Nonlinear evolution of drift instabilities

Tang

1987

The Physics of Fluids

Self Cite

PPPL-2354 DE86 013642Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation tech niques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms respon sible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with e/T e ~ (<^i/tti)/(k±p,) 2 .The associated quasilinear diffusion, which increases with collisionality, takes the form of D q i ~ -yi/k±, where u>; and 7; are the linear frequency and growth rate, re spectively. In the steady state, the diffusion process becomes stochastic in nature.The relevant mechanisms here are related to the velocity-space nonlinearities and DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED background fluctuations. The magnitude of the diffusion at this stage can be com parable to that of quasilinear diffision in the presance of collisions, and it remains finite even in the collisionless limit.

“…Furthermore, as shown in Ref. 17, we can assume that the (1,1) and (1,-1) modes track each other (i.e., <p + = <p* and / + = /I).…”

Section: I'll Ie Fm = {1 / T/27tv Cs ) Exp(-v?/2vl) As In Refmentioning

confidence: 99%

“…17,22 The E x B convection (k\fl<p+ term) in Eq. (19) In the linear limit, it yields the usual linear growth rate and frequency given by Eqs.…”

Section: I'll Ie Fm = {1 / T/27tv Cs ) Exp(-v?/2vl) As In Refmentioning

confidence: 99%

Section: I'll Ie Fm = {1 / T/27tv Cs ) Exp(-v?/2vl) As In Refmentioning

confidence: 99%

mentioning

confidence: 99%

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Nonlinear evolution of drift instabilities in the presence of collisions

Federici

Tang

1987

The Physics of Fluids

Self Cite

“…The simulation runs studied here include those reported in published works of W. W, Lee and co-workers, 3 ' 2 as well as other runs carried out by the authors since those papers were written. They show the expected linear growth phase, a satura tion phase, and a "steady-state phase."…”

Section: Introductionmentioning

confidence: 99%

Nonlinear mechanisms for drift wave saturation and induced particle transport

Dimits

Physics of Fluids B: Plasma Physics

1991

Self Cite

A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisionai drift waves is pre sented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is deter mined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E X B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the elec tron flux has a much smoother dependence on the potential. In the 2 ^-dimensional ("pseudo-3D") geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. DISCLAIMERThis report was prepared is an account of -work sponsored by an agency of ihe Uniiiai Slates Government. Neither Ihe United Stales Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents thai its use would not infringe privately owned rights Refer ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise docs not necessarily constitute or imply its endorsement, recom mendation, or favoring by the United States Government or any agency thereof The views and opinions or authors expressed herein do not necessarily Hale or reflect those of Ihe United States Government or any agency thereof MASTER tp n jt/tl-J' •-

Partially Linearized Algorithms in Gyrokinetic Particle Simulation

Dimits

Journal of Computational Physics

1993

162

120

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the , relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms 1) enable us to suppress the intrinsic numerical noise in the simulation, and 2) also make it possible to regulate the weights of the fast-moving particles and, in mm, to eliminate the associated high frequency osciUations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas.