Self-consistent field theory of a helix traveling wave tubeamplifier

A self-consistent relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration in which a thin annular beam propagates through a sheath helix enclosed within a loss-free wall. A linear analysis of the interaction is carried out, subject to the boundary conditions imposed by the beam, helix, and wall. A detrimental dispersion equation is obtained which implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. The equation is valid for arbitrary azimuthal mode number and is solved numerically for the azimuthally symmetric case. The coupled-wave Pierce theory is recovered in the near-resonant limit. Numerical comparisons between the complete dispersion equation and the Pierce model are described. A discrepancy is found between the Pierce and the field theory even for low currents in the nominally ballistic regime, owing to the dielectric effect of the beam on the helix modes     

The microwave generation mechanism of arelativistic electron beampropagating through the dielectric-loaded cylindrical waveguide

The general dispersion relation is derived for the fundamental transverse magnetic modes driven by a cold relativistic electron beam in a dielectric-loaded cylindrical waveguide using the fluid Maxwell equations. It is then reduced to the algebraic equation for the space charge and cyclotron modes using a tenuous beam approximation. Solutions of the resulting equation are obtained by varying several parameters, such as the external magnetic field the dielectric constant and the thickness of the dielectric material. It is shown that the growth rate of the slow cyclotron instability is greatly increased for the region of B_o≲1000 G to the extent that it becomes comparable to the growth rate of a slow space-charge instability. In this region the magnetic-field effect on the slow space-charge mode is shown to increase the growth rate by up to 10%. In the limit of the critical external magnetic field defined as the field below which no beam equilibrium exists, it is found that two slow modes of cyclotron and space-charge modes become degenerate with a finite value of growth rate     

Computation of the electric and magnetic fields induced in a plasmacreated by ionization lasting a finite interval of time

S.C. Wilks et al. (1988) showed that when an infinite expanse of gas, carrying a linearly polarized electromagnetic wave, is instantly ionized, the initial wave is frequency upshifted. This phenomenon of frequency upconversion through flash ionization gives rise to steady-state transmitted and reflected electromagnetic waves and to a time-independent magnetic field. The case in which the final state of ionization is achieved not instantly but in a finite turn-on time, 0⩽t⩽t 0, which is followed by the steady state, is studied. It is shown that the electric field is obtained from the one-dimensional Helmholtz equation, d²F(t)/dt² +ω₀²g(t)F( t)=0, if electrons are born at rest when they are created during ionization. As a result, the instantaneous frequency of the upshifted radiation is ω(t)=√g(t). The electric field can be solved exactly for specific choices of g(t). It is solved using WKB approximations for arbitrary g(t). The magnetic field is then found by integrating Faraday's law. It is found that the steady-state electric field amplitude depends on the steady-state value o f g(t) but does not depend on the ionization time t₀. Conversely, the static magnetic field amplitude decreases with increasing turn-on time     

A slow wave free-electron laser in a longitudinal wiggler field

Linearized Vlasov-Maxwell equations are solved to obtain the growth rate of free electron laser instability from a tenuous relativistic electron beam propagating in a partially dielectric loaded waveguide immersed in combined axial and longitudinal wiggler magnetic fields. The instability appears via cyclotron resonance interactions for wave perturbations very close to w-kV_z-w_c=nk ₀V_Z where n is the general harmonic number. For n=0, the gain is similar to a slow wave cyclotron amplifier. For n⩾1, the growth rate is substantially larger than the standard slow wave free electron laser scheme utilizing a transverse wiggler field     

Excitation of slow EM waves in a waveguide having a thin, annularplasma sheet

A thin, annular plasma sheet in a waveguide slows down the phase velocity of electromagnetic modes in a plasma density window for frequencies below the electron cyclotron frequency via Cerenkov interaction. At lower densities, the plasma is not effective enough to reduce the phase velocity of the EM wave below c. At higher densities the plasma expels the radiation field, leading to enhancement of phase velocity. The lowest mode having azimuthal number l=0 is most unstable. The radial mode having amplitude maximum at r=a, viz the plasma boundary, has the largest growth rate     

A study of a parallel mode launch into a magnetic beach

A parallel mode launch in the electron cyclotron range of frequencies is performed on axis in the east end cell of the Phaedrus-B tandem mirror. Propagation of the energy launched toward a magnetic beach in a radially hollow density profile was studied experimentally. A strong refractive dispersal of the launched energy was observed and shown to be in good agreement with a WKB-type ray tracing model using a cold plasma Appleton-Hartree dispersion relation. Measurements of plasma density and electron temperature indicate that the use of this dispersion relation is well justified. These results are compared with additional ray tracing studies for radially hollow and nonhollow, high ( f_launch<f_p) and low (f _launch>f_p) density models. For the experimental conditions examined, a reversal of refractive behavior is shown to exist as the energy propagates from a low density (f_launch>f_p) region to a high density (f_launch<f_p) region     

A Raman regime free-electron laser in a partially dielectric-loadedwaveguide

A partially dielectric-loaded waveguide supports modes with phase velocity ν_ph>c/∈^1/2, where ∈ is the dielectric constant of the lining. The coupling of a fast mode (with ν_ph>c) with a slow mode (with c /∈^1/2<ν_ph<c) via a negative-energy beam mode gives rise to the explosive growth of all the three waves at the expense of the energy of the beam. The slow mode of lower frequency can be launched from an external source and can become an efficient wiggler for the generation of the fast free-electron laser mode     

Effect of finite V⊥ on Cerenkov FEL in adielectric loaded waveguide

Allowance for finite V_⊥ of an annular electron beam propagating through a dielectric-loaded waveguide immersed in an axial magnetic field opens up the possibility of excitation of TE modes. The interaction is observed using Cerenkov and cyclotron resonances. On approximating the field distribution at the electron orbits to some suitable form, an analytical solution to the Vlasov equation is obtained, leading to a comprehensive dispersion relation for azimuthally symmetric TE_0n modes. In the special case where all the guiding centres lie on the axis, a fluid treatment for the arbitrary azimuthal-mode number is applicable. In these cases the growth rate increases with V_⊥     

Effect of a high-frequency field on the reflection of ion acousticwaves from the sheath at a grid

Experiments are described which show that the reflection coefficient for ion acoustic waves (IAW) from the sheath at a grid is affected by an HF electric field with a frequency f_HF≲5f_pi(f_pi =ion plasma frequency). For peak-to-peak amplitudes of the HF voltage drop across the sheath Φ₀≲k_B T_e/e and f_HF>f _pi, the energy distribution of the ions passing through the grid develops a hot tail and the reflected wave suffers enhanced Landau damping. If Φ₀≳k_BT_e/e and f_HF<f_pi, a large-amplitude IAW is excited at the grid; a well-defined ion beam is formed; and local growth of the reflected wave is observed. Test waves launched from the grid show the same propagation characteristics as the reflected waves     

Electrical characteristics of pulsed glow discharges

The i-v characteristics, energy partitioning, and time evolution of the discharge current and reduced field (E/N) for a nitrogen discharge are simulated using a self-consistent calculation of the electron energy distribution function and the vibrational level populations. The model includes diffusion losses and takes account of the external circuit parameters. The results discussed are for pressures of 1-100 torr, discharge currents in the range of 10^-3-5.0 A, and a reduced field (E/N) in the range of 150-250 Td. For a typical discharge in a tube of 2-cm diam. and a current of a few amperes, the results show that the energy stored in the vibrational manifold saturates a few milliseconds after the initiation of the discharge     

等离子体填充带状螺旋线的色散方程

利用线性场理论和螺旋线的导带模型，对填充等离子体的带状螺旋线进行了严格的场分析.在给出各区域电磁场分量表达式的基础上，利用螺旋带的边界条件，导出了等离子填充带状螺旋线中电磁波传播的色散方程. 关键词： 等离子体 带状螺旋线 色散方程     

Finite conductivity and the interchange instability in railgun arcs

A first-order perturbation expansion of the MHD (magnetohydrodynamic) equation is used to describe the onset of the interchange instability due to the high accelerations in railgun plasma-arc armatures. J.D. Powell (1986) considered the problem of perturbing an initial isothermal equilibrium with appropriate distributed current and density profiles, treating the perturbation equations with infinite conductivity. Here, the authors model the arc the same way, but they include the effects of finite conductivity σ. A fourth-order mode equation is derived and solved numerically. The authors find continuous spectra of unstable modes for a nonzero plasma acceleration g, whose growth rates are mostly greater than √kg, depending on the values of k and σ. The resistivity always raises growth rates higher than Powell's especially for large k and large resistivity. The resulting growth rates in typical railgun situations are large enough to permit full development of the instability     

Small-signal analysis of a rectangular helix structure traveling-wave-tube

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube (TWT) for a solid sheet electron beam. The `hot' dispersion equation is obtained by means of the self-consistent field theory. The small signal analysis, which includes the effects of the beam parameters and slow-wave structure (SWS) parameters, is carried out by theoretical computation. The numerical results show that the bandwidth and the small-signal gain of the rectangular helix TWT increase as the beam current increases; and the beam voltage not obviously influences the small signal gain. Among different rectangular helix structures, the small-signal gain increases as the width of the rectangular helix SWS increases, however, the bandwidth decreases whether structure parameters a and L or ψ and L are fixed or not. In addition, a comparison of the small-signal gain of this structure with a conventional round helix is made. The presented analysis will be useful for the design of the TWT with a rectangular helix circuit.     

Stimulated acceleration and confinement of deuterons in focuseddischarges. II

For pt.I see ibid., vol.16, no.3, p.368-73, June 1988. Methods of increasing, by a factor greater than five, the neutron yield/short Y _n from D-D fusion reactions in a plasma focus (PF) enhance both the D⁺-ion acceleration to energy values E _d>1-8 MeV and the ion confinement in the pinch region. Nuclear activation of C and N in the (doped) filling gas of the discharge chamber and of solid targets of C and BN bombarded by the ion beam in the direction of the electrode axis (0°) confirms earlier determination of the energy spectrum of the trapped ions (dφ_t/dE∝φ_0tE ^-m) and of the ejected beam (dφ_b/dE∝φ_0bE _d^-m, m=2.5±0.5 for 0.1 MeV≲E≲3 MeV). A Thomson (parabola) spectrometer with nanosecond time resolution determines the time of emission t( E) of the beam at 0°. Ion acceleration and trapping occur within the small (filamentary) elements of the magnetic fine structure of the pinch, which can be dispersed on a relatively large confinement volume after the pinch disintegration. It has been found that φ_t/φ_b≳10-10³ for E_d≳1 MeV, depending on Y_n     

Experimental study of a plasma-filled backward wave oscillator

Experimental studies of a plasma-filled X-band backward-wave oscillator (BWO) are presented. Depending on the background gas pressure, microwave frequency upshifts of up to 1 GHz appeared along with an enhancement by a factor of 7 in the total microwave power emission. The bandwidth of the microwave emission increased from ⩽0.5 GHz to 2 GHz when the BWO was working at the RF power enhancement pressure region. The RF power enhancement appeared over a much wider pressure range in a high beam current case (10-100 mT for 3 kA) than in a lower beam case (80-115 mT for 1.6 kA). The plasma-filled BWO has higher power output than the vacuum BWO over a broader region of magnetic guide field strength. Trivelpiece-Gould modes (T-G modes) are observed with frequencies up to the background plasma frequency in a plasma-filled BWO. Mode competition between the T-G modes and the X-band Tm₀₁ mode prevailed when the background plasma density was below 6×10¹¹ cm^-3 . At a critical background plasma density of ≃8×10¹¹ cm^-3 power enhancement appeared in both X-band and the T-G modes. Power enhancement of the S-band in this mode collaboration region reached up to 8 dB. Electric fields measured by the Stark-effect method were as high as 34 kV/cm while the BWO power level was 80 MW. These electric fields lasted throughout the high-power microwave pulse     

Townsend-type breakdown as a criterion for high-frequency vacuumarc interruption at submillimeter gaps

In vacuum circuit breakers, multiple reignitions give rise to HF current arcing (≈500 A; ≈200 kHz). Due to the small contact distance and the very large current gradient, at every arc-current zero pressures of several tens of millibars can be expected. Very soon thereafter (≈30 ns) this gap is dielectrically stressed by the first component of the restriking voltage (≈10 MHz), originating from parasitic impedances. The combination of the associated high electric field and the relatively high neutral density may cause Townsend-type breakdown, leading to another half-sine of continued arcing. Both dielectric stress and residual neutral density are expressed as a function of di/dt, yielding values of interruptible di/dt as a function of the contact distance with the Townsend breakdown criterion. Comparison with experiments shows fair agreement in the range of di/dt of 100-1000 A/μs and distances of 0.1-0.5 mm for two different circuits     

填充等离子体的介质同轴波导中的切伦科夫辐射

 利用自洽线性场理论，导出了薄环形相对论电子注通过填充等离子体的介质同轴波导中的注波互作用色散方程，得到了注波互作用产生切伦科夫辐射的同步条件和波增长率。分析了填充等离子体后的波与电子注之间的能量交换及等离子体密度对色散特性、波增长率和注波能量交换的影响。分析结果表明：切伦科夫辐射是由沿介质同轴波导传播的慢波与沿薄环形相对论电子注传播的负能空间电荷波耦合所致，且其耦合强度与电子注的密度成正比；输出频率和波增长率随着填充等离子体密度的增大而提高；保持一定的输出频率，增大电子注的束流可得到高的微波输出功率。     

Monte Carlo simulation of electron swarms in nitrogen in uniformE×B fields

The motion of electrons in nitrogen in uniform E× B fields is simulated using the Monte Carlo technique for 240⩽E/N⩽600 Td (1 Td=1×10^-17 V cm²) and 0⩽B/N⩽0.45×10^-17 T cm³ . The electron-molecule collision cross sections adopted are the same cross sections as those used previously for the numerical solution of the Boltzmann equation. The swarm parameters obtained from the Monte Carlo simulation are compared with the Boltzmann solution and with the experimental data available in the literature. In relation to E×B fields, it is concluded that the Monte Carlo approach provides an independent method of substantiating the validity of the equivalent electric-field approach     

Multimode simulations without particles in the quasi-opticalgyrotron

A set of coupled nonlinear differential equations, involving the slow amplitude and phase variation for each mode, is used to simulate the multimode dynamics in the quasi-optical gyrotron. The interaction among various modes is mediated by coupling coefficients of known analytic dependence on the normalized current I, the interaction length μ, and the frequency detunings Δ_i corresponding to the competing frequencies ω_i. The equations include all the possible resonant combinations of up to four different frequencies, ω_i-ω_j+ω _k-ω_l≃0, among a set of N participating modes, keeping terms up to fifth order in the wave amplitudes. The formalism is quite general and can be used to study mode competition, the existence of a final steady state and its stability, and its accessibility from given initial conditions. It is shown that when μ/β_⊥≫1, μ can be eliminated as an independent parameter. The control space is then reduced to a new normalized current I and the desynchronism parameters ν_i=Δ_iμ for the interacting frequencies. Numerical simulations for cold beams of various cross sections demonstrate that ν_i is the most important parameter for the system behavior. Overmoding is not determined by the frequency separation δω among the cavity modes per se, but by the separation among the corresponding desynchronism parameters