One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet.

Area of Science:

• Plasma Physics
• Magnetohydrodynamics
• Computational Physics

Background:

• The Harris sheet is a fundamental model in plasma physics, maintained by pressure gradients.
• Nonlinear force-free equilibria are crucial for understanding magnetic phenomena but are challenging to derive.
• Existing models often rely on pressure balance, limiting their applicability.

Purpose of the Study:

• To present the first nonlinear force-free Vlasov-Maxwell equilibrium.
• To introduce a novel method for finding such equilibria.
• To explore the transition between pressure-balanced and force-free states.

Main Methods:

• Utilizing an analogy between Vlasov-Maxwell equilibria and pseudoparticle motion in a conservative potential.
• Developing a nonlinear force-free solution.
• Generalizing the solution to a family of equilibria.

Main Results:

• A nonlinear force-free Vlasov-Maxwell equilibrium is derived.
• Magnetic shear, not pressure gradients, maintains force balance.
• Plasma pressure and density remain constant within the equilibrium.

Conclusions:

• The presented force-free solution offers a new perspective on magnetic equilibria.
• This work bridges the gap between pressure-balanced and force-free Harris sheet models.
• The methodology can be extended to a broader class of plasma equilibria.