Microwave cavity

A microwave cavity or radio frequency cavity (RF cavity) is a special type of resonator, consisting of a closed (or largely closed) metal structure that confines electromagnetic fields in the microwave or RF region of the spectrum. The structure is either hollow or filled with dielectric material. The microwaves bounce back and forth between the walls of the cavity. At the cavity's resonant frequencies they reinforce to form standing waves in the cavity. Therefore, the cavity functions similarly to an organ pipe or sound box in a musical instrument, oscillating preferentially at a series of frequencies, its resonant frequencies. Thus it can act as a bandpass filter, allowing microwaves of a particular frequency to pass while blocking microwaves at nearby frequencies. A microwave cavity acts similarly to a resonant circuit with extremely low loss at its frequency of operation, resulting in quality factors (Q factors) up to the order of 106, for copper cavities, compared to 102 for circuits made with separate inductors and capacitors at the same frequency. For superconducting cavities, quality factors up to the order of 1010 are possible. They are used in place of resonant circuits at microwave frequencies, since at these frequencies discrete resonant circuits cannot be built because the values of inductance and capacitance needed are too low. They are used in oscillators and transmitters to create microwave signals, as filters to separate a signal at a given frequency from other signals, wavemeter or frequency meter, Echo Box for pulsed radars to generate artificial targets and to measure the spectrum and transmit frequency, and in microwave relay stations, satellite communications, and microwave ovens. RF cavities can also manipulate charged particles passing through them by application of acceleration voltage and are thus used in particle accelerators and microwave vacuum tubes such as klystrons and magnetrons.

Theory of operation

Most resonant cavities are made from closed (or short-circuited) sections of waveguide or high-permittivity dielectric material (see dielectric resonator). Electric and magnetic energy is stored in the cavity. This energy decays over time due to several possible loss mechanisms. The section on 'Physics of SRF cavities' in the article on superconducting radio frequency contains a number of important and useful expressions which apply to any microwave cavity: The energy stored in the cavity is given by the integral of field energy density over its volume,

U = μ 0 2 ∫ | H → | 2 d V {\displaystyle U={\frac {\mu _{0}}{2}}\int {|{\overrightarrow {H}}|^{2}dV}} , where:

H is the magnetic field in the cavity and μ0 is the permeability of free space. The power dissipated due just to the resistivity of the cavity's walls is given by the integral of resistive wall losses over its surface,

P d = R s 2 ∫ | H → | 2 d S {\displaystyle P_{d}={\frac {R_{s}}{2}}\int {|{\overrightarrow {H}}|^{2}dS}} , where:

Rs is the surface resistance. For copper cavities operating near room temperature, Rs is simply determined by the empirically measured bulk electrical conductivity σ see Ramo et al pp.288-289

R s n o r m a l = ω μ 0 2 σ {\displaystyle R_{s\ normal}={\sqrt {\frac {\omega \mu _{0}}{2\sigma }}}} . A resonator's quality factor is defined by

Q o = ω U P d {\displaystyle Q_{o}={\frac {\omega U}{P_{d}}}} , where:

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