Turbulence Mode Decomposition and Anisotropy in Magnetically Dominated Collisionless Plasmas

Abstract: We use the 3D fully kinetic simulation to study different turbulence modes and turbulence anisotropy of relativistic turbulence in magnetically dominated collisionless plasmas. We extend the method developed by Cho & Lazarian (2002) for decomposing non-relativistic magnetohydrodynamic (MHD) turbulence into Alfvén, fast, and slow modes to the regime of collisionless plasmas. We find that Alfvén and slow modes are anisotropic, following the Goldreich & Sridhar (1995) scaling, while fast modes are isotropic. We observe a larger kinetic energy fraction of fast modes compared to that in the non-relativistic MHD turbulence, suggesting a stronger coupling of Alfvén and fast modes in relativistic magnetized turbulence in collisionless plasmas. We further examine the dynamic alignment and find a weaker scale dependence of the alignment angle than previously proposed. The dominant thermal fluctuations in the kinetic range can cause flattening of the turbulent velocity structure function and weakening of the turbulence anisotropy and dynamic alignment near the kinetic scales.

• The paper extends turbulence mode decomposition techniques from non-relativistic MHD to relativistic, collisionless pair plasmas using high-resolution 3D PIC simulations.
• It reveals a strong energetic coupling between Alfvén and fast modes, with the kinetic simulation showing a more than twofold increase in fast mode energy relative to MHD.
• Weak dynamic alignment and reduced anisotropy at sub-electron scales highlight the limitations of traditional turbulence theories in magnetically dominated collisionless regimes.

Turbulence Mode Decomposition and Anisotropy in Magnetically Dominated Collisionless Plasmas

Introduction

The paper "Turbulence Mode Decomposition and Anisotropy in Magnetically Dominated Collisionless Plasmas" (2604.20963) presents a detailed investigation of turbulence in relativistic, magnetically dominated, collisionless pair plasmas using fully kinetic 3D particle-in-cell (PIC) simulations. The work systematically extends the seminal mode decomposition techniques, previously developed for non-relativistic MHD turbulence, into the kinetic and relativistic regimes. The principal focus is on characterizing the anisotropy, spectral properties, and mode couplings—especially the partitioning and interactions among Alfvén, slow, and fast modes—and understanding the scale dependence of dynamic alignment and its impact on turbulence structure and energy cascade.

Simulation Framework

A rigorous computational strategy underpins the analysis. The authors employ a high-resolution 3D PIC simulation (RUNKO) for relativistic, strongly magnetized, weakly collisional pair plasma, with physical parameters $\sigma_0=10$, $\Theta_0=0.3$, and post-heating $\beta\approx0.3$. This regime simulates turbulence where the Alfvén speed $v_A$ approaches $c$ and the plasma is magnetically dominated, mirroring many high-energy astrophysical environments. For comparative context, an isothermal MHD simulation is performed using AthenaK; this baseline is crucial for isolating kinetic/relativistic effects. Both simulations achieve extended inertial ranges, and turbulence is driven solenoidally in MHD and magnetically in the PIC case.

Structure Functions and Turbulence Anisotropy

A second-order velocity structure function analysis is deployed, leveraging the local magnetic field reference frame to capture anisotropies with respect to the instantaneous topology of the field. The results reinforce that, in both MHD and PIC cases, the inertial range turbulence adheres to the predictions of Goldreich-Sridhar ($SF_v(r_\perp)\propto r^{2/3}$, $SF_v(r_\parallel)\propto r^1$). However, the PIC simulations exhibit systematically weaker anisotropy, especially as the kinetic (dissipation) range is approached. Unlike the sharp spectral steepening due to numerical dissipation in MHD, the PIC system transitions to flattened spectra at sub-electron skin-depth scales, a direct consequence of thermal fluctuations generated by collisionless plasma heating.

Mode Decomposition: Alfvén, Slow, and Fast Modes

The authors successfully implement the Cho-Lazarian (CL02) formalism for mode decomposition in the kinetic regime. For both models, Alfvén and slow modes display strong anisotropy in the inertial range, whereas fast modes remain isotropic across all scales. A notable quantitative distinction arises in the PIC simulation: the kinetic energy fraction in fast modes ($f_f \approx 0.27$) is more than twice that in the MHD simulation ($f_f \approx 0.11$), with a corresponding reduction in the Alfvén mode fraction. This demonstrates a strong energetic coupling between Alfvén and fast modes in relativistic and kinetic plasma turbulence, in contradiction to the weak coupling observed in non-relativistic MHD and previously postulated by incompressible turbulence theory. The observed slope of the fast mode structure function in the PIC case is also shallower, suggesting mode interactions modified by kinetic dynamics and enhanced compressibility effects.

Polarization Alignment and Scale-Dependent Anisotropy

The theory of polarization dynamic alignment (Boldyrev 2006) posits that velocity and magnetic field fluctuations become increasingly aligned at smaller scales, leading to modified inertial range slopes and enhanced perpendicular anisotropy. The present results reveal that polarization alignment is weak in both PIC and MHD, with the scale-dependent alignment slope $\alpha$ remaining significantly below the theoretical value of $\Theta_0=0.3$0. In MHD, alignment increases with decreasing scale but saturates near $\Theta_0=0.3$1; in the PIC system, alignment is rapidly destroyed in the kinetic range and can even transition to negative $\Theta_0=0.3$2, indicating dominant thermal fluctuations and breakdown of fluid-theoretic alignment concepts due to strong kinetic effects. The results show limited alignment near the driving scales and an absence of substantial perpendicular anisotropy in the kinetic regime.

Theoretical and Practical Implications

The findings necessitate a reexamination of the applicability of non-relativistic MHD turbulence phenomenology to relativistic, collisionless plasma systems. In particular:

• Energetic coupling between Alfvén and fast modes: The enhanced energy transfer and non-negligible fast mode content in PIC turbulence imply that compressible mode interactions cannot be neglected in modeling transport, cascade, and dissipation in astrophysical environments where kinetic effects are important.
• Limitation of dynamic alignment: The observed weak alignment and its suppression by thermal fluctuations highlight the constraints of scale-dependent alignment as a universal paradigm, especially in collisionless, high-$\Theta_0=0.3$3 plasmas.
• Kinetic effects overwrite fluid-scale anisotropy: The reduction of anisotropy at sub-inertial scales signifies the importance of kinetic dissipation and may impact theoretical models of particle transport, heating, and acceleration by turbulence in environments such as pulsar wind nebulae and accretion disk coronae.

The results also call for new or extended turbulence theories that incorporate kinetic physics, relativistic compressibility, and feedback from nonthermal particle populations.

Conclusion

This study provides a high-fidelity analysis of turbulence mode decomposition and anisotropy in magnetically dominated, collisionless plasmas via fully kinetic simulation. The key outcomes are the robust observation of strong coupling between Alfvén and fast modes in the relativistic collisionless regime and the identification of relatively weak or absent dynamic alignment at inertial and kinetic scales compared to MHD predictions. The numerical framework and analysis techniques presented here set a foundation for further investigations, particularly at higher resolution and across a wider span of plasma parameters, to explore convergence in alignment scaling and the role of driving and plasma conditions. The results have direct implications for the modeling of astrophysical turbulence and for interpreting high-resolution kinetic observations in laboratory and space plasmas.

Future directions should include systematic parameter studies covering plasma $\Theta_0=0.3$4, magnetization, and driving mechanisms, combined with comprehensive analyses of the impact on transport coefficients, dissipative heating rates, and nonthermal particle acceleration. Ultimately, a kinetic theory of turbulence tailored for high-energy astrophysical plasmas must account for these findings.