Non-abelian Plasma Instabilities Research Articles

Unstable dynamics of Yang-Mills fields at early times of heavy ion collisions

The quark gluon plasma as produced in heavy ion collisions is exposed to early anisotropies in momentum space due to its rapid expansion. Such anisotropies can lead to non-abelian plasma instabilities, driven by unstable gluonic modes that grow exponentially fast. These plasma instabilities can be simulated using a discretized version of gauge-covariant Boltzmann-Vlasov and Yang-Mills equations. In the non-expanding case, a turbulence cascade forms, which is associated with an approximately linear growth of energy in collective fields. Early longitudinal expansion slows down the growth of unstable modes, and the formation of soft gluonic fields depends crucially on the initial conditions assumed.

Instabilities of an anisotropically expanding non-Abelian plasma:3D+3Vdiscretized hard-loop simulations

We study the (3+1)-dimensional evolution of non-Abelian plasma instabilities in the presence of a longitudinally expanding background of hard particles using the discretized hard loop framework. The free streaming background dynamically generates a momentum-space anisotropic distribution which is unstable to the rapid growth of chromomagnetic and chromoelectric fields. These fields produce longitudinal pressure that works to isotropize the system. Extrapolating our results to energies probed in ultrarelativistic heavy-ion collisions we find, however, that a pressure anisotropy persists for a few fm/c. In addition, on time scales relevant to heavy-ion collisions we observe continued growth of plasma instabilities in the strongly non-Abelian regime. Finally, we find that the longitudinal energy spectrum is well-described by a Boltzmann distribution with increasing temperature at intermediate time scales.

Perturbative and non-perturbative Kolmogorov turbulence in a gluon plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.

Non-Abelian plasma instabilities: SU(3) versus SU(2)

We present the first $3+1$ dimensional simulations of non-Abelian plasma instabilities in gauge-covariant Boltzmann-Vlasov equations for the QCD gauge group SU(3) as well as for SU(4) and SU(5). The real-time evolution of instabilities for a plasma with stationary momentum-space anisotropy is studied using a hard-loop effective theory that is discretized in the velocities of hard particles. We find that the numerically less expensive calculations using the group SU(2) essentially reproduce the nonperturbative dynamics of non-Abelian plasma instabilities with higher rank gauge groups provided the mass parameters of the corresponding hard-loop effective theories are the same. In particular, we find very similar spectra for the turbulent cascade that forms in the strong-field regime, which is associated with an approximately linear growth of energy in collective fields. The magnitude of the linear growth however turns out to increase with the number of colors.

Collective modes and instabilities in anisotropically expanding ultrarelativistic plasmas

The time evolution of collective modes in an expanding ultrarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semianalytically by means of integrodifferential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully $3+1$ dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces drastically the lower bound on the delay in the onset of growth that was found previously by considering only collective gauge fields as seeds. This makes it appear much more likely that non-Abelian plasma instabilities seeded by small initial rapidity fluctuations could play an important role in the early stage of heavy-ion collisions at LHC energies.

Non-Abelian Plasma Instabilities in Nuclear Collisions(Current Topics)

Non-Abelian Plasma Instabilities in Nuclear Collisions(Current Topics)

Nonabelian plasma instabilities in Bjorken expansion

Plasma instabilities are parametrically the dominant nonequilibrium dynamics of a weakly coupled quark-gluon plasma. In recent years the time evolution of the corresponding collective colour fields has been studied in stationary anisotropic situations. Here I report on recent numerical results on the time evolution of the most unstable modes in a longitudinally expanding plasma as they grow from small rapidity fluctuations to amplitudes where non-Abelian self-interactions become important.

Instabilities of an anisotropically expanding non-Abelian plasma:1D+3Vdiscretized hard-loop simulations

Non-Abelian plasma instabilities play a crucial role in the nonequilibrium dynamics of a weakly coupled quark-gluon plasma, and they importantly modify the standard perturbative bottom-up thermalization scenario in heavy-ion collisions. Using the auxiliary-field formulation of the hard-loop effective theory, we study numerically the real-time evolution of instabilities in an anisotropic collisionless Yang-Mills plasma undergoing longitudinal free-streaming expansion. In this first real-time lattice simulation we consider the most unstable modes, long-wavelength coherent color fields that are constant in transverse directions and which therefore are effectively 1+1 dimensional in space-time, except for the auxiliary fields which also depend on discretized momentum rapidity and transverse velocity components. We reproduce the semianalytical results obtained previously for the Abelian regime, and we determine the nonlinear effects which occur when the instabilities have grown such that non-Abelian interactions become important.

Lessons from non-Abelian plasma instabilities in two spatial dimensions

Plasma instabilities can play a fundamental role in quark-gluon plasma equilibration in the high energy (weak coupling) limit. Early simulations of the evolution of plasma instabilities in non-Abelian gauge theory, performed in one spatial dimension, found behavior qualitatively similar to traditional QED plasmas. Later simulations of the fully three-dimensional theory found different behavior, unlike traditional QED plasmas. To shed light on the origin of this difference, we study the intermediate case of two spatial dimensions. Depending on how the 'two-dimensional' theory is formulated, we can obtain either behavior.

Non-Abelian plasma instabilities for extreme anisotropy

Thermalization of quark-gluon plasmas in heavy-ion collisions is a difficult theoretical problem. One theoretical goal has been to understand the physics of thermalization in the relatively simplifying limit of arbitrarily high energy collisions, where the running coupling ${\ensuremath{\alpha}}_{\mathrm{s}}$ is weak. One of the current roadblocks to achieving this goal is lack of knowledge about the behavior of plasma instabilities when particle distributions are highly anisotropic. In particular, it has not been known how the magnetic fields generated by plasma instabilities scale with anisotropy. In this paper, we use numerical simulations in a first attempt to determine this scaling.

Non-abelian plasma instabilities for strong anisotropy

We numerically investigate gauge field instabilities in anisotropic SU(2) plasmas using weak field initial conditions. The growth of unstable modes is stopped by non-abelian effects for moderate anisotropy. If we increase the anisotropy the growth continues beyond the non-abelian saturation bound. We find strong indications that the continued growth is not due to over-saturation of infrared field modes, but instead due to very rapid growth of high momentum modes which are not unstable in the weak field limit. The saturation amplitude strongly depends on the initial conditions. For strong initial fields we do not observe the sustained growth.

Turbulent spectrum created by non-Abelian plasma instabilities

Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the Kolmogorov spectrum for turbulence in hydrodynamics or for energy cascades in other systems. In this paper, we theoretically analyze processes responsible for this cascade and find a steady-state spectrum f_k ~ k^-2, where f_k is the phase-space density of particles with momentum k. The exponent -2 is consistent with results from numerical simulations. We also discuss implications of the emerging picture of instability development on the "bottom-up" thermalization scenario for (extremely high energy) heavy ion collisions, emphasizing fundamental questions that remain to be answered.

Dynamics of quark-gluon-plasma instabilities in discretized hard-loop approximation

Non-abelian plasma instabilities have been proposed as a possible explanation for fast isotropization of the quark-gluon plasma produced in relativistic heavy-ion colli- sions. We study the real-time evolution of these instabilities in non-abelian plasmas with a momentum-space anisotropy using a hard-loop effective theory that is discretized in the velocities of hard particles. We extend our previous results on the evolution of the most un- stable modes, which are constant in directions transverse to the direction of anisotropy, from gauge group SU(2) to SU(3). We also present first full 3+1-dimensional simulation results based on velocity-discretized hard loops. In contrast to the effectively 1+1-dimensional transversely constant modes we find subexponential behavior at late times.

Fate of non-Abelian plasma instabilities in3+1dimensions

Plasma instabilities can play a fundamental role in plasma equilibration. There are similarities and differences between plasma instabilities in Abelian and non-Abelian gauge theories. In particular, it has been an open question whether non-Abelian self-interactions are the limiting factor in the growth of non-Abelian plasma instabilities. We study this problem with 3+1 dimensional numerical simulations. We find that non-Abelian plasma instabilities behave very differently from Abelian ones once they grow to be nonperturbatively large, in contrast with earlier results of 1+1 dimensional simulations. In particular, they grow more slowly at late times, with linear rather than exponential dependence of magnetic energy on time.

Hard-Loop Dynamics of Non-Abelian Plasma Instabilities

Non-Abelian plasma instabilities may be responsible for the fast apparent quark-gluon thermalization in relativistic heavy-ion collisions if their exponential growth is not hindered by nonlinearities. We study numerically the real-time evolution of instabilities in an anisotropic non-Abelian plasma with an SU(2) gauge group in the hard-loop approximation. We find exponential growth of non-Abelian plasma instabilities both in the linear and in the strongly nonlinear regimes, with only a brief phase of subexponential behavior in between.

Apparent Thermalization due to Plasma Instabilities in the Quark-Gluon Plasma

Hydrodynamical modeling of heavy-ion collisions at RHIC suggests that the quark-gluon plasma (QGP) "thermalizes" in a remarkably short time scale, about 0.6 fm/c. We argue that this should be viewed as indicating fast isotropization, but not necessarily complete thermalization, of the nonequilibrium QGP. Non-Abelian plasma instabilities can drive local isotropization of an anisotropic QGP on a time scale which is faster than ordinary perturbative scattering processes. As a result, we argue that theoretical expectations based on weak-coupling analysis are not necessarily in conflict with hydrodynamic modeling of the early part of RHIC collisions, provided one recognizes the key role of non-Abelian plasma instabilities.