Yu P Bliokh, G S Nusinovich*, J Felsteiner, Y Carmel*, A G Shkvarunets*, J C Rodgers*, V L Granatstein* Physics Department, Technion-lsrael Institute of Technology Haifa, Israel *lnstitute for Research in Electronics and Applied Physics, University of Maryland College Park, MD, USA

Abstract – Plasma-assisted slow-wave oscillators (pa- sotrons) are unique sources of microwave radiation, in which beam propagation in the absence of external magnetic fields is provided by ion focusing and the electron interaction with the RF field is essentially two-dimensional

The nanne «Pasotron» is an acronynn for plasnna- assisted slow-wave oscillator [1] The pasotron utilizes the ion focusing nnechanisnn [2] for the beann transport in the absence of a guiding nnagnetic field The absence of solenoids nnakes the pasotron to be a connpact, lightweight nnicrowave source A schenne ofthe pasotron is presented in Fig 1 A plasnna e-gun is used as a beann source The electron beann ionizes the neutral gas which fills the channber, the beann space-charge field expels the plasnna electrons and the rennaining ions fornn a channel which partially connpensates the beann space charge and keeps the beann from radial divergence The beam excites an electromagnetic wave in a slow-wave structure (SWS) in the same manner as in conventional TWT or BWO tubes Typical parameters of the pasotron are the following: beam current 30- 120 A, voltage 40 – 55 kV, pulse duration 80 \^s, microwave power from 05 MW with efficiency 50 % to 1 MW with efficiency 30 %

Fig 1 Scheme of the pasotron

Let us consider at first the channel formation The chamber forms an equipotential surface and the beam creates inside the chamber a bath-shaped potential well Ions oscillate in the well and the most important are the axial oscillations [3] In our experiments the characteristic time required for the beam charge compensation is large compared with the period of these oscillations and ions have time to visit any point along the system independently of their birth place It means that an homogeneous ion channel is formed along the whole system even if the gas density is strongly inhomogeneous

In the pasotron the gas density, on the one hand, should be large enough in order to provide the beam transport On the other hand, the presence of the gas inside the SWS may cause a microwave breakdown These conflicting objectives have been satisfied using the above-mentioned effect ofthe ion motion The gas is concentrated mainly in the drift region and inside the SWS the gas pressure is some orders of magnitude smaller The measured gas pressure is shown in Fig 2 The right-hand scale shows the local neutralization time which is calculated using the local gas density The solid line marks the beam pulse duration, and the dashed line marks the measured time ofthe channel formation along all the system One can see that the local neutralization time in the SWS is longer that the pulse duration and only the axial motion of the ions can explain the channel formation along the whole system The calculated theoretically channel formation time (10 [^s) is in a good agreement with experiment The developed theory ofthe channel formation [3] allows us to explain two phenomena which are unusual for traditional microwave sources There are the hysteresis-like dependence of the on-axis current density on the beam current [4] and the dependence of the starting current of the microwave excitation on the beam current rise time [5]

Fig 2 Gas pressure distribution

Thus, the beam transport in pasotron is much richer in physical effects than the traditional method of beam transport in a guiding magnetic field The microwave excitation in the pasotron also looks unusual In contrast to a magnetically confined beam the beam particle motion in the pasotron is multi-dimensional in principle [6] The axial motion in the microwave field occurs in the same manner as in traditional devices and will not be considered here The radial motion is determined by the common action of the ion channel and the beam self-fields and the radial fields of the excited synchronous wave The profile of the resulting radial potential well depends on the wave phase Θ If the wave amplitude is small, the axially uniform potential well is slightly deformed by the wave fields Oscillating electrons fill this well and form a so-called phase-mixed beam [7] If the wave amplitude is large enough, the shape of the well is transformed drastically (Fig3) The radial field of the wave becomes stronger than the channel focusing field Depending on their phase, some electrons remain trapped by the well, while other electrons are ejected The electron bunch which is formed during the beam instability development is placed exactly in the last region of phases On the one hand, this radial motion increases the efficiency of the beam-wave energy exchange because the wave field is stronger near the SWS boundary On the other hand, the most «active» electrons, which form the bunch, are excluded from the process of wave excitation when they reach the chamber wall Under optimal conditions this happens when the wave amplitude reaches the saturation level The theoretical determination of these conditions [8] and their experimental realization allowed us to achieve 50 % efficiency of microwave excitation in the pasotron [9]

The next effect has an absolutely different nature but leads to similar consequences Let us consider the beam propagation in the ion channel in more detail The density of ions in the channel is proportional to the beam

Fig 3 Potential well for the large wave amplitude

density, n =         , where / is the space-charge com

pensation ratio The focusing force is proportional to the ion density, oc n = fn^ The defocusing force of the

beam space charge is partially compensated by the focusing action of the magnetic field of the beam current and the resulting defocusing force is proportional to

(here γ is the beam relativistic factor) Thus, the resulting radial force is proportional to

Under the beam instability development the longitudinally homogeneous beam splits up into bunches The beam density now depends on the wave phase Θ The ion density depends on the average beam density, n = f <        ,               therefore the focusing force is propor

tional to f <n^>. ks regard to the defocusing force, it

depends on the local beam density, that is on η^^φ) As a result, the total radial force appears as


The factor fr^-l in the second term is always small for a weakly relativistic beam It means that during the bunch formation the second term becomes larger than the first one and the focusing force changes into a defocusing one for the bunch electrons These electrons move out from the axis The longitudinal bunching continues and the electron motion along the wave phase and in the radial direction looks as it is shown in Fig 4 Fig 5 presents the beam electron trajectories in the presence of the excited wave During the beam instability development, practically all electrons are grouped into bunches and when these bunches reach the chamber

Fig 4 Electron trajectories along the wave phase and in the radial direction

wall the beam disappears Beyond the place where the beam reaches the wall, the wave amplitude does not change This is a specific nonlinear mechanism of the beam instability saturation in the pasotron The saturation amplitude does not depend on the input amplitude

Fig 5 Wave amplitude (top) and electron trajectories (bottom)

therefore the output amplitude also does not depend on the input amplitude The output amplitude does not depend on the SWS length All these unusual properties of the pasotron have been confirmed experimentally: the collector current disappears when microwave generation is started, and the contraction of the SWS does not affect the output microwave power

Fig 6 Pasotron spectrum in vicinity of the carrier

The presence of ions in microwave devices is the source of the so-called ion noise It seems natural to expect that the noise level in the pasotron should be very high Surprisingly, this is not the case The noise level in the pasotron is 50 dB below the carrier frequency (Fig

6)   [10] Eq (1) makes clear this phenomenon Because

of the smallness of the factor f/ – I, the second term becomes dominating early in the development of the beam instability It is easy to see that in this case the radial force does not depend on the ion density The ions do not affect the beam instability development and the role of the ion density fluctuations is strongly reduced


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[5]  Yu P Bliokh at a., Phys Rev E 70, 046501, 2004

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2000 T M Abu-elfadi etal, Phys Plasmas 10, 3746, 2003

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[8]  T M Abu-elfadi etal, IEEE Trans Plasma Sci 30, 1126, 2002

[9]  A G Shkvarunetsetal, Phys Plas Lett 9, 4114, 2002

[10]G S Nusinovich etal, IEEE Trans El Dev 52, 845, 2005

Джерело: Матеріали Міжнародної Кримської конференції «СВЧ-техніка і телекомунікаційні технології», 2006р