Instability of the Brillouin-Flow Equilibrium in Magnetically Insulated Structures

Swegle, John A.; Ott, Edward

doi:10.1103/physrevlett.46.929

Cited by 43 publications

(21 citation statements)

References 8 publications

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“…However, as discussed in Sec. II B, a number of observations suggest that instabilities in the MITL's flow-electron plasma can result in electrostatic-and electromagnetic-field fluctuations, and that these can subject the electrons to effective collisions [16,21,22,24,28,29,33,. These observations imply that the frequency of such collisions can be sufficiently high to cause the flow electrons to have a small, but non-negligible, component of their drift velocities directed toward the anode.…”

Section: Introductionmentioning

confidence: 92%

Analytic model of a magnetically insulated transmission line with collisional flow electrons

Stygar

Wagoner

Ives³

et al. 2006

Phys. Rev. ST Accel. Beams

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We have developed a relativistic-fluid model of the flow-electron plasma in a steady-state onedimensional magnetically insulated transmission line (MITL). The model assumes that the electrons are collisional and, as a result, drift toward the anode. The model predicts that in the limit of fully developed collisional flow, the relation between the voltage V a , anode current I a , cathode current I k , and geometric impedance Z 0 of a 1D planar MITL can be expressed as V a I a Z 0 h, where h 1=4 ÿ 1 1=2 ÿ lnb 2 ÿ 1 1=2 c=2 ÿ 1 and I a =I k . The relation is valid when V a * 1 MV. In the minimally insulated limit, the anode current I a;min 1:78V a =Z 0 , the electron-flow current I f;min 1:25V a =Z 0 , and the flow impedance Z f;min 0:588Z 0 . {The electronflow current I f I a ÿ I k . Following Mendel and Rosenthal [Phys. Plasmas 2, 1332 (1995)], we define the flow impedance Z f as V a =I 2 a ÿ I 2 k 1=2 .g In the well-insulated limit (i.e., when I a I a;min ), the electron-flow current I f 9V 2 a =8I a Z 2 0 and the flow impedance Z f 2Z 0 =3. Similar results are obtained for a 1D collisional MITL with coaxial cylindrical electrodes, when the inner conductor is at a negative potential with respect to the outer, and Z 0 & 40 . We compare the predictions of the collisional model to those of several MITL models that assume the flow electrons are collisionless. We find that at given values of V a and Z 0 , collisions can significantly increase both I a;min and I f;min above the values predicted by the collisionless models, and decrease Z f;min . When I a I a;min , we find that, at given values of V a , Z 0 , and I a , collisions can significantly increase I f and decrease Z f . Since the steady-state collisional model is valid only when the drift of electrons toward the anode has had sufficient time to establish fully developed collisional flow, and collisionless models assume there is no net electron drift toward the anode, we expect these two types of models to provide theoretical bounds on I a , I f , and Z f .

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Section: Introductionmentioning

confidence: 92%

Analytic model of a magnetically insulated transmission line with collisional flow electrons

Stygar

Wagoner

Ives³

et al. 2006

Phys. Rev. ST Accel. Beams

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“…The theory of non-neutral, laminar, E؋B drifting flows in crossed electric and magnetic fields has so far focused on the flow stability inside smooth wall cavities, [1][2][3][4][5][6] related to the magnetic gap insulation. In that context, the stability analysis of cathode layers ͑laminar flows touching the cathode͒ to short wavelength kdϾ1, slow wave /ckӶ1 perturbations has shown that ͑i͒ for an instability, both the Buneman Hartree Ϫku(x)ϭ0 and the cyclotron resonance Ϫku(x)ϭ⍀ must be satisfied at separate layers inside the flow ͑ii͒ the growth rate tends rapidly to zero 1,2 at the low space charge limit e 2 /⍀ 2 Ӷ1.…”

Section: Introductionmentioning

confidence: 99%

Destabilization of diocotron modes inside structured anode cavities

Riyopoulos

1999

Physics of Plasmas

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Previous stability analysis of low space charge ωe2/Ω2≪1, E×B drifting flows inside smooth anode cavities has shown that they are practically stable against slow wave ω/ck≪1 diocotron instabilities when the flow touches the cathode (cathode layer). It is shown here that the presence of periodically structured anode destabilizes cathode layer modes when their phase velocity matches that of an empty cavity eigenmode, as structured cavities support slow waves in vacuum. An analytic dispersion relation that self-consistently includes the structured anode effects is obtained in the guiding center approximation. The growth rate, related to the onset of magnetron oscillations, scales as γ/ω∼ωD/ω≃1/kd; it is independent of, and remains finite as, ωe2/Ω2→0. The most unstable frequency corresponds to a resonant layer below the flow surface (slightly below the Buneman–Hartree frequency) and the growth rate is found symmetric relative to the detuning from resonance.

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“…The truncation is obtained by assuming a certain characteristic for the system dynamics which is expressed by an equation of state. Perhaps, the simplest used approximation is the cold fluid, which completely neglects thermal effects by assuming a vanishing temperature [6][7][8][9][10][11][12]. Other examples of largely used equations of state are isothermal [13][14][15][16][17] and adiabatic [18,19].…”

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confidence: 99%

Adiabatic-Nonadiabatic Transition in Warm Long-Range Interacting Systems: The Transport of Intense Inhomogeneous Beams

et al. 2012

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We investigate the role of the temperature in the onset of singularities and the consequent breakdown in a macroscopic fluid model for long-range interacting systems. In particular, we consider an adiabatic fluid description for the transport of intense inhomogeneous charged particle beams. We find that there exists a critical temperature below which the fluid model always develops a singularity and breaks down as the system evolves. As the critical temperature is approached, however, the time for the occurrence of the singularity diverges. Therefore, the critical temperature separates two distinct dynamical phases: a nonadiabatic transport at lower temperatures and a completely adiabatic evolution at higher temperatures. These findings are verified with the aid of self-consistent N-particle simulations. For long-range self-interacting systems, it is generally very difficult to obtain a fully kinetic description of the dynamics. This is the case in plasmas, charged particle beams, and self-gravitating systems among others, where the collision duration time diverges in the thermodynamic limit [1][2][3][4][5]. A largely used tool to overcome this difficulty is the employment of macroscopic fluid models. In contrast to the kinetic description that requires the knowledge of the evolution of the distribution function in the full phase space, the fluid description is simpler because it is based on local macroscopic variables obtained by averaging over the momentum space. Moreover, because the fluid variables consist of readily understood macroscopic quantities, the physical interpretation of the phenomena under investigation is generally more direct. Nevertheless, except for very specific cases, the fluid description leads to an infinite hierarchy of equations which, in practice, have to be truncated to be analyzed. The truncation is obtained by assuming a certain characteristic for the system dynamics which is expressed by an equation of state. Perhaps, the simplest used approximation is the cold fluid, which completely neglects thermal effects by assuming a vanishing temperature [6][7][8][9][10][11][12]. Other examples of largely used equations of state are isothermal [13][14][15][16][17] and adiabatic [18,19]. At any rate, the validity of the fluid description resides not only on the choice of equation of state but also on the fact that the infinite hierarchy has to be convergent; i.e., the macroscopic fluid variables may not present singularities. In the case of cold fluids, a wellknown cause of singularities is the onset of the so-called wave breaking where the fluid description looses its validity due to a divergence in the particles density at a certain position and time. This phenomenon is associated with a filamentation in the phase space and may have relevant consequences such as temperature increase, energy redistribution, and particle acceleration, depending on the system.In this Letter, we investigate the role of the temperature in the onset of singularities in the macroscopic quantities and the consequen...

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Instability of the Brillouin-Flow Equilibrium in Magnetically Insulated Structures

Cited by 43 publications

References 8 publications

Analytic model of a magnetically insulated transmission line with collisional flow electrons

Analytic model of a magnetically insulated transmission line with collisional flow electrons

Destabilization of diocotron modes inside structured anode cavities

Adiabatic-Nonadiabatic Transition in Warm Long-Range Interacting Systems: The Transport of Intense Inhomogeneous Beams

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