Larmor precession

(electromagnetism) A common rotation superposed upon the motion of a system of charged particles, all having the same ration of charge to mass, by a magnetic field.

A precession in a magnetic field of the motion of charged particles or of particles possessing magnetic moments.

The Larmor theorem states that, for electrons moving in a single central field of force, the motion in a uniform magnetic field H is, to first order in H, the same as a possible motion in the absence of H except for the superposition of a common precession of angular frequency given by Eq. (1).
1.
Here e/c is the magnitude of the electronic charge in electromagnetic units, and m is the electronic mass. The frequency ω_L is called the Larmor frequency and is numerically equal to 2π times 1.40 MHz per oersted or 2π times 111 MHz per SI unit of magnetic field strength (ampere-turn per meter). See also Precession.

In stating the Larmor theorem, use was made of the phrase “a possible motion.” If H is applied sufficiently slowly, it can be proved that the motion is the same as in the absence of H, except for the superposition of the Larmor precession. However, a sudden application of H may change, for example, a circular orbit into an elliptical one.

According to elementary electromagnetic theory, a current loop of area A and of current I possesses a magnetic moment μ of magnitude IA and of direction normal to the loop. Thus an electron moving in a circular orbit has an orbital magnetic moment.

The electron also has orbital angular momentum, which by quantum theory must equal ℏJ, where J is an integer and ℏ is Planck's constant h divided by 2π. In terms of the equivalent magnetic moment, Eq. (1) may be written in the form of Eq. (2).
2.
In this form the Larmor precession is exhibited by any magnetic moment μ including magnetic moments associated with spin angular momentum as well as those associated with orbital angular momentum. In this form the Larmor precession applies to experiments in molecular beams, electron paramagnetic resonance (EPR), and nuclear magnetic resonance (NMR). See also Angular momentum; Electron paramagnetic resonance (EPR) spectroscopy; Electron spin; Magnetic resonance.

In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moments of electrons, atomic nuclei, and atoms about an external magnetic field. The magnetic field exerts a torque on the magnetic moment,

where is the torque, is the magnetic dipole moment, is the angular momentum vector, is the external magnetic field, is the cross product, and is the gyromagnetic ratio which gives the proportionality constant between the magnetic moment and the angular momentum. The angular momentum vector precesses about the external field axis with an angular frequency known as the Larmor frequency,

ω = − γB

where ω is the angular frequency,^[1] is the gyromagnetic ratio, and B is the magnitude of the magnetic field^[2] and g is the g-factor (normally 1, except for in quantum physics).

A famous 1935 paper published by Lev Landau and Evgeny Lifshitz predicted the existence of ferromagnetic resonance of the Larmor precession, which was verified experimentally and independently by J. H. E. Griffiths (UK) and E. K. Zavoiskij (USSR) in 1946.

Larmor precession is important in nuclear magnetic resonance, electron paramagnetic resonance and muon spin resonance.

To calculate the spin of a particle in a magnetic field, one must also take into account Thomas precession.

See also

• Rabi cycle
• Georgia State University HyperPhysics page on Larmor Frequency

Notes

1. ^ Spin Dynamics, Malcolm H. Levitt, Wiley, 2001
2. ^ http://books.google.com/books?id=1J2hzvX2Xh8C&pg=PA192&lpg=PA192&dq=Larmor's+Theorem&source=bl&ots=AWrslwM4Iw&sig=Pc_sZdUja2NZm0RvRUbRjAEH6eA&hl=en&ei=oAhcSuisApCy8AT9yZXVDQ&sa=X&oi=book_result&ct=result&resnum=2

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