Competition of modes resonant with arbitrary cyclotron harmonics ina gyrotron with nonfixed axial structure of the high-frequencyfield

A general theory is developed for self-consistent calculations of mode competition in a gyrotron with nonfixed axial structure of the RF field for arbitrary cyclotron harmonics. The theory is applied to the gyrotron operating at the Kernforschungszentrum Karlsruhe with a frequency of 150 GHz. The formalism presented allows a self-consistent calculation of mode competition for the operating and parasitic modes at the cyclotron resonance at arbitrary harmonics. Specific calculations are carried out for the cases n₀=1, n₁ =2 and n₀=2, n₁=1. It is emphasized that the formalism considered applies only to the case in which the azimuthal orthogonality condition is satisfied: n₀m₁≠n₁ m₀. There are circumstances when this condition is not satisfied     

Relativistic harmonic content of nonlinear electromagnetic waves inunderdense plasmas

The relativistic harmonic content of large-amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady-state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w_p/w ₀)≪1 and critical density (w_p/w₀)≃1 limits. For weak nonlinearities, eE₀/mcω₀<1, the nonlinear source term for the third harmonic is derived for arbitrary w_p/w₀. Arguments are given for extending these results for arbitrary wave amplitudes. It is also shown that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady-state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third-harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results     

Free electron laser pumped by a powerful traveling electromagneticwave

A three-wave free-electron laser (FEL) was operated with a powerful 8.4-GHz electromagnetic pump wave replacing the usual magnetostatic wiggler. The presence of a uniform axial magnetic field B₀ produced cyclotron-harmonic idler waves. Peaks in the emission spectrum corresponding to cyclotron harmonics were observed covering a frequency range from 16.5 to 130 GHz. The frequency spectrum of this novel FEL mechanism was tuned continuously by the variation of B₀     

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 slow wave free-electron laser

A simple calculation of a free-electron laser in the Compton regime that uses a dielectric-lined waveguide is presented. The introduction of a dielectric lining in a free-electron laser considerably reduces the requirements on beam voltage for generating a given frequency ω₁=k₀c/(1 - v_b η/c), where k₀ is the wiggler wave period η is the effective index of refraction (1<η<√ϵ) and ϵ is the permittivity. The system supports electromagnetic waves whose Poynting flux is largely concentrated in the dielectric; hence the electron beam is required to propagate close to the dielectric lining. The mode structure and dispersion behavior of the guiding system without the beam are discussed. a thin annular beam is introduced, and a perturbation theory is used to obtain the frequency and growth rate of radiation     

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     

The type and extent of non-LTE in argon arcs at 0.1-10 bar

A 30-A, 3-mm-diameter, wall-stabilized argon arc with 1% hydrogen is examined spectrometrically at pressures of 0.1-10 bar. Values of T_g, and T_exa diverge as pressure decreases below 5 bar (n_e⩽1×10¹⁷ cm^-3) at r=0. T_exβ is 20-40% larger than the other temperatures. The results are dependent on the transition probability scale used     

Analytical solution for capacitive RF sheath

A self-consistent solution for the dynamics of a high voltage, capacitive radio frequency (RF) sheath driven by a sinusoidal current source is obtained under the assumptions of time-independent, collisionless ion motion and inertialess electrons. Expressions are obtained for the time-average ion and electron densities, electric field and potential within the sheath. The nonlinear oscillation motion of the electron sheath boundary and the nonlinear oscillating sheath voltage are also obtained. The effective sheath capacitance and conductance are also determined. It was found that: (1) the ion-sheath thickness S _m is √50/27 larger than a Child's law sheath for the DC voltage and ion current density; (2) the sheath capacitance per unit area for the fundamental voltage harmonic is 2.452 ϵ₀ /S_m, where ϵ₀ is the free space permittivity; (3) the ratio of the DC to peak value of the oscillating voltage is 54/125; (4) the second and third voltage harmonics are, respectively, 12.3 and 4.2% of the fundamental; and (5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 (λ_D/S_m)^2/3 (e ²n₀/mu_e), where n ₀ is the ion density, λ_D is the Debye length at the plasma-sheath edge, and u_e is the mean electron speed     

The Rippled-Field Magnetron (Cross-Field Free Electron Laser)

Millimeter-wave emission from the rippled-field magnetron (cross-field free electron laser (FEL)) is investigated experimentally and theoretically. In this device, electrons move in quasi-circular orbits under the combined action of a radial electric field, a uniform axial magnetic field, and a radial azimuthally periodic wiggler magnetic field. In excess of 300 kW of RF power is observed in two narrow spectral lines whose frequency can be tuned continuously from ~25 to ~50 GHz by variation of the axial magnetic field. The observations are interpreted as a FEL type of instability, associated with a resonance in the particle motion of a layer of electrons embedded in the dense spacecharge cloud. The resonance is shown to occur when 2kw?0 ? (?>0/?0) ?1 -(?p/?0)2, where kw is the wiggler wavenumber, ?0 is the azimuthal electron velocity, ?0 is the relativistic cyclotron frequency in the axial magnetic field, wp is the relativistic plasma frequency, and ?0 = [1 - (?0/c)2]-1/2 of the resonant electron layer.     

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     

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     

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_⊥     

Validity conditions for complete and partial local thermodynamicequilibrium of nonhydrogenic level systems and their application tocopper vapor arcs in vacuum

Validity conditions for complete and partial local thermodynamic equilibrium (CLTE and PLTE) of homogeneous, time-dependent, and optically thin plasmas are derived. For Cu I, electron densities of n_e⩾(5×10²²-5×10²³ ) m^-3 are required for the establishment of CLTE. For Cu I and Cu II, n_e⩾(5×10²¹-5×10²¹ -5×10²²) m^-3 is necessary for PLTE (for electron temperatures of 1-2 eV). Application to low-current copper vapor arcs in vacuum shows that CLTE can be expected for r<200-600 μm (r=distance from the cathode spot). A further limitation follows for temperatures of 2 eV or higher if diffusion effects are taken into consideration. Consequently, the use of the LTE formulas in plasma spectroscopy of low-current vacuum arcs is very limited     

Radiation cooling rates of a selenium plasma

The development of a scalable hydrogenic ionization model is described. The model utilizes correct energy and level structure data for each ionization stage and can be coupled self-consistently to a radiation transport calculation of the full nonhydrogenic X-ray spectrum. Thus it can be used to calculate accurately the effects of opacity on radiation emission rates that are of relevance to plasmas designed to produce recombination pumped population inversions due to rapid plasma cooling. The model is applied to a selenium plasma. It is found that, at ion densities where X-ray lasing has been observed, line emission from Δn≠0 transitions is a more important contributor to selenium's cooling rate than line emission from the Δn=0 transitions. Plasma opacity can also play an important role     

Pressure limits for the vacuum arc deposition technique

Observations of the cathodic copper plasma expansion at low pressures of He, Ar, and SF₆ showed that, for background gas mass densities of ρ_g=1 to 4×10^-4 kg/m ³ and higher, the plasma and gas are separated into two volumes. A shock wave acts as a boundary between the two volumes. The boundary attains a stationary position once its expansion velocity decreases to the velocity of sound in the background gas. This position corresponds to a distance R_c to the cathode that agrees with a snowplow expansion model, giving R_c ^βf=E_r, where f is a function of the arc current and background gas characteristics, E _r is the erosion rate of the cathode, and β varies between 2.1 and 2.5. The interaction model is based on kinetic energy exchanges between two gas-like volumes without other energy losses. A maximum pressure limit for vacuum arc deposition is set for ρ_g /I=2 to 9×10^-6 kg/m³ A     

A planar electromagnet microwiggler for free electron lasers

The authors have designed and tested an electromagnet planar microwiggler for use in free electron lasers (FELs), constructed of current conductors wound on ferromagnetic cores. A prototype with a period of 1 cm and a gap of 0.5 cm produced a peak field on axis in excess of 4.6 kG, with a linear B/H characteristic to about 3.2 kG. The field of each half-period of the wiggler is independently tunable by adjusting the current delivered to each, thus allowing for precision tuning and/or wiggler tapering. General scaling laws are employed to predict the performance of a geometrically similar design with a period of 5 mm     

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 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     

Acoustic double layers in multispecies plasma

Particle simulation in a one-dimensional bounded system is used to examine the formation of acoustic double layers in the presence of two ion species. Double-layer formation depends critically on the details of the distribution functions of the supporting ion populations, and their relative drifts with respect to the electrons. The effect of having two ion components, an H⁺ and an O⁺ beam, on double-layer evolution from ion acoustic turbulence driven by an electron drift relative to the H⁺ beam of ≈0.5u _e, where uu_e is the electron thermal speed, is examined. The ratio of ion drifts is taken to be consistent with acceleration by a quasi-static auroral potential drop (i.e. V _H/V_O=√M_O/ M_H=4.0). Acoustic double layers form in either ion species on the time scale τ≈100ω_ps^-1, where ω_ps is the ion plasma frequency for species `s' and s=H or O, and for drifts relative to the electrons lower than that required for double layer formation in simulations of single ion component plasma     

Theoretical studies of the ion-hose instability in a plasma-focusedfree-electron laser

An `ion-focused' relativistic electron beam traversing a magnetic wiggler is subject to a transverse two-steam or `in-hose' instability, resulting from the coupling of transverse displacements of the beam centroid to the `slosh' motion of the (beam-focused) nonneutral ion plasma, and driven by the `V×B' deflection in the wiggler field. The equations of motion are resolved into an inhomogeneous `beam breakup' equation, and asymptotic growth is computed in the limit of linear focusing. The effect of nonlinearities is assessed numerically with a `distributed-mass' model. As examples, ion-hose growth is considered in a UV FEL and a microwave FEL two-beam accelerator