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Submitted on 1 Jan 1979
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NONLINEAR INTERACTION OF BEAM WAVES AND PLASMA WAVES
D. Wall, R. Franklin
To cite this version:
D. Wall, R. Franklin. NONLINEAR INTERACTION OF BEAM WAVES AND PLASMA WAVES.
Journal de Physique Colloques, 1979, 40 (C7), pp.C7-593-C7-594. �10.1051/jphyscol:19797287�. �jpa- 00219275�
JOURNAL DE PHYSIQUE CoZZoque C7, suppl6ment au n07, Tome 40, JuiZZet 1979, page C7- 593
NONLINEAR INTERACTION (3F BEAM WAVES AND PLASMA WAVES
D.N. wallx, R.N. ~ r a n k l i n ~ .
Department of Engineering Science, University o f Oxford.
For some time now the explosive nature of the the linear beam-plasma instability can be avoided a s three wave interaction in which a negative energy wave indicated in Fig. 1. This is due to the finite radial decays to two positive energy waves has been examined extent of plasma and beam. The instability could be theoretically 1
.
Experimental demonstrations in 'switched onf by operating at a sufficiently low beam plasmas, with one exception 2, have involved cyclotron speed but that regime was avoided in the work which waves 3,4 rather than non-magnetised plasma wave follows.modes. This paper describes measurements on an Attempts were made to observe the decay of a electron beam-plasma configuration demonstrating the beam to two plasma waves according to scheme underlying interaction but, because the experiment is b d
+c'
indicated in Fig. 1. However, the clarity5
carried out in space, and because the group velocities of earlier work on the scheme
&+f+
s involving a r e not all in the same direction, the interaction is not decay of electron waves to electron waves and ion one of indefinite growth in the first order approximation. waves could not he achieved. This was due to theThe experimental apparatus used was the Culham competing non-linear effect in which the beam wave single-ended Q-machine ARIADNE modified by the interacts with the beam electrons and excites sideband substitution of an electron gun assembly f o r the cold end instabilities of the beam wave 6
.
An observation of7 plate. This electron gun was part of a standard b -+
e
+ s has been reported recently.
travelling-wave-tube cathode with its helical wave Accordingly the measurements were restricted structure. The beam was extracted at a conventional to the mixing case in' which two waves were injected operating voltage and subsequently slowed down by an and a third observed. The resonant nature of the auxiliary electrode before injection into the plasma. process was demonstrated by fixing one freqiency and The plasma was formed in the usual manner in a varying the other to maximize the amplitude of the Q-machine and typical operating conditions were with a product wave. The process .was demonstrated to occur.
plasma frequency of 80MHz, the ions being potassium, with the injected waves both plasma waves and also for.
and the plasma column diameter 2.5 cm. The density the beam wave-plasma wave case.
of electrons within the system was measured and the In order to demonstrate frequency and wave beam diameter found to be approximately 2.5 mm. The matching the product wave frequency had to be beam density depended on the beam current and voltage identified and in a separate experiment under the same and could be varied up to one eighth of the plasma plasma conditions its wave length under linear
density. conditions was measured. A comprehensive s e t of
If the beam i s sufficiently fast and tenuous then
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797287
data obtained in this way i s shown a s Fig. 2, where the offset from the curve is a measure of frequency and wave number mismatch. To show the three-wave nature of the .process, the product wave amplitude was measured a s a function of the injected wave amplitude under fixed plasma conditions and wave frequencies.
Results given in Fig. 3 indicate that until other compet- ing non-linear effects intervene the product amplitude
f3
is proportional toIt should be remarked that the explosive scheme b -3 b' + & I T could not be observed in our experiment because the beam densities were not high enough nor the plasma length sufficient. Interactions were also observed in the low frequency spectrum. The waves concerned were excited by the presence of the electron beam and their frequency depended on the magnitude of the magnetic field confining the plasma column.
Comparison with other work suggests that these a r e 8
Bernstein waves excited by the E sc B drift of ions at the edge of the electron beam region. Certainly the data of Fig.4 is consistent with the dispersion of such waves being excited by a beam whose speed varied a s E/B, i. e
.
it increased with increasing electron beam density and decreased with increasing magnetic field.The work was greatly assisted by earlier exper- iments of and discussions with Dr. P . D. Edgley.
*Now at UKAEA, Winfrith Heath, Dorset.
+Now at The City University, London.
References.
1. Weiland, and Wilhelmsson, 1977 Coherent Nonlinear Interaction of Waves in Plasma (Pergamon)
2. Hopman, 1971 JCPIG X p.323 3 . Sugaya, et a1 1977 P.R.Litt. 39, 27 4. Sugaya, e t a1 1978 Phys.Lett. e A , 265.
5. Franklin, et a1 1971 ICPIG X p.324
6. van Wakeren, e t a1 1972 P.R.Lett. 28, 295
7. Kerst, e t a1 1979 Phys.Letts. 69A, 329 8. Yamada, M. et a1 1977 Phys. Fluids 20, 450.
0 . 2 0.4 0.6 0.8 1.0
wavenumber (cm-')
bunched plasm wave amplitud
reference signal (dB)
Z
-
field current (Amp)
