Multipactor effect
Encyclopedia
The multipactor effect is a phenomenon in radio frequency
(RF) amplifier
vacuum tube
s and waveguide
s, where, under certain conditions, secondary electron
emission in resonance with an alternating electric field leads to exponential electron multiplication, possibly damaging and even destroying the RF device.
(or near vacuum) via an electron avalanche
caused by secondary electron emission. The impact of an electron to a surface can, depending on its energy and angle, release one or more secondary electrons
into the vacuum. These electrons can then be accelerated by the RF fields and impact with the same or another surface. Should the impact energies, number of electrons released and timing of the impacts be such that a sustained multiplication of the number of electrons occurs, the phenomenon can grow exponentially and may lead to operational problems of the RF system such as damage of RF components or loss/distortion of the RF signal.
between electron flight time and rf field cycle is a mechanism for multipactor development.
The existence of multipactor is dependent on the following three conditions being met: The average number of electrons released is greater than or equal to one per incident electron (this is dependent on the secondary electron yield of the surface) and the time taken by the electron to travel from the surface from which it was released to the surface it impacts with is an integer multiple of one half of the RF period and the average secondary electron yield is greater than or equal to one.
, distance or gap between the surfaces
, angular frequency of the RF field
, peak plate to plate RF voltage
, peak electric field between the surfaces, equal to 
/
.
The RF voltage varies sinusoidally. Consider the time at which the voltage at electrode A passes through 0 and starts to become negative. Assuming that there is at least 1 free electron near A, that electron will begin to accelerate to the right toward electrode B. It will continue to accelerate and reach a maximum velocity ½ of a cycle later just as the voltage at electrode B begins to become negative. If the electron(s) from electrode A strike electrode B at this time and produce additional free electrons, these new free electrons will begin to accelerate toward electrode A. The process may then repeat causing multipactor. We now find the relationship between the plate spacing, RF frequency, and RF voltage that causes the strongest multipactor resonance.
Consider a point in time at which electrons have just collided with electrode A at position d/2. The electric field is at zero and is beginning to point to the left so that the newly freed electrons are accelerated toward the right. Newton’s equation of motion of the free electrons is
The solution to this differential equation is
where we’ve assumed that when the electrons initially leave the electrode they have zero velocity. We know that resonance happens if the electrons arrive at the rightmost electrode after one half of the period of the RF field,
. Plugging this into our solution for 
we get
Rearranging and using the frequency
instead of the angular frequency gives
.
The product
is called the frequency-gap product. Keep in mind that this equation is a criterion for greatest amount of resonance, but multipactor can still occur when this equation is not satisfied.
Multipactor was identified and studied in 1934 by Philo T. Farnsworth, the inventor of electronic television, who attempted to take advantage of it as an amplifier. More commonly nowadays, it has become an obstacle to be avoided for normal operation of particle accelerators, vacuum electronics, radars, satellite communication devices, and so forth. A novel form of multipactor has been proposed (Kishek, 1998), and subsequently experimentally observed, in which charging of a dielectric
surface considerably changes the dynamics of the multipactor discharge.
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
(RF) amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...
s and waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
s, where, under certain conditions, secondary electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
emission in resonance with an alternating electric field leads to exponential electron multiplication, possibly damaging and even destroying the RF device.
Description
The multipactor effect occurs when electrons accelerated by radio-frequency (RF) fields are self-sustained in a vacuumVacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
(or near vacuum) via an electron avalanche
Electron avalanche
An electron avalanche is a process in which a number of free electrons in a medium are subjected to strong acceleration by an electric field, ionizing the medium's atoms by collision , thereby forming "new" electrons to undergo the same process in successive cycles...
caused by secondary electron emission. The impact of an electron to a surface can, depending on its energy and angle, release one or more secondary electrons
Secondary electrons
Secondary electrons are electrons generated as ionization products. They are called 'secondary' because they are generated by other radiation . This radiation can be in the form of ions, electrons, or photons with sufficiently high energy, i.e. exceeding the ionization potential...
into the vacuum. These electrons can then be accelerated by the RF fields and impact with the same or another surface. Should the impact energies, number of electrons released and timing of the impacts be such that a sustained multiplication of the number of electrons occurs, the phenomenon can grow exponentially and may lead to operational problems of the RF system such as damage of RF components or loss/distortion of the RF signal.
Mechanism
The mechanism of multipactor depends on the orientation of an RF electric field with respect to the surface. There are two types of multipactor: two-surface multipactor on metals and single-surface multipactor on dielectrics.Two-surface multipactor on metals
This is a multipactor effect that occurs in the gap between metallic electrodes. Often, an RF electric field is normal to the surface. A resonanceResonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
between electron flight time and rf field cycle is a mechanism for multipactor development.
The existence of multipactor is dependent on the following three conditions being met: The average number of electrons released is greater than or equal to one per incident electron (this is dependent on the secondary electron yield of the surface) and the time taken by the electron to travel from the surface from which it was released to the surface it impacts with is an integer multiple of one half of the RF period and the average secondary electron yield is greater than or equal to one.
Single-surface multipactor on dielectrics
This is a multipactor effect that occurs on a dielectric surface. Often, an RF electric field is parallel to the surface. The positive charge accumulated on the dielectric surface returns electrons back to the surface. A single surface multipactor event is also possible on a metallic surface in the presence of a crossed static magnetic field.Frequency-Gap Product in Two Surface Multipactor
The conditions under which multipactor will occur in two surface multipactor can be described by a quantity called the frequency-gap product. Consider a two surface setup with the following definitions:, distance or gap between the surfaces, angular frequency of the RF field, peak plate to plate RF voltage, peak electric field between the surfaces, equal to /.The RF voltage varies sinusoidally. Consider the time at which the voltage at electrode A passes through 0 and starts to become negative. Assuming that there is at least 1 free electron near A, that electron will begin to accelerate to the right toward electrode B. It will continue to accelerate and reach a maximum velocity ½ of a cycle later just as the voltage at electrode B begins to become negative. If the electron(s) from electrode A strike electrode B at this time and produce additional free electrons, these new free electrons will begin to accelerate toward electrode A. The process may then repeat causing multipactor. We now find the relationship between the plate spacing, RF frequency, and RF voltage that causes the strongest multipactor resonance.
Consider a point in time at which electrons have just collided with electrode A at position d/2. The electric field is at zero and is beginning to point to the left so that the newly freed electrons are accelerated toward the right. Newton’s equation of motion of the free electrons is
The solution to this differential equation is
where we’ve assumed that when the electrons initially leave the electrode they have zero velocity. We know that resonance happens if the electrons arrive at the rightmost electrode after one half of the period of the RF field,
. Plugging this into our solution for we getRearranging and using the frequency
instead of the angular frequency gives.The product
is called the frequency-gap product. Keep in mind that this equation is a criterion for greatest amount of resonance, but multipactor can still occur when this equation is not satisfied.History
This phenomenon was first observed by the French physicist Camille Gutton, in 1924, at Nancy.Multipactor was identified and studied in 1934 by Philo T. Farnsworth, the inventor of electronic television, who attempted to take advantage of it as an amplifier. More commonly nowadays, it has become an obstacle to be avoided for normal operation of particle accelerators, vacuum electronics, radars, satellite communication devices, and so forth. A novel form of multipactor has been proposed (Kishek, 1998), and subsequently experimentally observed, in which charging of a dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
surface considerably changes the dynamics of the multipactor discharge.