[Paper Review] Current driven kink instabilities in relativistic jets: dissipation properties

G. Bodo, G. Mamatsashvili+2 more|arXiv (Cornell University)|Nov 29, 2021

Astrophysics and Cosmic Phenomena34 references16 citations

TL;DR

This study investigates current-driven kink instabilities in relativistic, highly magnetized plasma jets, focusing on magnetic energy dissipation via thin current sheets. Using relativistic MHD simulations, it finds that dissipation occurs in two stages—initial peak during helicoidal sheet formation, followed by weaker turbulence—with total dissipated energy independent of numerical dissipation, and strongly dependent on equilibrium pitch profile, axial magnetic field, and magnetization.

ABSTRACT

We analyze the evolution of current driven kink instabilities of a highly magnetized relativistic plasma column, focusing in particular on its dissipation properties. The instability evolution leads to the formation of thin current sheets where the magnetic energy is dissipated. We find that the total amount of dissipated magnetic energy is independent of the dissipation properties. Dissipation occurs in two stages: a peak when the instability saturates, which is characterized by the formation of a helicoidal current sheet at the boundary of the deformed plasma column, followed by a weaker almost flat phase, in which turbulence develops. The detailed properties of these two phases depend on the equilibrium configuration and other parameters, in particular on the steepness of the pitch radial profile, on the presence of an external axial magnetic field and on the amount of magnetization. These results are relevant for high energy astrophysical sources, since current sheets can be the sites of magnetic reconnection where particles can be accelerated to relativistic energies and give rise to the observed radiation.

Motivation & Objective

• Understand the dissipation mechanisms of magnetic energy in relativistic jets driven by current-driven kink instabilities.
• Investigate how equilibrium configuration—particularly pitch profile and axial magnetic field—impacts dissipation efficiency and turbulence evolution.
• Quantify the role of magnetization and radial field structure in determining energy conversion and particle acceleration potential.
• Characterize the two-stage dissipation process: initial peak from helicoidal current sheets and subsequent weaker turbulent phase.
• Assess the implications for particle acceleration and polarization in high-energy astrophysical sources like blazars and GRBs.

Proposed method

• Numerical simulations using ideal relativistic magnetohydrodynamics (RMHD) equations with a γ-law and Taub-Matthews equation of state.
• Simulations initialized with force-free equilibrium configurations: Type I (Bodo et al. 2013) and Type II (Mizuno et al. 2009), varying pitch profile and axial field presence.
• Employed high-resolution adaptive mesh refinement to resolve thin current sheets and turbulence development.
• Tracked magnetic energy conversion into kinetic and thermal energy, and analyzed mode-resolved energy spectra.
• Compared cases with varying magnetization (σ), pitch steepness, and external axial field to isolate parameter effects.
• Used normalized magnetic energy and wavenumber-integrated energy spectra to quantify dissipation rates and timescales.

Experimental results

Research questions

• RQ1 How does the total magnetic energy dissipation depend on numerical dissipation properties in relativistic kink instability evolution?
• RQ2 What are the distinct phases of energy dissipation, and how do their durations and strengths depend on equilibrium configuration?
• RQ3 How do the pitch profile and presence of an external axial magnetic field influence the efficiency and morphology of current sheet formation?
• RQ4 What is the role of magnetization in determining the total energy conversion and the evolution of turbulence?
• RQ5 How do the magnetic field structures in the two dissipation phases affect the polarization properties of emitted radiation?

Key findings

• The total amount of dissipated magnetic energy is independent of numerical dissipation properties, indicating that energy release is governed by large-scale dynamics rather than resolution-dependent diffusion.
• Dissipation occurs in two distinct phases: a sharp peak at instability saturation due to helicoidal current sheet formation, followed by a prolonged, weaker phase dominated by turbulent current sheets.
• The Ref case (steep pitch profile with vanishing external Bz) shows the highest fraction of magnetic energy converted into thermal and kinetic energy, outperforming shallower and external-field cases.
• Higher magnetization increases both the total available energy and the dissipation efficiency, with current sheets forming in progressively lower magnetization regions during evolution.
• Turbulence persistence varies: it lasts until the final simulation time (t = 500) in the Ref case, decays faster in Eq2, and dies out rapidly in PitchHi, suggesting different degrees of relaxation.
• The transition from ordered helicoidal sheets to disordered turbulence implies a shift from high to low polarization in emitted radiation, with implications for observational signatures.