[Paper Review] Magnetohydrodynamic equations for cold quark gluon plasmas: Multi fluidity and Solitary wave stability

Azam Ghaani, Kurosh Javidan|arXiv (Cornell University)|Dec 29, 2017

High-Energy Particle Collisions Research3 references3 citations

TL;DR

This paper derives a multi-fluid magnetohydrodynamic (MHD) model for cold quark-gluon plasmas (QGP) using the reductive perturbation method, showing that small-amplitude perturbations lead to stable solitary waves governed by a modified derivative nonlinear Schrödinger (mDNLS) equation rather than the KdV equation. The inclusion of a background magnetic field stabilizes these waves, which exhibit field-strength-dependent width and velocity, indicating robust solitonic behavior in dense astrophysical environments like neutron stars.

ABSTRACT

By means of magnetohydrodynamic equations in a non relativistic multi fluid framework, we study the behavior of small amplitude perturbations in cold Quark Gluon Plasmas (QGP). Magnetohydrodynamic equations, along with the QGP equation of state are expanded using the reductive perturbation method. It is shown that such a medium should be considered as multi fluid magnetohydrodynamic (MHD) system. The result is a nonlinear wave equation which complies with a modified form of the "derivative nonlinear Schrodinger" equation instead of the KdV equation. We show that the complete set of equations, by considering the magnetic field which is supported by the Maxwell's equations, create stable solitary waves. An interesting result is the existence of an electric field component along the direction of magnetic field which causes charge separability in the medium. Properties of this solitonic solution is studied by considering different values for the QGP characters such as background mass density and strength of the magnetic field (at the scale of compact stars).

Motivation & Objective

• To model cold quark-gluon plasmas (QGP) as a multi-fluid magnetohydrodynamic (MHD) system under strong magnetic fields.
• To investigate the collective behavior of small-amplitude perturbations in cold QGP using the reductive perturbation method (RPM).
• To determine whether solitonic wave solutions emerge in such media and how their properties depend on background mass density and magnetic field strength.
• To assess the stability of solitary waves in cold QGP when electromagnetic effects are included, particularly the role of the magnetic field in suppressing wave breaking.

Proposed method

• Formulate a non-relativistic two-fluid MHD model for cold QGP, treating up and down quarks as separate fluids.
• Incorporate the MIT bag model equation of state (EOS) to describe the thermodynamic properties of the QGP medium.
• Apply the reductive perturbation method (RPM) to the coupled MHD equations to derive a reduced nonlinear wave equation for small-amplitude perturbations.
• Derive a modified derivative nonlinear Schrödinger (mDNLS) equation governing transverse magnetic field and mass density perturbations.
• Use Maxwell’s equations to self-consistently include electromagnetic fields, particularly the electric field component parallel to the magnetic field.
• Numerically simulate wave evolution to analyze soliton width, amplitude, phase speed, and stability under varying background parameters.

Experimental results

Research questions

• RQ1 Does the inclusion of a strong background magnetic field stabilize solitary waves in cold QGP, preventing wave breaking seen in KdV-type models?
• RQ2 What is the governing nonlinear wave equation for small-amplitude perturbations in cold QGP when multi-fluid and electromagnetic effects are included?
• RQ3 How do the soliton’s width, amplitude, and phase speed depend on the background mass density and magnetic field strength?
• RQ4 What role does the electric field component along the magnetic field play in charge separability and wave dynamics?
• RQ5 Can stable solitonic solutions emerge in cold QGP without relying on weak higher-order derivative terms in the energy density?

Key findings

• Solitary waves in cold QGP are governed by a modified derivative nonlinear Schrödinger (mDNLS) equation, not the KdV equation, indicating fundamentally different soliton dynamics.
• The presence of a background magnetic field stabilizes solitary waves, preventing the wave breaking typically seen in KdV-type models.
• Soliton phase speed increases with increasing magnetic field strength, while it decreases with increasing background mass density.
• The width of the solitary wave decreases as the magnetic field strength increases, but remains relatively insensitive to changes in mass density.
• The amplitude of the solitary wave is only weakly affected by variations in the magnetic field, indicating robustness under field fluctuations.
• An electric field component parallel to the magnetic field emerges, enabling charge separability in the medium, which is a novel feature of the multi-fluid MHD model.