Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence

In gyrokinetic theory there are two quadratic measures of fluctuation energy, left invariant under nonlinear interactions, that constrain the turbulence. The recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported on the novel consequences that this constraint has on the direction and locality of spectral energy transfer. This paper builds on that work. We provide detailed analysis in support of the results of Plunk and Tatsuno but also significantly broaden the scope and use additional methods to address the problem of energy transfer. The perspective taken here is that the fluctuation energies are not merely formal invariants of an idealized model (two-dimensional gyrokinetics) but are general measures of gyrokinetic turbulence, i.e. quantities that can be used to predict the behavior of the turbulence. Though many open questions remain, this paper collects evidence in favor of this perspective by demonstrating in several contexts that constrained spectral energy transfer governs the dynamics.Comment: Final version as published. Some cosmetic changes and update of reference

Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.Comment: Revtex, 4 pages, 3 figures; replaced to match published versio

Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas

This letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales

The first three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of $k^{-2.8}$ as observed in \emph{in situ} spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic \Alfven wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at sub-ion-Larmor radius scales, which provides the first evidence of the ion entropy cascade in an electromagnetic turbulence simulation.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Free energy cascade in gyrokinetic turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a forward (from large to small scales), extremely local, and self-similar cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large eddy simulation techniques for gyrokinetics.Comment: 4 pages, 2 Postscript figure

Collision-dependent power law scalings in 2D gyrokinetic turbulence

Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely-decaying 2D electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.Comment: 7 pages, 5 figures, accepted for publication in Physics of Plasma

Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence

Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by the dimensionless ratio D of the collision time to the eddy turnover time measured at the scale of the thermal Larmor radius. When D >> 1, a broad spectrum of fluctuations at sub-Larmor scales is found in both position and velocity space. The distribution function develops structure as a function of v_{perp}, the velocity coordinate perpendicular to the local magnetic field. The cascade shows a local-scale nonlinear interaction in both position and velocity spaces, and Kolmogorov's scaling theory can be extended into phase space.Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific Plasma Theory Conference. Ver.2 includes corrected typos & updated reference

Mott transition in the π\pi-flux SU(44) Hubbard model on a square lattice

We employ the projector quantum Monte Carlo simulations to study the ground-state properties of the square-lattice SU(4) Hubbard model with a $\pi$ flux per plaquette. In the weak coupling regime, its ground state is in the gapless Dirac semi-metal phase. With increasing repulsive interaction, we show that, a Mott transition occurs from the semimetal to the valence bond solid, accompanied by the $Z_4$ discrete symmetry breaking. Our simulations demonstrate the existence of a second-order phase transition, which confirms the Ginzburg-Landau analysis. The phase transition point and the critical exponent $\eta$ are also estimated. To account for the effect of a $\pi$ flux on the ordering in the strong coupling regime, we analytically derive by the perturbation theory the ring-exchange term which describes the leading-order difference between the $\pi$-flux and zero-flux SU(4) Hubbard models.Comment: 8 pages, 9 figure

Dietary potassium influences kidney maintenance of serum phosphorus concentration

Dietary potassium influences kidney maintenance of serum phosphorus concentration. In studying the metabolic effects of diet potassium (K+) variation in normal humans, we noted that varying diet K+ within its normal range influenced inorganic phosphorus (Pi) homeostasis and serum calcitriol (1,25-dihydroxyvitamin D) levels. In six men who ingested a constant whole-foods diet containing (per 70kg body wt) 27mmol/day Pi and 52 mEq/day K+, we increased diet K+ to 156 mmol/day with supplements first of potassium bicarbonate (KHCO3) alone and then of potassium chloride (KCL) alone, each for eight days interrupted by an eight-day recovery period of no K+ supplement. Urine Pi decreased promptly with either K+-salt, each inducing a persisting retention of 7 to 10 mmoles Pi, which was dumped during recovery. Fasting serum [Pi] increased with either K+ supplement (P = 0.022, repeated measures analysis of variance); the composite mean serum [Pi] for the two K+-supplement periods exceeded that for the two periods without supplements (P < 0.01, paired t-test). Conversely, the concentration of serum calcitriol decreased with either K+ supplement (P = 0.020). Among subjects, the diet K+-induced increases in serum [Pi] correlated with those in plasma [K+] (r = 0.64, P = 0.027); the decreases in serum calcitriol concentration correlated with the increases in serum [Pi] (r = -0.69, P = 0.014). There were no significant differences among periods in serum parathyroid hormone, ionized calcium, urine cyclic AMP excretion, plasma renin activity, body weight, serum albumin, or creatinine clearance; plasma volume decreased slightly during KCL but not during KHCO3 periods. Thus, diet K+ variation exerts an anion-independent regulatory effect on renal handling of Pi that influences the set-point at which serum [Pi] is maintained at constant diet Pi. That effect of serum [Pi] set-point is directionally appropriate and quantitatively sufficient to provide “fine modulation” of serum calcitriol concentration under ordinary physiological conditions of normal diet K+ variations and normal diet Pi