In
accelerator physics, shunt impedance is a measure of the strength with which an
eigenmode of a resonant
radio frequency
Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
structure (e.g., in a
microwave cavity) interacts with charged particles on a given straight line, typically along the axis of rotational symmetry. If not specified further, the term is likely to refer to ''longitudinal effective shunt impedance''.
Longitudinal shunt impedance
To produce longitudinal
Coulomb force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
s which add up to the (longitudinal)
acceleration voltage , an eigenmode of the resonator has to be excited, leading to power dissipation
. The definition of the longitudinal effective shunt impedance,
, then reads:
:
with the longitudinal effective
acceleration voltage .
The time-independent shunt impedance,
, with the time-independent
acceleration voltage is defined:
:
One can use the
quality factor
In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
to substitute
with an equivalent expression:
:
where W is the maximum energy stored. Since the quality factor is the only quantity in the right equation term that depends on wall properties, the quantity
is often used to design
cavities
Cavity may refer to:
Biology and healthcare
*Body cavity, a fluid-filled space in many animals where organs typically develop
**Gastrovascular cavity, the primary organ of digestion and circulation in cnidarians and flatworms
*Dental cavity or too ...
, omitting material properties at first (see also
cavity geometry factor).
Transverse shunt impedance
When a particle is deflected in transverse direction, the definition of the shunt impedance can be used with substitution of the (longitudinal) acceleration voltage by the transverse effective
acceleration voltage, taking into account transversal Coulomb ''and''
Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
s.
:
This does not necessarily imply a change in particle energy since a particle can also be deflected by magnetic fields (see
Panofsky-Wenzel theorem).
Polarization angle
Because the transverse deflection can be described with polar coordinates, one may define a deflection or polarization angle using the transverse
acceleration voltage components. Polar coordinates are used because it is possible to add up voltage components like vectors, but not shunt impedances.
References
{{Reflist
Accelerator physics