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29 Gyroradius

Published: 2016/02/26

Channel: John Weiss

04B Small Gyroradius Expansion | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

GYRORADIUS - HOW TO PRONOUNCE IT!?

Published: 2017/02/18

Channel: WordBox

Gyroradius

Published: 2016/01/22

Channel: WikiAudio

Cyclotron - Gyroradius

Published: 2014/01/08

Channel: Ben Wehunt

How to Pronounce Gyroradius

Published: 2015/08/13

Channel: Emma Saying

How to Pronounce Gyroradius

Published: 2015/03/07

Channel: Pronunciation Guide

How to pronounce Gyroradius

Published: 2016/01/02

Channel: How to pronounce

Week 1, Online Lecture 2: Orbits in Magnetic Fields II

Published: 2014/03/30

Channel: Physics 1C

Gusti Wolf

Published: 2016/01/22

Channel: WikiAudio

Gustav Diessl

Published: 2016/01/22

Channel: WikiAudio

28 Right Hand Rule

Published: 2016/02/26

Channel: John Weiss

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Published: 2016/01/22

Channel: WikiAudio

30 Solenoids

Published: 2016/02/27

Channel: John Weiss

27 Meters

Published: 2016/02/24

Channel: John Weiss

04A Orbits In E-B Fields | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

Magnetic mirror - Video Learning - WizScience.com

Published: 2015/09/17

Channel: Wiz Science™

27 RC Circuits

Published: 2016/02/24

Channel: John Weiss

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Published: 2015/09/10

Channel: Wiz Science™

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Published: 2012/04/04

Channel: fletchac

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Published: 2007/10/09

Channel: GoogleTechTalks

1e Particle motion in given electromagnetic fields: the drifts

Published: 2015/09/15

Channel: Plasma Physics and Applications

Gusti Huber

Published: 2016/01/22

Channel: WikiAudio

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Published: 2016/11/28

Channel: psimanjuntak

Gustav Kirchhoff

Published: 2016/01/22

Channel: WikiAudio

"Introduction to Plasma Astrophysics I" - Eliot Quataert

Published: 2016/07/19

Channel: Institute for Advanced Study

30 Ampere's Law

Published: 2016/02/27

Channel: John Weiss

Frontiers of Radiative...Magnetic Reconnection - Dmitri A. Uzdensky

Published: 2016/10/12

Channel: Institute for Advanced Study

29 Magnetic Force on a Wire

Published: 2016/02/26

Channel: John Weiss

03A Single Particle Orbits | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

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Published: 2014/01/08

Channel: Ben Wehunt

02A Criteria For Plasma State | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

BECLOGGING - HOW TO PRONOUNCE IT!?

Published: 2017/02/18

Channel: WordBox

DNUOS - HOW TO PRONOUNCE IT!?

Published: 2017/02/18

Channel: WordBox

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Published: 2014/03/31

Channel: Kenny Townsend

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Published: 2016/08/29

Channel: English Communicator

28B Magnetic Mirrors | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

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Published: 2017/06/08

Channel: Lucius Fox

28 Magnetic Force

Published: 2016/02/24

Channel: John Weiss

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Published: 2014/01/07

Channel: Ben Wehunt

05A Particle Bounce-Drift Motions | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

27B Fusion History | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

27A Controlled Fusion | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

SPREADSHEAT - HOW TO PRONOUNCE IT!?

Published: 2017/02/18

Channel: WordBox

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Published: 2016/10/23

Channel: Clear English

28A Inertial Magnetic Fusion | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

26B Plasma Turbulence | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

Electron

Published: 2014/07/21

Channel: Audiopedia

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Published: 2011/11/01

Channel: David Osipyan

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Published: 2015/08/13

Channel: Emma Saying

From Wikipedia, the free encyclopedia

The **gyroradius** (also known as **radius of gyration**, **Larmor radius** or **cyclotron radius**) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the gyroradius is given by

where is the mass of the particle, is the component of the velocity perpendicular to the direction of the magnetic field, is the electric charge of the particle, and is the strength of the magnetic field.^{[1]}

The angular frequency of this circular motion is known as the **gyrofrequency**, or **cyclotron frequency**, and can be expressed as

in units of radians/second.^{[1]}

It is often useful to give the gyrofrequency a sign with the definition

or express it in units of Hertz with

- .

For electrons, this frequency can be reduced to

- .

In cgs units, the gyroradius is given by

and the gyrofrequency is

- ,

where is the speed of light in vacuum.

For relativistic particles the Lorentz factor must be included:

- .

For calculations in accelerator and astroparticle physics, the formula for the gyroradius can be rearranged to give

- ,

where is the speed of light, is the unit of Giga-electronVolts, and is the elementary charge.

If the charged particle is moving, then it will experience a Lorentz force given by

- ,

where is the velocity vector and is the magnetic field vector.

Notice that the direction of the force is given by the cross product of the velocity and magnetic field. Thus, the Lorentz force will always act perpendicular to the direction of motion, causing the particle to gyrate, or move in a circle. The radius of this circle, , can be determined by equating the magnitude of the Lorentz force to the centripetal force as

- .

Rearranging, the gyroradius can be expressed as

- .

Thus, the gyroradius is directly proportional to the particle mass and perpendicular velocity, while it is inversely proportional to the particle electric charge and the magnetic field strength. The time it takes the particle to complete one revolution, called the period, can be calculated to be

- .

Since the period is the reciprocal of the frequency we have found

and therefore

- .

- ^
^{a}^{b}Chen, Francis F. (1983).*Introduction to Plasma Physics and Controlled Fusion, Vol. 1: Plasma Physics, 2nd ed*. New York, NY USA: Plenum Press. p. 20. ISBN 0-306-41332-9.

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