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Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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Magnetostatic Boundary Conditions01:28

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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Potential Due to a Magnetized Object01:24

Potential Due to a Magnetized Object

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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
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Paramagnetism01:30

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Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Relativistic Spin Magnetohydrodynamics.

Samapan Bhadury1, Wojciech Florkowski2, Amaresh Jaiswal1

  • 1School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Jatni-752050, India.

Physical Review Letters
|November 18, 2022
PubMed
Summary
This summary is machine-generated.

This study derives relativistic magnetohydrodynamics equations from kinetic theory for spin-1/2 particles. It reveals spin-magnetic field coupling at the gradient order, explaining phenomena like the Einstein-de Haas effect.

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Area of Science:

  • Plasma Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Relativistic kinetic theory describes particle behavior in extreme conditions.
  • Magnetohydrodynamics (MHD) models plasma dynamics under magnetic fields.
  • Spin-1/2 particles exhibit quantum mechanical spin, influencing their interactions.

Purpose of the Study:

  • To derive relativistic dissipative nonresistive magnetohydrodynamics equations.
  • To investigate the role of spin polarization in plasma dynamics.
  • To elucidate the emergence of spin-related physical effects from fundamental principles.

Main Methods:

  • Utilizing kinetic theory and the relativistic Boltzmann equation.
  • Employing a relaxation-time approximation for collision integrals.
  • Calculating nonequilibrium corrections to particle distribution functions.

Main Results:

  • Obtained equations for relativistic dissipative nonresistive magnetohydrodynamics in the small polarization limit.
  • Demonstrated the natural emergence of Einstein-de Haas and Barnett effects.
  • Identified spin-magnetic field coupling at the gradient order in hydrodynamic equations.

Conclusions:

  • The developed framework successfully links kinetic theory to macroscopic relativistic MHD.
  • Spin polarization plays a crucial role in the emergent transport properties of plasmas.
  • This work provides a new theoretical basis for understanding spin-dependent phenomena in relativistic plasmas.