Damped diocotron quasi-modes of non-neutral plasmas and inviscid fluids

Spencer, Ross L.; Rasband, S. Neil

doi:10.1063/1.872497

Cited by 33 publications

(46 citation statements)

References 7 publications

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“…14,16,17 For simplicity, we consider a perturbation that consists of a single Fourier component, e.g., Јϭ (r,t)cos(mz/H)e in ϩc.c. We may define the Laplace transform of the Fourier coefficient , as follows:…”

Section: Appendix E: Quasimodesmentioning

confidence: 99%

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission

Schecter

Montgomery

2004

Physics of Fluids

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This paper further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a discrete vortex Rossby ͑VR͒ wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius r * , outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at r * . Previous theories for the decay rate were based on ''balance models'' of the vortex dynamics. Such models filter out inertia-buoyancy ͑IB͒ oscillations, i.e., gravity waves. However, if the Rossby number is greater than unity, the core VR wave can excite a frequency-matched outward propagating IB wave, which has positive feedback. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the hydrostatic primitive equations. Starting from conservation of wave activity ͑angular pseudomomentum͒, an expression for the decay rate is derived. This expression explicitly demonstrates a competition between the destabilizing influence of IB wave emission, and the stabilizing influence of potential vorticity stirring at r * . Moreover, it shows that if the radial gradient of potential vorticity at r * exceeds a small threshold, the VR wave will decay, and the vortex will symmetrize, even at large Rossby numbers.

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Section: Appendix E: Quasimodesmentioning

confidence: 99%

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission

Schecter

Montgomery

2004

Physics of Fluids

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“…Because this is a driven system, we first look for normal modes. Notice, however, that with E 0 = 0 and γ = 0 (undamped free response) this mode equation has a continuous spectrum, similar to the diocotron mode equation in non-neutral plasmas [14,15,16,17,18,19]. And, as with the diocotron mode, this equation also has a damped quasimode.…”

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confidence: 99%

“…Following Ref. [15], Eq. (6) can be solved along a contour in the complex r-plane to uncover this damped quasimode.…”

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confidence: 99%

Neutral-plasma oscillations at zero temperature

Bergeson

Spencer²

2003

Phys. Rev. E

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We use cold plasma theory to calculate the response of an ultracold neutral plasma to an applied rf field. The free oscillation of the system has a continuous spectrum and an associated damped quasimode. We show that this quasimode dominates the driven response. We use this model to simulate plasma oscillations in an expanding ultracold neutral plasma, providing insights into the assumptions used to interpret experimental data [Phys. Rev. Lett. 85, 318 (2000)].PACS numbers: 52.55. Dy, 32.80.Pj, 52.27.Gr, 52.35.Fp Recent experimental [1,2, 3,4,5,6] and theoretical work [7,8,9,10,11,12,13] has studied the formation and evolution of ultracold plasmas. In the laboratory, cold plasmas are created either by directly photo-ionizing laser-cooled atoms, or by exciting the atoms to high-lying Rydberg states that spontaneously ionize. A fraction of the electrons escape the plasma and the resulting electric field drives the ion expansion. Models of the expansion suggest that the density profile in the plasma is approximately Gaussian, and that it expands in a self-similar manner. It can be expressed aswhere σ = σ 2 0 + v 2 t 2 is the time-dependent width of the distribution, v is the asymptotic expansion velocity, and t is time.The experimental justification of this density profile for the case of an expanding plasma is based on the plasma's response to a spatially uniform applied rf field. In those experiments, Xe atoms initially cooled to ∼ 10µK were ionized by a dye laser. The initial electron energy (E e /k B ) ranged from a few to 1000 K, and the initial electron density ranged from 0.2 to 2.5 × 10 9 cm −3 . The plasmas were nearly charge-neutral, and at electron energies above 70 K, the kinetic energy of the electrons allowed significant loss. The resulting net positive charge in the cloud drove the plasma expansion.As the plasma expanded and its density decreased, the applied rf field pumped energy into the plasma. The heating was assumed to be largest where the applied rf frequency matched the local plasma frequency. Because of collisions in the plasma, the local heating presumably raised the overall plasma temperature, and a small number of the more weakly-bound electrons were ejected. The experiment measured the rate at which electrons were ejected from the expanding plasma as a function of time for a fixed applied rf frequency. This signal was presumed to be proportional to the rate at which the rf field heats the plasma, and was a measure of the weighted time-dependent density profile.The peak of this signal was interpreted to correspond to the "average" density of the plasma,with v a constant. This density was experimentally determined by setting the applied frequency ω equal to the average plasma frequency, ω p , and using the relationω p = q 2n (t)/m e ǫ 0 , where q is the electron charge, m e is the electron mass, and ǫ 0 is the permittivity of free space. The derived density,n, is time dependent. For a different applied rf frequency ω, the signal peaks at a different time. A least-squares fit ofn(t) to E...

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“…A formal Laplace transform solution to the initial value problem leads to a simple procedure for computing the complex frequency of a quasimode. The procedure has been derived for the quasimodes of 2D Euler vortices (Briggs et al 1970;Corngold 1995;Spencer and Rasband 1997) and for the quasimodes of 3D barotropic cyclones in density stratified fluids (Schecter et al 2002;Schecter and Montgomery 2004). Below, we describe the analogous procedure for a shallow-water cyclone, without derivation.…”

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confidence: 99%

Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia–Gravity Waves from an Intense Mesoscale Cyclone

Schecter

Montgomery

2006

Journal of the Atmospheric Sciences

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The spontaneous radiation of spiral inertia-gravity (IG) waves from monotonic cyclones is reexamined. Such radiation can occur most significantly in a parameter regime that includes strong supercell mesocyclones and hurricanes. First, linear theory is reviewed. In linear theory, a generic deformation of the cyclone excites discrete vortex Rossby (VR) waves. Each VR wave emits a frequency-matched spiral IG wave into the environment. The emission has positive feedback on the VR wave, causing both to grow. However, the VR wave also deposits wave activity into its critical layer at the radius r * . If the radial gradient of potential vorticity at r * exceeds a threshold, critical layer absorption suppresses the radiative instability. On the other hand, numerical simulations of a shallow-water cyclone show that nonlinear changes to the critical layer can revive a damped VR wave and its radiation field after a brief period of decay. For such revival, it suffices that ⍀ b /|␥ | տ 1. This inequality contains two characteristic frequencies. The denominator |␥ | is the absolute value of the (negative) growth rate of the damped wave. The numerator ⍀ b is the mixing rate of the critical layer, which is proportional to the square root of the initial wave amplitude.After damping is reversed, the radiative VR wave exhibits undulatory growth. Analysis shows that growth proceeds because radiation steadily removes negative wave activity from the cyclone. Secondary amplitude oscillations are due to back-and-forth exchanges of positive wave activity between the VR wave and its critical layer.

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Damped diocotron quasi-modes of non-neutral plasmas and inviscid fluids

Cited by 33 publications

References 7 publications

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission

Neutral-plasma oscillations at zero temperature

Conditions That Inhibit the Spontaneous Radiation of Spiral Inertia–Gravity Waves from an Intense Mesoscale Cyclone

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