Chandrasekhar number

Chandrasekhar number
Name	Chandrasekhar number
Related	Rayleigh number, Prandtl number, Ekman number

Chandrasekhar number The Chandrasekhar number is a dimensionless parameter that measures the relative importance of magnetic forces to viscous forces in magnetohydrodynamic flows; it connects classical problems studied by Subrahmanyan Chandrasekhar with theoretical work in Hartmann number-like regimes and stability analyses used by researchers at institutions such as Princeton University, University of Cambridge, and University of Chicago. It appears in stability criteria developed alongside investigations into phenomena observed in experiments at facilities like the Max Planck Institute for Plasma Physics, Lawrence Livermore National Laboratory, and in astrophysical contexts studied at the Harvard–Smithsonian Center for Astrophysics, California Institute of Technology, and Kavli Institute for Theoretical Physics. The parameter is central to linear stability studies that link the work of Eugene N. Parker, Hannes Alfvén, and Lord Kelvin on magnetic fluids and buoyancy.

Definition and physical significance

The Chandrasekhar number quantifies the ratio of the Lorentz force to viscous force in a conducting fluid and is used to assess magnetic damping in convective and shear flows examined in analyses by Subrahmanyan Chandrasekhar, Edward Lorentz (physicist), and researchers at Imperial College London. It is significant in determining the onset of magnetically modified instabilities in configurations considered by S. A. Balbus, John W. Miles, and laboratories such as Culham Centre for Fusion Energy. In astrophysics, it helps connect magnetoconvection treatments applied to the Sun, Jupiter, and accretion discs around objects studied at European Southern Observatory and Royal Astronomical Society-linked programs. In engineering contexts, it guides interpretation of experiments at the Paul Scherrer Institute, Oak Ridge National Laboratory, and industrial studies influenced by Siemens-era magnetofluid research.

Mathematical formulation

The Chandrasekhar number is commonly expressed in nondimensional form as Q = (B0^2 d^2)/(μ ρ ν η) for a characteristic magnetic field B0, length scale d, magnetic permeability μ, density ρ, kinematic viscosity ν, and magnetic diffusivity η; variants of this expression appear in treatments by Subrahmanyan Chandrasekhar, E. P. Grossmann, and derivations taught at Massachusetts Institute of Technology and University of Oxford. In linear stability equations derived in monographs by S. Chandrasekhar and extended by authors affiliated with Princeton Plasma Physics Laboratory and École Polytechnique, Q multiplies terms arising from the curl of the Lorentz force and appears alongside dimensionless groups like the Prandtl number and Rayleigh number. In spectral analyses used by researchers at Los Alamos National Laboratory and National Center for Atmospheric Research, Q determines eigenvalue separation and modifies neutral stability curves originally computed by teams at University of California, Berkeley and Yale University.

Applications in magnetohydrodynamics

The Chandrasekhar number is applied in studies of magnetoconvection in stellar interiors addressed by groups at Max Planck Institute for Astrophysics and Institute of Astronomy, Cambridge, in terrestrial dynamo modeling pursued at University of Leeds and University of Maryland, and in laboratory magnetohydrodynamics experiments at Johns Hopkins University and Dresden University of Technology. It is used in stability thresholds for the magnetorotational instability examined by S. A. Balbus and James M. Stone, in analysis of Hartmann flows investigated at École Normale Supérieure and Technische Universität München, and in modeling of liquid metal blankets in fusion reactor studies at ITER and EUROfusion. The parameter also appears in numerical simulations produced by teams at Princeton University, Stanford University, and Argonne National Laboratory that explore transitional regimes between laminar and magnetically influenced turbulence.

Derivation and scaling analysis

Derivations of the Chandrasekhar number follow nondimensionalization of the incompressible magnetohydrodynamic equations first assembled in the theoretical program of Subrahmanyan Chandrasekhar and elaborated by researchers at University of Cambridge and Heidelberg University. Balancing the Lorentz term B0^2/(μ ρ d) against viscous diffusion ν/d^2 yields the scaling that defines Q; this approach mirrors techniques used by G. I. Taylor, L. D. Landau, and courses at University of Chicago and Columbia University. Asymptotic analyses performed in the tradition of Sir Geoffrey Taylor and modern treatments by groups at Harvard University produce limiting forms that relate Q to combinations of the Hartmann number and magnetic Reynolds number used in dynamo theory efforts at Imperial College London and University of Cambridge.

Typical values and examples

Typical Chandrasekhar numbers vary widely: laboratory liquid-metal experiments reported by teams at INEEL and Wendelstein 7-X-related collaborations may have Q in the range 10^2–10^6, while astrophysical settings like solar convection zones discussed at National Solar Observatory and Space Telescope Science Institute can correspond to vastly larger effective Q when using large-scale field estimates referenced by Cambridge University Press texts. Numerical studies from Los Alamos National Laboratory, Princeton and Max Planck Institute for Solar System Research demonstrate parameter sweeps across many orders of magnitude to map stability boundaries comparable to those first charted by Subrahmanyan Chandrasekhar.

Related dimensionless numbers

The Chandrasekhar number is often presented alongside the Hartmann number, Magnetic Reynolds number, Reynolds number, Prandtl number, and Rayleigh number in textbooks and reviews from Cambridge University Press and Springer Nature; these groups include scientists from University of Texas at Austin, University of Oslo, and University of Tokyo. Comparative studies by researchers at CERN-adjacent institutes and national laboratories clarify regimes where Q dominates or is subordinate to other nondimensional groups in magnetohydrodynamics and dynamo theory.

Category:Magnetohydrodynamics