EXPERIMENTAL FROM

STUDY

A RELATIVISTIC

MAGNETIC Yu. and

OF

THE

MICROWAVE

ELECTRON

BEAM

RADIATION

IN A S T R O N G

FIELD I. Abrashitov, K. I . M e k l e r

S.

D. K o r o v i n ,

UDC 533.9.07

The r e s u l t s are given of an e x p e r i m e n t a l study of the microwave radiation f r o m a powerful r e l ativistic electron beam in a longitudinal magnetic field. The design and the c h a r a c t e r i s t i c s of the bandpass microwave filters used in the analysis of the radiation s p e c t r a are described. Rad i a t i o n s p e c t r a h a v e b e e n obtained for different values of magnetic field. It is shown that the obs e r v e d radiation is in fact c y c l o t r o n radiation f r o m the beam. The r e a s o n s for the high r a d i a tion intensity are discussed.

It has been r e p o r t e d [1-3] that powerful microwave radiation is produced when a beam p a s s e s through a vacuum in a magnetic field. In this paper we study the s p e c t r u m of this radiation. The experiments were c a r r i e d out on the "Inar" apparatus. A 1 - M e V e l e c t r o n b e a m with a c u r r e n t of 10 kA and a d i a m e t e r of 2.5 cm was injected into the drift c h a m b e r along a s t r o n g magnetic field H = 3 - 1 2 kOe. The length of the c h a m b e r was 230 cm, the d i a m e t e r 11 cm, and the r e s i d u a l p r e s s u r e 10 -8 m m Hg. The diode c u r r e n t reached 10 kA but as a result of e l e c t r o static s u p p r e s s i o n [n the space charge the c u r r e n t in the drift c h a m b e r did not exceed 3 kA (in our g e o m e t r y this value c o r r e s p o n d s to the c r i t i c a l c u r r e n t ) . In contrast to [1, 2], the beam was injected into a glass c h a m b e r placed in a homogeneous magnetic field r a t h e r than into a specially shaped waveguide. The m i c r o w a v e radiation s p e c t r a were analyzed by means of bandpass filters. Figure I is a d i a g r a m of the e x p e r i m e n t a l apparatus, of one microwave channel, and of the r e c o r d [ n g unit. The radiation received by the horn antenna (A) is fed to the filter input along an extended waveguide through the directional coupler (DC) which acts as a stepwise attenuator. The filter consists of two cutoff waveguides (CW-1 and CW-2), two matched loads (ML), and a double T-junction (DT). The first cutoff waveguide p a s s e s frequencies above f~ = o/2al~ where a~ is the width of the wider wall of the waveguide. The part of the s p e c t r u m which is p a s s e d through this waveguide goes to the double T - p i e c e . Here the signal is divided, half of the power being absorbed by ML-1 and the other half being fed to CW-2 in which the width of the wider wall a 2 is s m a l l e r than a~. Frequencies f >f2=c/a2 are absorbed by ML-2 and the frequencies fl
I 301

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L

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I ""

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r

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Fig. 1 -dB i I0"

p/~J dB 60-20-

30-

\ 1~ f, GHz

4020-

0

Fig, 2

r a t u s te eliminate e l e c t r o m a g n e t i c detectors.

Fig. 3

noise and the effect of x - r a y radiation en the s e m i e o n d u c t o r m i c r o w a v e

Strong radiation was r e c o r d e d e v e r ~he e n t i r e frequency range of 8-35 GHz. It can be s e e n f r o m Fig. 3, that for a fixed value of the m a g n e t i c f i e l d t h e radiation s p e c t r u m h a s a c l e a r l y defined m a x i m u m . As the m a g netic field is i n c r e a s e d this m a x i m u m shifts t o w a r d s higher f r e q u e n c i e s , and t h e r e is a l i n e a r r e l a t i o n s h i p between the frequency fmax and the value of the field (within the limits of e x p e r i m e n t a l e r r o r ) . The cyclotron frequency of a r e l a t i v i s t i c e l e c t r o n in a l a b o r a t o r y s y s t e m is /He = (l/2n)(eH/me)(l/y)['l/('l

-- (vl /c) cos 0) J,

where ~/= ( 1 - v 2 / e 2 ) - J 2 is the r e l a t i v i s t i c factor, v is the total velocity, vii is the component of this velocity along the magnetic field, and 0 is the angle between the d i r e c t i o n of motion and the radiation direction. In the e x p e r i m e n t s the radiation was r e c o r d e d p e r p e n d i c u l a r to the b e a m and along its direction so that cos 0 = 0 and 1. Knowing the value of the m a g n e t i c field, fmax(O =7r/2) and fmax(0 =0), we can find T and vii . When H = 5 . 5 kOe, fmax(0 =7r/2) =12 GHz and fmax(0 =0) =33.5, and this gives y = l . 4 and v[[=0.7c. T h e s e values of and vii are in good a g r e e m e n t with those found by o t h e r methods and quoted in [3]; We can t h e r e f o r e conclude that the m a x i m u m in the radiation s p e c t r u m c o r r e s p o n d s te the fundamental of the cyclotron frequency. It is to be noted that the intensity of the radiation r e c e i v e d at 0 =0 ~ is about an o r d e r of magnitude s m a l l e r than for 0 = 90 ~ The p o w e r r e c e i v e d in the direction p e r p e n d i c u l a r to the b e a m was e s t i m a t e d with due allowance f o r the p o l a r d i a g r a m of the horn antenna. The r e s u l t s show that at the frequency fmax the radiation in the given direction f r o m unit volume of the b e a m p e r unit solid angle is ~"102 W, while the total intensity of the radiation f r o m individual e l e c t r o n s in 1 c m ~- volume is N10--T W according to the Schott equation [4]. In o u r e x p e r i m e n t s the b e a m was p r o p a g a t i n g p r a c t i c a l l y in f r e e s p a c e (large v a c u u m c h a m b e r , homogeneous m a g n e t i c field) and so the powerful radiation cannot be explained by the p r e s e n c e of a high-Q r e s o n a t o r in the s y s t e m . Thus, the b e a m i t s e l f must be the cause of this v e r y intensive radiation. If the b e a m contains density i r r e g u l a r i t i e s with a l i n e a r size s m a l l e r than the e l e c t r o n g y r o radius rile, it is p o s s i b l e to get c o h e r e n t radiation with an intensity which is s o m e r3Hen b (Anb/nb)z t i m e s g r e a t e r than the level of the incoherent radiation. S m a l l - s c a l e d e n s i t y i r r e g u l a r i t i e s could be c a u s e d e i t h e r by the way the b e a m is produced (microexplosive cathode emission) or by b e a m instability (if a s u p e r e r t t i c a l b e a m is injected, f o r e x a m p l e ) . However, the 302

wide s c a t t e r in v e l o c i t i e s A v • v in the b e a m would m e a n that density i r r e g u l a r i t i e s would be s m e a r e d out a f t e r a few cyclotron r e v o l u t i o n s . It thus a p p e a r s that the i r r e g u l a r i t i e s must be s e l f - s u s t a i n i n g , i.e., t h e r e m u s t be an i r r e g u l a r i t y which p r o d u c e s a modulation in the density. In o r d e r to study effects c a u s e d by the injection of a s u p e r c r i t i c a l c u r r e n t we c a r r i e d out m e a s u r e m e n t s with I < I c r . Since the c r i t i c a l c u r r e n t in a v a c u u m [5] depends only weakly on the b e a m radius, it is always possible to get a c u r r e n t below the c r i t i c a l v a l u e ' b y reducing the t o t a l c u r r e n t . The c u r r e n t was limited in radius by m e a n s of a graphite d i a p h r a g m . When this was done the f r e q u e n c y f m a x (~ = ,Z/2) d e c r e a s e s by a factor of 1.5; this c o r r e s p o n d s to an i n c r e a s e in y to a value of 2. The radiation intensity r e m a i n e d almost constant. Thus, the high radiation intensity is not r e l a t e d to a s u p e r c r i t i c a l c u r r e n t . It s e e m s that in a m a g n e t i c field t h e r e m a y be an instability in the b e a m itself which develops at the cyclotron f r e q u e n c i e s as a r e s u l t of the a n i s o t r o p y of the distribution function in the b e a m s y s t e m . However, this suggestion r e q u i r e s f u r t h e r study. In conclusion, the authors wish to e x p r e s s t h e i r gratitude to D. D. Ryutov and B. N. B r e i z m a n for fruitful discussion and i n t e r e s t in this work, and V. S. Koidan and V. V. Konyukhov f o r valuable advice and a s s i s tance in c a r r y i n g out the e x p e r i m e n t s . LITERATURE 1.

2.

3.

4g 5.

CITED

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