Numerical simulation of ion acoustic turbulence

Extensive simulation studies of ion acoustic turbulence carried out at the Max Planck Institute and at the Los Alamos National Laboratory are compared. Simulations of theB=0 case carried out at the two laboratories agree when the Sagdeev scaling law without theT _e/T_i dependence is used to compare them. Typical results are shown. The level of turbulence is found to be quite high in spite of the low anomalous collision frequency. The role of the differential drift distribution in these simulations is discussed extensively.     

Spectral density of ion acoustic plasma turbulence

Plasma wave spectral density has been measured as a function of wavenumber and frequency by a two-step technique: an analog analyzer measures the cross-power spectral density, and then a digital computer performs the spatial Fourier transform.     

Formation of wave packets in the ion acoustic turbulence

Formation and propagation of wave packets are observed in a current-driven ion acoustic turbulence by the microwave scattering method. The packet size is approximately equal to the group velocity divided by the frequency spread on the dispersion curve.     

Renormalized perturbation theory for a multiplicative noise system

We study an anharmonic overdamped oscillator driven by both additive and multiplicative Gaussian white noise. Within the Martin-Siggia-Rose formalism we employ renormalized perturbation theory to calculate the stationary correlation function and the response function of the oscillator variable. Due to the absence of a simple fluctuation-dissipation theorem renormalization cannot make use of exact stationary moments, but is perormed with the help of renormalization conditions.     

Renormalized perturbation theory flow equations for the Anderson impurity model

We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values \(\tilde \mu = (\tilde \Delta ,\tilde U)\) of the hybridization Δ and Coulomb interaction U of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution of \(\tilde \mu = (\tilde \Delta )\) with Δ. By exploiting the fact that \(\tilde \mu = (\tilde \Delta )\) can be determined analytically in the limit Δ → ∞ we solve the flow equations numerically to obtain estimates for the renormalized parameters in the range 0 <U/πΔ< 3.5.     

Renormalized field theory of critical dynamics

We formulate a Gell'Mann-Low-type renormalization group approach to the critical dynamics of stochastic models described by Langevin or Fokker-Planck equations including mode-coupling terms.Dynamical correlation and response functions are expressed in terms of path integrals, which are investigated by well-known methods of renormalized perturbation theory.Dynamical scaling laws and relations between static and dynamic critical exponents are derived. The leading temperature-dependence of correlation and response functions is obtained from the Kadanoff-Wilson short-distance expansion. We also consider corrections to dynamic scaling which are due to a finite lattice constant.     

Renormalized field theory of dynamical percolation

The stochastic processes recently introduced by Grassberger and Cardy are shown to belong to the same universality class as dynamic percolation. To first order in =6–d, whered is the spatial dimensionality, known critical exponents of random percolation are rederived and the new dynamic exponent z=2–1/6+0(²) is calculated by use of the field-theoretic renormalization group method. The relation of the statistics of big clusters (animals) to the Yang-Lee edge singularity in random fields is presented.     

Renormalized perturbation theory of the Van der Pol oscillator

The renormalized perturbation expansion for the linewidth of the Van der Pol oscillator is extended to fifth order. The results of the previously obtained fourth order are thereby improved for pump strengthsa5. No indication of a breakdown of the expansion, even for strong pumping, is found.     

Renormalized Fokker-Planck equation for the problem of the beam-beam interaction in electron storage rings

It is shown that the beam-beam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron oscillations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the resonances, thus avoiding the problem of the divergent perturbative series which arises in the study of nonintegrable Hamiltonian systems. A “renormalized” Fokker-Planck equation is established which contains new diffusive terms corresponding to the presence of resonances. The solution of this equation is exhibited explicitly in a simplified case. This allows an analytical approach to the problem of the beam-beam instability, which sets an upper limit to the maximum attainable luminosity in storage rings.     

Renormalized kinetic theory of nonequilibrium many-particle classical systems

The far-from-equilibrium statistical dynamics of classical particle systems is formulated in terms of self-consistently determined phase-space density response, fluctuation, and vertex functions. Collective and single-particle effects are treated on an equal footing. Two approximations are discussed, one of which reduces to the Vlasov equation direct interaction approximation of Orszag and Kraichnan when terms that are explicitly due to particles are removed.Work performed under the auspices of the U.S. Department of Energy.     

Reflectionless potentials for the acoustic spectral problem

The classical acoustic spectral problem is considered, and the class of reflectionless potentials for this problem is constructed.     

Renormalized theory of magnetic field generation in resonance absorption

DC magnetic field generation in resonance absorption is studied, in a non-linear regime, when it becomes of sufficient order of magnitude to affect wave propagation, as well as electron-ion collisions or thermal dispersion do. It is shown that a simple expression obtained in the linear regime is still valid in the non-linear theory. Scaling laws are set up.     

Ion acoustic turbulence and anomolous transport

Theoretical interpretation of ion acoustic turbulence is shown to require the use of renormalized turbulence theory for calculating the turbulent spectra and transport coefficients. The physics of solitons, double layers, and ion phase space holes have an impact on the one-dimensional problem.     

Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D_T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter—the Mach number, M?1—the next approximation gives a larger contribution to D_T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D_T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green’s function of the problem. We include an additional term in the general formula for D_T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D_T=CM³u₀/p₀. The spectrum E(x) was assumed to be smooth at distances Δ x～M²?1.     

Scattering of ion beam by the current-driven ion wave turbulence

The effective scattering of an ion beam by the ion wave turbulence is investigated experimentally. The results are compared with the values predicted theoretically.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Transient vortex events in the initial value problem for turbulence

A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied. The coherent mechanism is characterized by locally transverse vortex configurations that are intrinsically helical in both physical and Fourier space when there is a peak of the maximum vorticity parallel omega parallel(infinity)(t). At no time are nonhelical, antiparallel vorticity elements observed. This event precedes the appearance of the traditional signatures of an energy cascade such as strong growth of the dissipation, spectra approaching -5/3, and strongly Beltramized vortex tubes. Comparing how different large-eddy simulations reproduce these properties demonstrates the importance of properly modeling nonlinear transport of both energy and helicity.