Wave topology in Hall magnetohydrodynamics.

Area of Science:

• Plasma physics
• Magnetohydrodynamics
• Wave phenomena

Background:

• Ideal magnetohydrodynamics (MHD) simplifies plasma behavior.
• Hall magnetohydrodynamics (HMHD) offers greater accuracy at smaller scales by including the Hall effect.
• A complete description of HMHD eigenmodes was previously lacking.

Purpose of the Study:

• To derive the complete spectrum and eigenvectors of Hall magnetohydrodynamics (HMHD) waves.
• To identify the topological structure of HMHD wave modes.
• To clarify the relationship between HMHD and ideal MHD wave spectra.

Main Methods:

• Derivation of HMHD wave spectrum and eigenvectors.
• Analysis of wave mode topology.
• Comparison with ideal MHD in the limit of vanishing Hall parameter.

Main Results:

• The HMHD wave spectrum consists of three branches: slow magnetosonic-Hall, shear Alfvén-Hall, and fast magnetosonic-Hall waves.
• These branches continuously reduce to ideal MHD counterparts as the Hall parameter approaches zero.
• HMHD wave structure exhibits nontrivial topology with a Weyl point and nonzero Chern numbers, unlike ideal MHD.

Conclusions:

• HMHD wave spectrum is homotopic to ideal MHD, with no additional branches.
• The key distinction lies in the topological properties of HMHD waves.
• The findings clarify the nature of wave propagation in Hall magnetohydrodynamics.