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Negative-mass Instability in Nonlinear Plasma Waves

Description: The negative-mass instability (NMI), previously found in ion traps, appears as a distinct regime of the sideband instability in nonlinear plasma waves with trapped particles. As the bounce frequency of these particles decreases with the bounce action, bunching can occur if the action distribution is inverted in trapping islands. In contrast to existing theories that also infer instabilities from the anharmonicity of bounce oscillations, spatial periodicity of the islands turns out to be unimportant, and the particle distribution can be unstable even if it is at at the resonance. An analytical model is proposed which describes both single traps and periodic nonlinear waves and concisely generalizes the conventional description of the sideband instability in plasma waves. The theoretical results are supported by particle-in-cell simulations carried out for a regime accentuating the NMI effect.
Date: January 30, 2013
Creator: Dodin, I. Y.; Schmit, P. F.; Rocks, J. & Fisch, N. J.
Partner: UNT Libraries Government Documents Department

Theory of Fine-scale Zonal Flow Generation From Trapped Electron Mode Turbulence

Description: Most existing zonal flow generation theory has been developed with a usual assumption of qrρθ¡ << 1 (qr is the radial wave number of zonal flow, and ρθ¡ is the ion poloidal gyrora- dius). However, recent nonlinear gyrokinetic simulations of trapped electron mode (TEM) turbulence exhibit a relatively short radial scale of the zonal flows with qrρθ¡ ~ 1 [Z. Lin et al., IAEA-CN/TH/P2-8 (2006); D. Ernst et al., Phys. Plasmas 16, 055906 (2009)]. This work reports an extension of zonal flow growth calculation to this short wavelength regime via the wave kinetics approach. A generalized expression for the polarization shielding for arbitrary radial wavelength [Lu Wang and T.S. Hahm, to appear in Phys. Plasmas (2009)] which extends the Rosenbluth-Hinton formula in the long wavelength limit is applied.
Date: June 11, 2009
Creator: Hahm, Lu Wang and T.S.
Partner: UNT Libraries Government Documents Department

Enhancement of particle-wave energy exchange by resonance sweeping

Description: When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism can cause increased saturation levels of instabilities and even allow the free energy associated with instability to be tapped in a system in which background dissipation suppresses linear instability.
Date: January 1, 1996
Creator: Berk, H.L. & Breizman, B.N.
Partner: UNT Libraries Government Documents Department

Enhancement of particle-wave energy exchange by resonance sweeping

Description: It is shown that as the resonance condition of the particle-wave interaction is varied adiabatically, that the particles trapped in the wave will form phase space holes or clumps that can enhance the particle-wave energy exchange. This mechanism can cause much larger saturation levels of instabilities, and even allow the free energy associated with instability, to be tapped in a system that is linearly stable due to background dissipation.
Date: October 1, 1995
Creator: Berk, H.L. & Breizman, B.N.
Partner: UNT Libraries Government Documents Department

Finite beta and resonant electron effects on trapped-electron instabilities

Description: Finite $beta$ (plasma pressure/magnetic pressure) and resonant electron effects on the dissipative trapped-electron instabilities are analyzed. These modifications are shown to have a strong stabilizing influence on the finite ion gyroradius and electron temperature gradient driven modes, respectively. For relevant tokamak parameters complete stabilization may be possible. Stability criteria for radially local and nonlocal cases are presented. (auth)
Date: October 1, 1975
Creator: Tang, W.M.; Liu, C.S.; Rosenbluth, M.N.; Catto, P.J. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Generalized Expression for Polarization Density

Description: A general polarization density which consists of classical and neoclassical parts is system-atically derived via modern gyrokinetics and bounce-kinetics by employing a phase-space Lagrangian Lie-transform perturbation method. The origins of polarization density are further elucidated. Extending the work on neoclassical polarization for long wavelength compared to ion banana width [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)], an analytical formula for the generalized neoclassical polarization including both finite-banana-width (FBW) and finite-Larmor-radius (FLR) effects for arbitrary radial wavelength in comparison to banana width and gyroradius is derived. In additional to the contribution from trapped particles, the contribution of passing particles to the neoclassical polarization is also explicitly calculated. Our analytic expression agrees very well with the previous numerical results for a wide range of radial wavelength.
Date: April 23, 2009
Creator: Hahm, Lu Wang and T.S.
Partner: UNT Libraries Government Documents Department

Toroidal Alfven Eigenmode induced ripple trapping

Description: Toroidal Alfven Eigenmodes are shown to be capable of inducing ripple trapping of high energy particles in tokamaks, causing intense localized particle loss. The effect has been observed in TFTR.
Date: March 1, 1995
Creator: White, R.B.; Fredrickson, E.; Darrow, D.; Zarnstorff, M.; Wilson, R.; Zweben, S. et al.
Partner: UNT Libraries Government Documents Department

Nonlinear theory of collisionless trapped ion modes

Description: A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level {delta}n/n{sub 0} is lower than the conventional mixing length estimate, {Delta}r/L{sub n} (ii) the ion temperature fluctuation level {delta}T{sub i}/T{sub i} significantly exceeds the density fluctuation level {delta}n/n{sub 0}; and (iii) the parallel ion velocity fluctuation level {delta}v{sub i}{sub {parallel}}/v{sub Ti} is expected to be negligible.
Date: March 1, 1996
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Trapped-Particle Instability Leading to Bursting in Stimulated Raman Scattering Simulations

Description: Nonlinear, kinetic simulations of Stimulated Raman Scattering (SRS) for laser-fusion-relevant conditions present a bursting behavior. Different explanations for this regime has been given in previous studies: Saturation of SRS by increased nonlinear Landau damping [K. Estabrook et al., Phys. Fluids B 1 (1989) 1282] and detuning due to the nonlinear frequency shift of the plasma wave [H.X. Vu et al., Phys. Rev. Lett. 86 (2001) 4306]. Another mechanism, also assigning a key role to the trapped electrons, is proposed here: The break-up of the plasma wave through the trapped-particle instability.
Date: November 8, 2001
Creator: Brunner, S. & Valeo, E.
Partner: UNT Libraries Government Documents Department

Destabilization of the trapped electron mode by magnetic curvature drift resonances

Description: Electron curvature drift resonances, ignored in earlier work on the trapped-electron modes, are found to exert a strong destabilizing influence in the lower collision frequency range of these instabilities. Effects arising from ion temperature gradients, shear, and finite ion gyroradius are included with these vector nebla-drifts in the analysis, and the resultant eigenvalue equation is solved by numerical procedures rather than the commonly used perturbation techniques. For typical tokamak parameters the maximum growth rates are found to be increased over earlier estimates by roughly a factor of 4, and requirements on magnetic shear strength for stabilization are likewise more severe and very difficult to satisfy. For inverted density profiles, this new destabilizing effect is rendered ineffective, with the result that the modes can be stabilized for achievable values of shear provided the temperature gradients are not too severe. Estimates of the particle and thermal energy transport are given for both normal and inverted profiles. (auth)
Date: December 1, 1975
Creator: Adam, J.C.; Tang, W.M. & Rutherford, P.H.
Partner: UNT Libraries Government Documents Department

Some effects of parallel energy propagation on the structure of dissipative trapped electron modes

Description: The limitation of ballooning by parallel energy propagation is investigated for the dissipative trapped electron mode, wherein the local energy influx is proportional to the poloidally dependent trapped particle fraction. For small energetic asymmetries [mg less than 2.5 ($Omega$/sub i/a/c/sub s/) (a/R/ sup $sup 3$/$sub 4$/] the structure along the field line is predominantly a phase shift, dictated by the condition that the asymmetric energy input be compensated by parallel energy flow. For large asymmetry, mode number, and parallel arc length, the phase and amplitude variations necessitate an integral equation treatment. (auth)
Date: January 1, 1976
Creator: Sauthoff, N. R.
Partner: UNT Libraries Government Documents Department

A Landau fluid model for dissipative trapped electron modes

Description: A Landau fluid model for dissipative trapped electron modes is developed which focuses on an improved description of the ion dynamics. The model is simple enough to allow nonlinear calculations with many harmonics for the times necessary to reach saturation. The model is motivated by a discussion that starts with the gyro-kinetic equation and emphasizes the importance of simultaneously including particular features of magnetic drift resonance, shear, and Landau effects. To ensure that these features are simultaneously incorporated in a Landau fluid model with only two evolution equations, a new approach to determining the closure coefficients is employed. The effect of this technique is to reduce the matching of fluid and kinetic responses to a single variable, rather than two, and to allow focusing on essential features of the fluctuations in question, rather than features that are only important for other types of fluctuations. Radially resolved nonlinear calculations of this model, advanced in time to reach saturation, are presented to partially illustrate its intended use. These calculations have a large number of poloidal and toroidal harmonics to represent the nonlinear dynamics in a converged steady state which includes cascading of energy to both short and long wavelengths.
Date: September 1, 1995
Creator: Hedrick, C.L.; Leboeuf, J.N. & Sidikman, K.L.
Partner: UNT Libraries Government Documents Department

Two-stream cyclotron radiative instabilities due to the marginally mirror-trapped fraction for fustion alphas in tokamaks

Description: It is shown here that the marginally mirror-trapped fraction of the newly-born fusion alpha particles in the deuterium-tritium (DT) reaction dominated tokamak plasmas can induce a two-stream cyclotron radiative instability for the fast Alfven waves propagating near the harmonics of the alpha particle cyclotron frequency {omega}{sub c{alpha}}. This can explain both the experimentally observed time behavior and the spatially localized origin of the fusion product ion cyclotron emission (ICE) in TFTR at frequencies {omega} {approx} m{omega}{sub c{alpha}}.
Date: July 1, 1995
Creator: Arunasalam, V.
Partner: UNT Libraries Government Documents Department

Comparison of Linear Microinstability Calculations of Varying Input Realism

Description: The effect of varying ''input realism'' or varying completeness of the input data for linear microinstability calculations, in particular on the critical value of the ion temperature gradient for the ion temperature gradient mode, is investigated using gyrokinetic and gyrofluid approaches. The calculations show that varying input realism can have a substantial quantitative effect on the results.
Date: September 8, 2003
Creator: Rewoldt, G.
Partner: UNT Libraries Government Documents Department

Self-consistent chaos in the beam-plasma instability

Description: The effect of self-consistency on Hamiltonian systems with a large number of degrees-of-freedom is investigated for the beam-plasma instability using the single-wave model of O`Neil, Winfrey, and Malmberg.The single-wave model is reviewed and then rederived within the Hamiltonian context, which leads naturally to canonical action- angle variables. Simulations are performed with a large (10{sup 4}) number of beam particles interacting with the single wave. It is observed that the system relaxes into a time asymptotic periodic state where only a few collective degrees are active; namely, a clump of trapped particles oscillating in a modulated wave, within a uniform chaotic sea with oscillating phase space boundaries. Thus self-consistency is seen to effectively reduce the number of degrees- of-freedom. A simple low degree-of-freedom model is derived that treats the clump as a single macroparticle, interacting with the wave and chaotic sea. The uniform chaotic sea is modeled by a fluid waterbag, where the waterbag boundaries correspond approximately to invariant tori. This low degree-of-freedom model is seen to compare well with the simulation.
Date: February 8, 1993
Creator: Tennyson, J. L.; Meiss, J. D. & Morrison, P. J.
Partner: UNT Libraries Government Documents Department

Trapped particle dynamics in toroidally rotating plasmas

Description: A detailed single particle orbit analysis is toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first order correction in {rho}{sub pi}(poloidal ion gyroradium)/L{sub v}(scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
Date: June 1, 1992
Creator: Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Annual progress report

Description: Considerable success has been achieved this year in research aimed at extending the asymptotic threshold nonlinear theory to plasmas governed by the Vlasov equation and in a group of linear studies concerned with drift instabilities in sheared magnetic fields. The nonlinear results are general and have been applied to the bump-on-tail instability and to the collisionless drift and the dissipative trapped electron instability in unsheared fields. The linear studies have dealt with the effects of resonant electrons, finite collisionality, finite-beta, neoclassical modifications and ion gyro-motion on trapped electron instabilities in sheared magnetic fields. (auth)
Date: September 19, 1975
Creator: Simon, A.
Partner: UNT Libraries Government Documents Department