B. Friedman

Modification of Turbulent Transport with Continuous Variation of Flow Shear in the Large Plasma Device

Continuous control over azimuthal flow and shear in the edge of the Large Plasma Device (LAPD) has been achieved using a biasable limiter which has allowed a careful study of the effect of flow shear on pressure-gradient-driven turbulence and transport in the LAPD. The LAPD rotates spontaneously in the ion diamagnetic direction; positive limiter bias first reduces, then minimizes (producing a near-zero shear state), and finally reverses the flow into the electron diamagnetic direction. Degradation of particle confinement is observed in the minimum shearing state and a reduction in the turbulent particle flux is observed with increasing shearing in both flow directions. Near-complete suppression of the turbulent particle flux is observed for shearing rates comparable to the turbulent autocorrelation rate measured in the minimum shear state. Turbulent flux suppression is dominated by amplitude reduction in low-frequency (<10 kHz) density fluctuations. An increase in fluctuations for the highest shearing states is observed with the emergence of a coherent mode which does not lead to net particle transport. The variations of density fluctuations are fit well with power laws and compare favorably to simple models of shear suppression of transport.

Modeling of plasma turbulence and transport in the Large Plasma Device

Numerical simulation of plasma turbulence in the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky et al., Rev. Sci. Instrum. 62, 2875 (1991)] is presented. The model, implemented in the BOUndary Turbulence code [M. Umansky, X. Xu, B. Dudson et al., Contrib. Plasma Phys. 180, 887 (2009)], includes three-dimensional (3D) collisional fluid equations for plasma density, electron parallel momentum, and current continuity, and also includes the effects of ion-neutral collisions. In nonlinear simulations using measured LAPD density profiles but assuming constant temperature profile for simplicity, self-consistent evolution of instabilities and nonlinearly generated zonal flows results in a saturated turbulent state. Comparisons of these simulations with measurements in LAPD plasmas reveal good qualitative and reasonable quantitative agreement, in particular in frequency spectrum, spatial correlation, and amplitude probability distribution function of density fluctuations. For comparison with LAPD measurements, the plasma density profile in simulations is maintained either by direct azimuthal averaging on each time step, or by adding particle source/sink function. The inferred source/sink values are consistent with the estimated ionization source and parallel losses in LAPD. These simulations lay the groundwork for more a comprehensive effort to test fluid turbulence simulation against LAPD data.The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the 3D fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves, the Kelvin-Helmholtz and rotational interchange instabilities. A general linear dispersion relation for partially ionized collisional plasmas including these modes is derived and analyzed. For LAPD relevant profiles including strongly driven flows it is found that all three modes can have comparable growth rates and frequencies. Detailed comparison with solutions of the analytic dispersion relation demonstrates that BOUT accurately reproduces all characteristics of linear modes in this system.

Energy dynamics in a simulation of LAPD turbulence

Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flute-like (k∥=0) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to k∥≠0 fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through ...

Analysis of plasma instabilities and verification of the BOUT code for the Large Plasma Device

The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid equations using the three-dimensional fluid code BOUT [M. Umansky et al., Contrib. Plasma Phys. 180, 887 (2009)], which has been successfully modified to treat cylindrical geometry. Instability drive from plasma pressure gradients and flows is considered, focusing on resistive drift waves and the Kelvin–Helmholtz and rotational interchange instabilities. A general linear dispersion relation for partially ionized collisional plasmas including these modes is derived and analyzed. For Large Plasma Device relevant profiles including strongly driven flows, it is found that all three modes can have comparable growth rates and frequencies. Detailed comparison with solutions of the analytic dispersion relation demonstrates that BOUT accurately reproduces all characteristics o...

Numerical simulation and analysis of plasma turbulence the Large Plasma Devicea)

Turbulence calculations with a 3D collisional fluid plasma model demonstrate qualitative and semi-quantitative similarity to experimental data in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)], in particular for the temporal spectra, fluctuations amplitude, spatial correlation length, and radial particle flux. Several experimentally observed features of plasma turbulence are qualitatively reproduced, and quantitative agreement is achieved at the order-of-magnitude level. The calculated turbulence fluctuations have non-Gaussian characteristics, however the radial flux of plasma density is consistent with Bohm diffusion. Electric polarization of density blobs does not appear to play a significant role in the studied case. Turbulence spectra exhibit direct and inverse cascades in both azimuthal and axial wavenumbers and indicate coupling between the drift instability and Kelvin-Helmholtz mode.

Turbulent transport of fast ions in the Large Plasma Device

Strong drift wave turbulence is observed in the Large Plasma Device [H. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] on density gradients produced by a plate limiter. Energetic lithium ions orbit through the turbulent region. Scans with a collimated ion analyzer and with Langmuir probes give detailed profiles of the fast ion spatial distribution and the fluctuating fields. The fast ion transport decreases rapidly with increasing fast ion gyroradius. Unlike the diffusive transport caused by Coulomb collisions, in this case the turbulent transport is nondiffusive. Analysis and simulation suggest that such nondiffusive transport is due to the interaction of the fast ions with stationary two-dimensional electrostatic turbulence.

Sheared-flow induced confinement transition in a linear magnetized plasma

A magnetized plasma cylinder (12 cm in diameter) is induced by an annular shape obstacle at the Large Plasma Device [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)]. Sheared azimuthal flow is driven at the edge of the plasma cylinder through edge biasing. Strong fluctuations of density and potential (δn/n~eδφ/kTe~0.5) are observed at the plasma edge, accompanied by a large density gradient (Ln=|∇lnn|-1~2cm) and shearing rate (γ~300kHz). Edge turbulence and cross-field transport are modified by changing the bias voltage (Vbias) on the obstacle and the axial magnetic field (Bz) strength. In cases with low Vbias and large Bz, improved plasma confinement is observed, along with steeper edge density gradients. The radially sheared flow induced by E×B drift dramatically changes the cross-phase between density and potential fluctuations, which causes the wave-induced particle flux to reverse its direction across the shear layer. In cases with higher bia...

Nonlinear instability in simulations of Large Plasma Device turbulence

Several simulations of turbulence in the Large Plasma Device (LAPD) [Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives k∥=0 potential energy fluctuations, which then three-wave couple to k∥≠0 potential energy fluctuations in order to access the adiabatic...

Turbulence and transport suppression scaling with flow shear on the Large Plasma Device

Continuous control over azimuthal flow and shear in the edge of the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Instr. 62, 2875 (1991)] has been achieved using a biasable limiter. This flow control has allowed a careful study of the effect of flow shear on pressure-gradient-driven turbulence and particle transport in LAPD. The combination of externally controllable shear in a turbulent plasma along with the detailed spatial diagnostic capabilities on LAPD makes the experiment a useful testbed for validation of shear suppression models. Motivated by these models, power-law fits are made to the density and radial velocity fluctuation amplitudes, particle flux, density-potential crossphase, and radial correlation length. The data show a break in the trend of these quantities when the shearing rate (γs=∂Vθ/∂r) is comparable to the turbulent decorrelation rate (1/τac). No one model captures the trends in the all turbulent quantities for all values of the shearing rate, but some models successfull...

A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. We define such a non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, periodic forces that randomize the state variables once every ...