In a resonant cavity, power may be dissipated both in the materials enclosed within resonator, usually dielectrics, as well as over the walls. It is possible therefore to respectively measure the complex permittivity of the dielectrics and/or the surface resistance of the conductors forming the walls of the resonant cavity.
In certain situations, since these characteristics are liable to vary as a function of the stored energy it is necessary to measure the quality factor Q0 at different electromagnetic field amplitudes. In the case of superconducting resonant cavities, used for example to accelerate particle beams, the measurement of Q0 as a function of the accelerating gradient (electric field) up to the sudden transition from a superconducting material to the normal conduction state (known as “quench”) represents a characterization that is indispensable.
In certain situations these measurements of the quality factor Q0 may become impractical due to the occurrence of resonant electron discharge phenomena, in particular during the phase of storage of energy in the resonant cavity, also known as the filling phase, during which the resonant cavity gradually stores up energy.
The resonant electron discharge (or “multipactor”) phenomenon in structures under vacuum at high frequency has been known since 1936 and is described in particular in the document by J. M. R. Vaughan, “Multipactor”, IEEE transaction on electron devices, vol. 35, no. 7, 1988.
The source of resonant electron discharge lies in the ability of a metallic or dielectric surface to emit one or more electrons, known as secondary electrons, when struck by an incident electron whose kinetic energy is within a particular range which will vary according to the material, typically between 0.1 and 1 kV. This phenomenon is random in nature and is defined by a statistical yield known as the secondary emission coefficient. Thus resonant electron discharge can only occur when the secondary emission coefficient is greater than 1. In addition, further conditions must also be fulfilled for resonant electron discharge to be maintained in the cavity.
In order to understand the problem posed by the resonant electronic discharge phenomenon during the characterization of the quality factor Q0 of a low-loss high-frequency resonant cavity, the method for measurement of the unloaded quality factor and its constraints must be recalled.
The principle involves “filling” the resonant cavity with energy using a power generator. Once the steady-state has been achieved, the incident power is cut-off and is resonant cavity is left to empty itself. The output signal and the damping time are then measured, allowing the quality factor Q0 to be calculated.
In order to carry out such measurements, the cavity is connected to two ports: an input port (called the incident port) and an output port (called the transmitted port). These ports are in general physically made up of a coaxial antenna which is introduced to a varying depth within the cavity. Each port is characterized by a coupling coefficient βe defined as the ratio Q0/Qe where Qe is the external quality factor associated with the port.
The external quality factor Qe is defined as the ratio of the energy stored to the power dissipated across the port, multiplied by the pulsatance ω0 (also called the angular frequency) at resonance. Consequently the incident and transmitted ports are respectively characterized by a coupling coefficient βi and βt, associated with a quality factor Qi and Qt.
Thus the system in its entirety, formed by the resonant cavity connected to the antennae, exhibits an overall quality factor QL under load where the power dissipated by the system is the sum of dissipations of the materials of the cavity and of the ports. The result, therefore, is the following relationship:
      1          Q      L        =            1              Q        0              +          1              Q        i              +          1              Q        t            
The quality factor under load QL is measured through the decrease over time of the transmitted power Pt which obeys the following relationship:Pt=Pt0e−t/τ
where τ is the damping time for the cavity, which is reciprocally equivalent to the filling time for the cavity.
In practice, the transmitted port coupling is chosen to be very small, that is, the quality factor Qt is very large in comparison with Q0 so that it can be neglected for the determination of the unloaded quality factor Q0, such that:Q0≈(1+βi)QL 
In addition it is known that at resonance of the cavity, the coupling coefficient of the incident port βi is given by:
      β    i    =            2      η        -          1      ±                                                  (                                                2                  η                                -                1                            )                        2                    -          1                    where η is the ratio P/Pi where P and Pi represent the absorbed power and incident power respectively.
The absorbed power is obtained from the difference between the incident power and the reflected power, measured via a directional coupler. The transmitted power can be neglected due to the very low coupling coefficient βt being chosen.
In practice, the incident coupling coefficient βi is chosen to be close to 1 (so called critical coupling condition) to minimize the power reflected by the cavity and also to maximise the power absorbed by the cavity, in order to obtain a maximum amount of stored energy, i.e. for example the maximum of the accelerating gradient for an accelerating cavity, for a given power supplied by the generator. Under these conditions then, the cavity filling time can become very long in comparison with the priming time for the resonant electron discharge. This favours conditions under which resonant electronic discharge occurs.
Although the electromagnetic field in the cavity increases with time during filling, this variation remains very small, consequently preserving the resonance conditions which allow the discharge to be primed and/or be maintained during the filling phase.
In order to resolve this problem, all that is required is to choose a very large incident coupling coefficient βi in order to reduce the filling time and thus prevent the stable conditions for secondary electronic emissions being established.
However, by doing this the relative error in the unloaded quality factor measurement, which is directly proportional to the incident coupling coefficient βi, becomes very large and incompatible with the desired measurement precision.
In the absence of the ability to ensure rapid filling of the cavity, various solutions have been implemented in order to attempt to overcome the resonant electron discharge phenomenon.
A first solution involves carrying out numerical simulations in order to anticipate the conditions under which resonant electron discharges occur and to geometrically modify the cavity in order to eliminate shapes which are liable to favour the occurrence of resonant electron discharges.
A second solution involves modifying the secondary emission coefficient by treating the internal surfaces of the cavity with the deposition of a thin layer or by chemical treatment.
A third solution involves applying a static magnetic or electric field where this is possible, in order to overcome the resonance conditions.
These solutions, however, introduce constraints and are only applicable during the design phase of the cavities, and are consequently not applicable to already existing cavities.
Once a resonant cavity has been constructed, there is a known process of “breaking in” the internal surfaces of the cavity during the discharge in the hope of modifying the secondary emission coefficient. In effect, as a consequence of repeated impacts by electrons, “braking in” results in desorption from the surfaces, which can modify the secondary emission coefficient.
In the case of superconducting cavities in which the very low temperatures favour the adsorption of residual gas molecules, breaking-in often takes several hours to overcome a single barrier and sometimes does not work. In this case it is still possible to carry out a heating and cooling cycle on the resonant cavity which lasts at least a day.
USPTO Backgrounds
USPTO Backgrounds