Cross-field free electron laser instability for a tenuous electron beam

Davidson, Ronald C.; McMullin, Wayne A.; Tsang, K. T.

doi:10.1063/1.864518

Cited by 29 publications

(8 citation statements)

References 21 publications

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“…Diode configuration and coordinate system. 1979;Bekefi 1982;Davidson, McMullin & Tsang 1984;Chang, Ott, Antonsen & Drobot 1984). Recent theoretical studies of the equilibrium and stability properties of sheared, nonneutral electron flow have represented major extensions of earlier work (Levy 1965;Buneman, Levy & Linson 1966;Briggs, Daugherty & Levy 1970;Davidson 1974) to include the important influence of relativistic, nonlinear, and kinetic effects at moderately high electron density.…”

Section: Introductionmentioning

confidence: 95%

Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

Davidson

Uhm

1989

Laser Part. Beams

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Use is made of the Vlasov-Maxwell equations to derive an eigenvalue equation describing the extraordinary-mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium f°b = (n b /2jim) 6(H-mc 2 ) 6(P y ), where n b = const, is the electron density at the cathode (x = 0), / / i s the energy, and P y is the canonical momentum in the >>-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with \o)-kV d \«a> v and k 2 xl«l, where &i 1 pb = 4jzn b e 2 /m and & c = eBjmc, and B Q e z is the applied magnetic field in the vacuum region x b

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Section: Introductionmentioning

confidence: 95%

Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

Davidson

Uhm

1989

Laser Part. Beams

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“…Multiple-scale perturbation theory is used to obtain an analytic approximation to weakly nonlinear, periodic, single-particle motion near the fundamental resonance. II the process of deriving the approximate motion it is found that, in the case of finite wiggler amplitude, the correct resonance condition is 2-yokvo :: (eBo/-yomo)(1 + a2)-1/ 2 , where a,,= 2-1/ 2 There are two motivations for transforming to the drift frame: first, to remove the static electric field; and second, to satisfy the condition that the motion is non-relativistic for typical velocities, i.e., v 2 /c 2 < 1.…”

Section: E X D/b'imentioning

confidence: 99%

“…The next step is the development of an approximation of the second term on the left-hand side of (19), wO-r 2 Lz, which includes lowest-order resonant nonlinear terms.…”

Section: (30)mentioning

confidence: 99%

Resonant operation of the cross-field free-electron laser: Kinetic and fluid equilibria

et al. 1988

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Multiple-scale perturbation theory is used to obtain periodic orbits of relativistic electrons in the external electric and magnetic fields of a planar cross-field free electron laser (FEL) operating near the fundamental resonance. The condition for this resonance is 2-yok.vo = (eBo/-yomo)(i +a2 )-1/ 2 , where k, is the wavenumber of the magnetic wiggler field, vo = E 0 /B 0 is the electron drift speed in the crossed uniform electric and magnetic fields, yo = (1 -vo/c 2 )'/ 2 is the relativistic factor associated with the Lorentz transformation between the laboratory frame and the drift frame, mo is the rest mass of the electron, aw = 2~'/ 2 (eBw/mockw) is the normalized r.m.s. vector potential of the wiggler field, and Bw is the magnitude of the wiggler field. The orbits are expressed in an approximate form suitable for use in linearized Vlasov stability analysis and are used to obtain Vlasov distribution functions which correspond to kinetic equilibria that are uniform and nonuniform (across the anode-cathode gap). Appropriate moments of these distribution functions yield corresponding fluid equilibria. These equilibria are developed as a basis for a linear stability analysis of the cross-field FEL operating near the fundamental resonance.t Present address: Thomson-CSF,

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“…Recent experimental investigations 1 [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been very successful over a wide range of beam energy and current ranging from experiments at low energy (150-250 keV) and low current (5 A-45 A), 19 to moderate energy (3.4 MeV) and high current (0.5 kA), 17 , 18 to high energy (20 MeV) and low current (40 A). 15 , 16 Theoretical studies have included investigations of nonlinear effects 20 - 3 2 and saturation mechanisms, the influence of finite geometry on linear stability properties, 33-38 novel magnetic field geometries for radiation generation 38 - 43 and fundamental studies of stability behavior. [44][45][46][47][48][49][50][51][52] In a recent calculation, 32 a self-consistent kinetic formalism has been developed to describe the sideband instability 24 within the framework of the Vlasov-Maxwell equations for a relativistic electron beam propagating through a helical wiggler magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Kinetic analysis of the sideband instability in a helical wiggler free-electron laser for electrons trapped near the bottom of the ponderomotive potential

1986

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A kinetic formalism based on the Vlasov-Maxwell equations is used to investigate properties of the sideband instability for a tenuous, relativistic electron beam propagating through a constant-amplitude helical wiggler magnetic field (wavelength x0 = 2Tr/k 0 , and normalized amplitude aw = w /mc 2 ko). The analysis is carried out for perturbations about an equilibrium BGK state in which the distribution of beam electrons G s(y') and the wiggler magnetic field coexist in quasi-steady equilibrium with a finite-amplitude, circularly polarized, primary A 2 electromagnetic wave (w s,k s) with normalized amplitude as eB/mc ks. Particular emphasis is placed on calculating detailed properties of the sideband instability for the case where a uniform distribution of trapped electrons G (y') is localized near the bottom of the ponderomotive potential moving with velocity vp = os/(k s+k 0) relative to the laboratory frame. For harmonic numbers n > 2, it is found that stable (Imw = 0) sideband oscillations exist for [w-(k+k 0)v p 2 _ n2 Here, (w,k) are the perturbation frequency and wavenumber in the laboratory frame, 0B (aw a sc 2 k' 2/' 2 1 is the bounce frequency, j mc 2 is the maximum energy of the trapped electrons in the ponderomotive frame, and k' and y are defined by k' = (k +k 0)/ p and yP = (1-v /c2)-. On the other hand, for the fundamental (n = 1) mode, instability exists (Imw > 0) over a wide range of system «1ad «1whrr 3 = 2 (2222, parameters B/ck < 1 and r 0 << 1, where r0 = (a w/ 4)(pT/Yp k0)(1+vP/c)(c/vPM 3 and i pT = (47rhnTe /m)1 is the plasma frequency of the trapped electrons. Moreover, the maximum growth rate and bandwidth of the sideband instability for the fundamental (n = 1) mode exhibit a sensitive dependence on the normalized pump strength B /rOk0c.

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Cross-field free electron laser instability for a tenuous electron beam

Cited by 29 publications

References 21 publications

Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

Resonant operation of the cross-field free-electron laser: Kinetic and fluid equilibria

Kinetic analysis of the sideband instability in a helical wiggler free-electron laser for electrons trapped near the bottom of the ponderomotive potential

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