Rigidity (electromagnetism)
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In
particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
, rigidity R is a measure of the resistance of a particle to deflection by magnetic fields, defined as the particle's momentum divided by its charge. For a fully ionised nucleus moving at
relativistic speed Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models consider ...
, this is equivalent to the energy per atomic number. It is an important quantity in
accelerator physics Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams ...
and
astroparticle physics Astroparticle physics, also called particle astrophysics, is a branch of particle physics that studies elementary particles of astrophysical origin and their relation to astrophysics and cosmology. It is a relatively new field of research emergi ...
.


Definitions


Motion within a magnetic field

The concept of rigidity is derived from the motion of a charged particle within a
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
: two particles follow the same trajectory through a magnetic field if they have the same rigidity, even if they have different masses and charges. This situation arises in many
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies to contain them in well-defined particle beam, beams. Small accelerators are used for fundamental ...
and
particle detector In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing elementary particle, particles, such as t ...
designs. If a charged particle enters a uniform magnetic field, with the field orientated perpendicular to the initial velocity, the
Lorentz force In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...
accelerates the particle in the direction which is perpendicular to both the velocity and magnetic field vectors. The resulting
circular motion In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate ...
of the particle has a radius known as the gyroradius r_p. The rigidity is then defined as: R = B \times r_p where B is the magnetic field. In this definition, the units of rigidity ''R'' are tesla-metres (N·s/C).


Energy per unit charge

Alternatively, an entirely equivalent definition of rigidity is: R = where p is the momentum of the particle, c is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
, and q is the
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
of the particle. For a fully ionised atomic nucleus moving at relativistic speed, this simplifies to R = where E is the particle energy and Z is the
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
. In this case the units of rigidity ''R'' are
volts The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). Definition One volt is defined as the electric potential between two point ...
. This definition is often utilised in the study of
cosmic rays Cosmic rays or astroparticles are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar ...
, where the mass and charge of each particle is generally unknown.


Conversions

If the particle momentum p, is given in units of GeV/''c'', then the rigidity in tesla-metres is: = 3.3356 \text \times where the factor 3.3356 (which has units of seconds per metre) is 10^9 (
giga- Giga- ( or ) is a unit prefix in the metric system denoting a factor of a short-scale billion or long-scale milliard (109 or 1,000,000,000). It has the symbol G. ''Giga-'' is derived from the Greek word (''gígas''), meaning "giant". The ...
) divided by the speed of light in m/s.


References

Accelerator physics {{accelerator-stub