has been comparatively little work on the TM mode case. However, the TM mode interaction competes effectively with the TE mode interaction at relativistic electron energies. The conditions for maximum temporal and spatial growth rates are shown. The TM mode growth rates are found to vanish when the RF wave group velocity equals the beam axial velocity (‘grazing incidence’). The single particle theory is used to derive a compact set of self-consistent non-linear equations for the TE and TM mode interactions. These equations are particularly appropriate for the cyclotron auto-resonance maser (CARM) regime but applicability extends to other regimes as well. The conditions for optimum efficiency are investigated for oscillator and amp...

Velocity diagnostics of mildly relativistic, high current electron beams

We describe two diagnostic methods for measuring the velocity components of mildly relativistic, high current electron beams. The first involves a measurement of the radial electrostatic potential and of the beam current and yields the time resolved, spatially averaged axial beam velocity v∥. The second requires a measurement of the beam cyclotron wavelength in the guiding magnetic field and yields a spatially averaged product γv∥, where γ=(1−v2⊥/c2−v2⊥/c2)−1/2 and v⊥ is the transverse beam velocity. By combining the two techniques we obtain v∥ and v⊥ for a 0.4–1.2 MV electron beam carrying a current of 1–2 kA.

Theory of free-electron lasers

A general analysis is presented of free-electron lasers in which a static periodic magnetic pump field is scattered from a relativistic electron beam. The steady-state formulation of the problem is fully relativistic and contains beam thermal effects. Growth rates associated with the radiation field, efficiencies, and saturated-field amplitudes are derived for various modes of operation. Effects of space charge on the scattering process are included and shown to play a dominant role in certain situations. Scaling laws for the growth rates and efficiencies at a fixed radiation frequency as a function of the magnetic-pump amplitude are obtained. The shear in beam axial velocity due to self-fields is discussed, and various methods of reducing it are suggested. Finally, a detailed illustration of a far-infrared ($\ensuremath{\lambda}=2$ \ensuremath{\mu}m) two-stage free-electron laser using a 3-MeV electron beam and a 2-cm-wavelength magnetic pump field is presented.

Cyclotron maser instability for general magnetic harmonic number

The cyclotron maser instability for general magnetic harmonic number transverse electric (TE) and transverse magnetic (TM) waveguide modes in a conducting cylinder of radius Rc are examined. The analysis is carried out for a hollow electron beam (radius R0) propagating parallel to a uniform axial magnetic field B0êz. It is assumed that ν/γ0≪1, where ν is Budker’s parameter and γ0mc2 is the electron energy in a frame of reference moving with the beam axial velocity βbcêz. One of the most important features of the analysis is that the instability growth rate for magnetic harmonic numbers s=2,3,... is comparable to the growth rate of the fundamental (s=1) mode, particularly for moderate electron energy [β0= (1−1/γ20)1/2≳0.4]. Moreover, it is shown that the instability growth rate can be maximized by appropriate choice of the geometric parameter R0/Rc.

Self-consistent theory of cyclotron maser instability for intense hollow electron beams

A self-consistent theory of the cyclotron maser instability, assuming azimuthally symmetric perturbations about a slowly rotating hollow electron beam propagating parallel to a uniform axial magnetic field B0êz is developed. The stability analysis is carried out within the framework of the linearize Vlasov–Maxwell equations. It is assumed that the beam is thin with radial thickness (2a) much smaller than the beam radius (R0), and that ωp2/ω2c≪1, where ωp and ωc are the electron plasma frequency and electron cyclotron frequency, respectively, in a frame of reference moving with the beam axial velocity cβb. The analysis is carried out for the specific choice of equilibrium electron distribution function in which all electrons have the same value of canonical angular momentum and the same value of energy in a frame of reference moving with axial velocity cβb. Stability properties are investigated including the important influence of finite radial geometry, finite beam temperature, and transverse magnetic perturbations (δB≠0). It is shown that instability exists for a very narrow range of axial wavenumbers satisfying ‖k−βbω/c‖≪1/R0. Detailed stability properties are calculated for a variety of system parameters.

The Linear and Self-Consistent Nonlinear Theory of the Electron Cyclotron Maser Instability

In this paper the linear and nonlinear theory of the electron cyclotron maser instability is considered. The configuration used to study the maser instability consists of relativistic electrons gyrating about and drifting along a uniform magnetic field within a parallel plate waveguide. Relativistic effects associated with the gyrating electrons are responsible for excitation of the transverse electric mode in the waveguide. Linear theory shows that the growth rate maximizes when the axial beam velocity coincides with the axial wave group velocity of the excited electromagnetic wave. This allows us to perform the nonlinear analysis in a frame where both the axial wave number and axial beam velocity vanish. We have found that the maser instability exists only if the perpendicular beam energy exceeds a threshold value. Our analysis also describes the temporal nonlinear evolution of the field amplitude and frequency of a single excited wave. The nonlinear wave dynamics are self-consistently determined from the nonlinear particle orbits through the force and wave equations. The nonlinear analysis shows that there are two possible mechanisms for the saturation of the unstable wave: 1) depletion of the available free energy associated with the rotating particles and 2) phase trapping of the gyrating electrons in the wave. The initial beam parameters determine which of the two mechanisms is responsible for saturation. Competition between the two saturation mechanisms leads to a peaking in the energy conversion efficiency as a function of beam energy. Numerical results of the nonlinear formalism show that energy conversion efficiencies from the particles to the wave can be as high as 60 percent in the beam frame. Furthermore, by appropriately contouring the external magnetic field, among other things, efficiencies as high as 70 percent can be realized.