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Major beam-wave instabilities

Cyclotron Resonant Maser (CRM) Instability

Cyclotron Auto-Resonant Maser (CARM) Instability

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Cyclotron Resonant Maser (CRM) Instability

CRM Instability

Figure A: Electrons gyrating (in the direction indicated by the magenta arrow) in a circular orbit, evenly distributed in azimuthal position, interact with an electric field (red arrow) which rotates in the same direction.

Figure B: After a few rotations, a phase bunch forms

Figure C: If the detuning is chosen correctly, deceleration occurs

This interaction occurs between a gyrating electron beam and an RF wave of a similar frequency. The interaction can in many cases be simplified further by considering only the component of the RF electric field which is in the plane of the gyration of the electron orbit (a good approximation if the interaction occurs in a waveguide whose axis is parallel to the electron drift motion and with a TE mode close to cut-off). The action of the RF field on the electrons causes them to become bunched due to the dependence of the electron gyrofrequency on the relativistic mass (electrons which are decelerated increase in gyrofrequency and advance in phase, those which are accelerated decrease in gyrofrequency and retard in phase).

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Of course at this point the space charge of the bunch becomes critical, electrons which are ACCELERATED away from the bunch increase in energy and orbital radius but decrease in gyrofrequency, and those which are DECELERATED away from the bunch experience the opposite effect. Therefore the action of space charge forces repelling electrons away from the spatial bunch actually enhances the bunch formation in angular terms. So far no energy has been extracted from the electron beam, and the action of the radiation has accelerated half of the electrons and decelerated the other half. If however the radiation frequency slightly exceeds the gyrofrequency (called detuning) then the electron bunch formed by the aforementioned process slips naturally into decelerating phase and energy extraction is possible. Ultimately the efficiency limit is defined by the effect called 'phase trapping'. After some amount of energy is extracted from the beam, the electrons gyrofrequency increases above the radiation field frequency culminating in the electrons swinging into accelerating phase with respect to the radiation field and extracting energy back from the radiation. Efficiencies ~40% are attainable in practice, and the interaction is only weakly dependent on the electron velocity spread. In plasma physics terminology the instability may be described as a resonance between an electromagnetic wave and the negative energy (fast) cyclotron mode of the electron beam.

Cyclotron AutoResonant Maser (CARM) Instability

The CARM instability is very similar to the CRM instability, indeed it consists of the same physical mechanism, but with the interaction occurring at a high group velocity, ~c, we must consider also the effect of the magnetic field components of the radiation. This significantly complicates the interaction, as energy may now be extracted from both the transverse (gyro) and axial (drift) components of the beam's momentum. No longer is a neat angular or spatial bunch formed, however the beam spreads out in space such that it forms a 'phase bunch' if the phase of each electron is measured WRT the local phase of the radiation. The reason it is classified separately from the CRM instability is a special efficiency enhancement predicted by the theory, if the interaction occurs at a velocity of '~c', then the detuning of the beam due to the radiation as it extracts the energy from the transverse and axial components of motion are just such that they exactly cancel. This means that if the beam and the wave are in favourable phase for energy extraction then they remain locked in that phase throughout the interaction.... no phase trapping occurs, hence 'autoresonant'. Unfortunately this interaction mode is extremely sensitive to the electron velocity spread, and high efficiencies have been experimentally elusive.

Cherenkov Interaction

If one uses some technique to reduce the radiation phase velocity below the speed of light (typically by using a corrugated metal wall or dielectric wall liner in a waveguide situation) then one can observe an interaction between radiation and a rectilinear electron beam. In this case the axial electric field component of an electromagnetic wave is coupled to the axial electron motion, causing the formation of space charge bunches in the electron beam. If the phase velocity of the radiation is slightly lower than the beam drift velocity then we have matched the radiation onto the negative energy (slow) space-charge mode of the beam. The electrons move into decelerating phase with respect to the wave and they lose energy, amplifying the wave. Ultimately the electrons will revert into accelerating phase after sufficient energy has been extracted to drop their drift velocity below the radiation phase velocity. At this point the interaction has passed its peak in efficiency and the system is said to be 'phase trapped'. Very high efficiencies may be attained >40%.

Superradiance

If an interaction occurs between a short pulse of radiation and electron beam of some duration, new parameters must be considered. Of primary importance is the differential group velocities of the electron beam and radiation pulse, the 'slippage velocity'. Due to this slippage, the radiation 'sees' different electrons as time evolves, which has implications for saturation behaviour. As the slippage velocity can be chosen to be such that the beam elements and radiation pulse spatially decouple from each other as the interaction approaches saturation, then the interaction saturates only when the total number of electrons has been exhausted. Interestingly, because in a waveguide situation the slippage velocity is a strong function of the radiation frequency, and the growth rate is greatest for a particular slippage velocity that just matches the above condition of decoupling as the interaction approaches saturation, then the interaction can grow from noise with the optimum frequency for energy extraction being auto-selected as a function of the beam and waveguide parameters. The growth behaviour is soliton-like, with the radiation pulse increasing in peak power and total energy, but decreasing in duration as the energy extraction proceeds. In addition the output power should scale as the square of the number of electrons in the interaction, considerably greater than the 4/3 scaling typical of a 'normal' saturated regime of operation.

This idea has considerable potential for applications. The power scaling being less significant than the short pulse high power nature of the output signal. Because the pulse amplitude grows as the duration shrinks, the pulse has a very rich frequency content. Applications for this radiation range widely, though non-linear material testing and also high resolution plasma diagnostics are of particular interest.