- Email: [email protected]
Superradiance of short electron pulses in waveguides
2% + __
Nuclear
Instruments
and Methods
in Physics
Research
A 375 (1996) 553-557
__
lfi!i!l
NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH
Secrlon A
ELSEVIER
Superradiance N.S. Ginzburg”‘*,
of short electron pulses in waveguides
1.V. Konoplev”, I.V. Zotovab, A.S. Sergeev”, V.G. Shpakb, M.I. Yalandinb, S.A. Shunailovb, M.R. Ulmaskulovb,
“Institute of Applied Physics. Ruxsim hItutitute
of Electrophwics.
of Science, 36 lllyano~n St., 6O_WOO,N. Novgorod. Russia
Academy
Russian Academy
of Science, 33 Kom.wmolskaya
St., 620219. Ekaterinhurg,
Russia
Abstract Specific features of superradiance in waveguide under group synchronism conditions are studied theoretically. Progress in experimental observation of cyclotron superradiance based on using a subnanosecond pulse generator with explosive electron emission is discussed.
1. Introduction Recently much attention has been given to superradiance (SR) in bunches of classical electron oscillating either in undulator field or in uniform magnetic field [l-8]. As a consequence of the development of nonthreshold SR instabilities, the energy of oscillatory motion is emitted in the form of a short electromagnetic pulse with the duration of about several periods of HF oscillations. This report is devoted to the cyclotron superradiance of electron bunches moving through waveguide systems. In Section 2 we study theoretically specific regimes of SR which may occur due to peculiarities of waveguide dispersion. Among them there are regimes of radiation near the cut-off frequency as well as regimes of group synchronism. At the last operating regimes the electron bunch longitudinal velocity coincides with the group velocity of the e.m. wave. It is found the increasing of the SR instability growth rate and energy extraction efficiency in such regimes. In Section 3 we describe experimental set up based on subnanosecond pulser with explosive electron emission which we intend to use for observation of cyclotron SR.
2. Superradiance
under group synchronism
condition
e.m. radiation when the dispersion curves of electromagnetic wave, h = L yw, and electron beam, w hy, = wH. are tangent (see Fig. la). In this case the cut-off frequency q. relativistic gyrofrequency wH = eH,,lmcy and radiation frequency w satisfy
where
y, = (I -vi/‘-)-
y = (I - QIcZ
~ vt
I
is the electron transverse velocity. Note that for ultrarelativistic electrons this frequency may be substantially higher than the electron oscillation frequency. In the analysis below we work in a comoving frame of reference K’, which is moving at the translational velocity of the electrons. Using Lorentz transformations, we easily find that the longitudinal wave number h’ and the transverse component of the magnetic field H ’ in the K’ frame tend to zero, and this process reduces to the radiation of an immovable (V,; = 0) ensemble of cyclotron oscillators at a quasicritical frequency (Fig. I b). Representing the radiation field in the form E’ = Re[E:(rJ )A’(z’. t’) exp(iqt’)] where the function E:(r:) characterizes the transverse structure of the waveguide mode, we will describe the evolution of the longitudinal cY”z.
and V_ = pIc
Let us analyze cyclotron SR under the group synchronism condition, when the translation velocity of the electron bunch is equal to the group velocity of an e.m. wave in the waveguide:
(1)
VI,= vGr This regime is realized during waveguide
propagation
*Corresponding author. Tel. +7 8312 365921, 362061, e-mail [email protected]. 016%9002/96/$15.00 Copyright PI/ SO168-900’(96)00062-9
0 1996 Published
of
fax +7 8312
Fig. I. Dispersion diagram of the group synchronism regime in the lab frame of reference (a) and in the comoving frame (b).
by Elsevier Science B.V. All rights reserved VIII. NEW DIRECTIONS
554
N.S.
Gkhurg
et al.
I Nucl. Instr.
and Meth.
field distribution A’(z’, t’). in accordance with the dispersion relation, by the inhomogeneous parabolic equation 7
i2
+ g
= 3if(Z)G( p+ ) (+,
The azimuthal self-bunching of the electrons is caused by the dependence of the gyrofrequency on the energy of the particles. It is described by the equations of a nonisochronous oscillator
Under the assumption that in the initial state the electrons are distributed uniformly in cyclotron-rotation phase, aside from fluctuations stemming the small parameter r, we can write the initial conditions on system (3), (4) as follows: ~+I~_,,=expi(~~),,+vcos0,,),
@,E[0.2~],
nI7=,, = 0. Here we are using dimensionless variables: 6, = (/3: + is the normalized transverse electron velocity: MYPI,, Ll =
2eA’ mcqp:;,
T Jm_,(R,,q)/c),
Z=,_‘p;,,qlc,
A = 2(w;, - w,)q& ;, is the detuning frequency from the cut-off frequency:
in Phys. Res. A 375 (1996)
S_T-SS7
determining the complex eigenfrequency. At the sufficiently small particle density (6 e I ) in the case of exact group synchronism (A = 0) the growth rate in Im R = (26)“’ sin(n/5). Correspondingly. the growth rate of the SR instability is given in dimensional variables by
(7) Note that the SR instability does not involve a threshold. This is a consequence of the infinite lifetime of the electron oscillators in the region of the interaction with the e.m. field. Because of the electron shift, the radiation frequency is above the cut-off Re R > 0 and there are fluxes of e.m. energy in both directions away from the electron bunch Re !l < 0. The dependence of the gain Im R, the frequency detuning Re 0 and the real and imaginery part of longitudinal wave number 1; on the parameter A are shown in Fig. 2. We see that a detuning from the grazing regime leads to a decrease in the growth rates. While the instability is cut off at a large negative detuning (w,‘, < w,). the instability persists at arbitrary large values of A in the region of positive detuning (WC,> w,). Under the condition A + I, the following asymptotic expressions hold:
of the cyclotron
is a form-factor written under the assumption that the electron bunch is hollow with an injection radius R,; I,, is the total current in the lab frame; A = 27rclq = 27rRly,; R is the radius of the waveguide, m is the azimutal index of the waveguide mode: and z+,is the nth root of the equation J,,(v) = 0. The function f(Z) describes the distribution of the electron density. Below we consider the case in which the electron bunch is relatively short, and the condition
holds; here b’ = by, is the length of the bunch, T’ is the time of the process development (the reciprocal growth rate: see Eq. (7)). Under condition (5) we can set f’(Z) = B&Z). where B = /3~&‘qlc and 6(Z) is the Dirac deltafunction. To describe the initial linear stage of the SR, we write the radiate field in the form a(Z, 7) = a(O) exp(-ih^lZI + iA + iRr) and linearizing the equations (3), (4). We find the characteristic equation (6 = GB)
Fig. 2. Real and imaginary part of the longitudinal wave number (a) and the growth rate and electron frequency shift (b) versus the detuning parameter A, G = 0.05.
N.S. Ginsburg
lx
la
555
et al. I Nuci. Instr. and Meth. in Phys. Res. A 375 (1996) 553-557
0.000
Lii:-
field times the reciprocal growth rate. The maximum amplitude has reached the case of exact group synchronism. Let us look at the basic characteristics of the SR in the lab frame of reference. In the group synchronism regime, the frequencies of the radiation in the positive and negative directions along the z axis are approximately equal and given by Eq. (2). The peak power of the SR passing through a fixed area outside the bunch is given by
77 0.8 0.5
2
0.3
0.0
(9)
l-3
b)
0
20
40
The average electron efficiency in the lab frame can be found with the help of the formula
7 60
Fig. 3. Time evolution of (a) the square modulus of the amplitude and (b) the electron efficiency. 1 -Group synchronism regime (A = 0). 2 - deviation from the group synchronism regime (A = I ). e = 0.05.
(8) These expressions correspond to a transition to a region of an intersection of the dispersion characteristics, in which there is no group synchronism [6]. Fig. 3 shows results of a numerical simulation of the nonlinear stage of the SR according to Eqs. (3) and (4). Shown here are plots of the time dependence of the square amplitude ]a(’ and the electron efficiency 77: = 1 - (I/ 27~)J,fm j/3: 1’ d@,,. We see that the bulk of the transverse oscillation energy of the electrons is transformed into the energy of e.m. radiation over a time on the order of a few
In the ultrarelativistic case the em high efficiency can be achieved under rather small transverse velocities p,, - yi),‘, because the energy of both the transverse and longitudinal motions of electrons is converted into the energy of e.m. oscillations in this frame.
3. The experimental
facilities and preliminary
tests
For experimental observation of cyclotron SR in millimeter waveband we intend to use subnanosecond pulse generator with explosive electron emission. The scheme of the experimental set up is shown in Fig. 4. It consists of 4 main units: a) a nanosecond, driver, b) pulse slicer and transmitting line, c) magnetically insulated coaxial vacuum diode (MICD) and d) microwave unit. The nanosecond pulse-repetitive driver used was a compact top-table RADAN-303 generator [9], whose basic component represented a 4-nanosecond double forming
Fig. 4. Experimental setup for investigation of the cyclotron superradiance of the subnanosecond electron bunch. 2 - double forming line; 3 - peaking spark gap; 4 -chopping spark gap; 5 - nonuniform transmitting line; 6 - thin-edge emitting cathode; 7 - kicker; 8 - guiding solenoid; 9 - circular waveguide: IO- 14 - microwave horn antenna.
1-gas spark gap: tubular explosive-
VIII. NEW DIRECTIONS
line. With a matched 50n load, the driver permitted generation of adjustable-amplitude pulses with II,.,< ranging between 150 and 200 kV according to the repetition frequency, which ran to 100 Hz. As our case required generating high-power pulses with durations under I ns, a special subnanosecond former ( “slicer” ) was designed [IO], Fig. 4. This former based on the cutting the subnanosecond pulse out of the nanosecond pulse and involved a peaking and a chopping gas spark gaps. Such a slicer depends for its operation on the subnanosecond time delay between the switching of the peaking spark gap and that of the chopping spark gap. This delay determines output pulse duration. A single-gap peaking-spark-gap slicer yielded a - 150 kV pulse with a minimum half-height duration of -300~s. The rate of voltage rise and fall for such a subnanosecond pulse was at a level of -(5-IO) X IO"V/s [I I]. a value which was approximately an order of magnitude higher than the corresponding characteristic of a nanosecond driver. The subnanosecond slicer does not permit to multiply the output voltage of the nanosecond driver. However, while the slicer output impedance is essentially less than impedance of the magnetically insulated coaxial vacuum diode (MICD), some increasing of the voltage amplitude across the cathode becomes possible. To provide the voltage amplitude gain and to match the 50R pulser and high-ohmic ( 150-200 0) MICD the output nonuniform adiabatic transmitting line is installed between these two units. Our preliminary tests have shown that the accelerating voltage of 200 kV is available for the device (Fig. 5a) when the subnanosecond slicer forms the original l50-kV pulses. Such accelerating pulse of minimum duration of 300 ps was applied in the initial tests of the subnanosecond electron accelerator produced a rectilinear hollow beam. The tubular thin-edge graphite cathode has an external diameter of 4 mm while its edge thickness does not exceed of 0.1 mm. The last circumstance is essential in the terms of decreasing the position spread of the electrons emitted. The external fraction of the beam electrons possesses an increased initial transverse velocities due to presence in MICD crossed E and H fields [ 121. As the experimentally-
I’
-.-._
-
1
1 ns/division Fig. S. Oscillogram
of the accelerating
I
I
Table I Main parameters pulse
of acceleration
and results of simulation
of SR
No ps 100 kV 0.1 kA
Electron pulse duration Voltage Peak current Pitch-factor Guiding magnetic tield Wavelength Wavrgmde radius Operating mode SR peak power SR pulse duration
I 1.5 kOe
9.3 mm 5.5 mm TEz, 2.1 MW 360 ps
-
measured e-beam current was as high as I kA (Fig. 5b), and as only -O.l-kA operating current is needed for the experimental study of cyclotron SR, so there is an essential margin to increase the beam quality. It may be done with the use of space-extended collimator installed in the drift tube close to the cathode. Even a weakly-collimated, 0.9kA subnanosecond e-beam (the diameters of the cathode and the collimator were 4 and 5 mm, respectively) had a thin “wall” (about 0.4 mm) that was checked from the beam imprint on the dosimetric film positioned at drift chamber. We hope that such ‘*cooled” e-beam could be acceptable to perform the pumping of the electrons transverse velocities and to obtain the electrons pitch angle of about I. To pump the beam transverse velocity a short active undulator (kicker) will be installed between the drift chamber and the guiding solenoid, as it shown in Fig. 4. The main parameters of the electron bunch and an estimation of the parameters of the SR pulse based on numerical simulation are given in Table I.
References V. Zheleanyakov. W. Kocharovsky and V1.V. Kochrovsky, Izv. Vuzov. Radiofiz. 29 ( 1986) 1095. R. Bonifacio, C. Maroli and N. Piovella. Opt. Commun. 68 (1988) 369.
I
1 ns/division
voltage pulse applied to the cathode (a), and the oscillogram
of subnanosecond
e-beam current (b).
N.S. Gkburg
et al. I NW!. Instr. und Mrth. in Phw
[3] R. Bonifacio. B.W.J. McNeil and P. Pierini. Phys. Rev. A 40 ( 1989) 4467. [4] R.H. Bonifacio, W.M. Sharp and W.M. Fawley. Nucl. Instr. and Meth. A 285 (1989) 217. [S] N.S. Ginzburg, Sov. JTP Lett. 14 ( 1988) 440. 161 N.S. Ginzburg. IV. Zotova, Sov. JTP Lett. 15 ( 1989) 83. [7] N.S. Ginzburg and AS. Sergeev, Sov. JETP Lett. 54 (1991) 44.5. [8] N.S. Ginzburg and A.S. Sergeev, Sov. JETP 99 (1991) 43X.
Res. A .?75 (1996) 5L-557
551
[9] B.M. Kovalchuk. G..&. Mesyats and V.G. Shpak. Proc. Int. Pulsed Power Conf., P.lD5, Lubbok, TX, 1976. [IO] G.A. Mesyats. V.G. Shpak. M.I. Yalandin and S.A. Shunailov. IEEE Proc. 9th Int. Pulsed Power Conf.. Albuquerque, NM, 1993, p. 835. [II] G.A. Mesyats, V. G. Shpak, S.A. Shunailov and M.I. Yalandin. Proc. SPIE Int. Symp. Intense Microwave Pulses. Vol. 2154 CA 1994 p. 262. 1121 S.D. ‘Koroiin an> I.V. Pegel. Sov. TP 62 (1992) 139.
VIII. NEW DIRECTIONS
Nuclear
Instruments
and Methods
in Physics
Research
A 375 (1996) 553-557
__
lfi!i!l
NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH
Secrlon A
ELSEVIER
Superradiance N.S. Ginzburg”‘*,
of short electron pulses in waveguides
1.V. Konoplev”, I.V. Zotovab, A.S. Sergeev”, V.G. Shpakb, M.I. Yalandinb, S.A. Shunailovb, M.R. Ulmaskulovb,
“Institute of Applied Physics. Ruxsim hItutitute
of Electrophwics.
of Science, 36 lllyano~n St., 6O_WOO,N. Novgorod. Russia
Academy
Russian Academy
of Science, 33 Kom.wmolskaya
St., 620219. Ekaterinhurg,
Russia
Abstract Specific features of superradiance in waveguide under group synchronism conditions are studied theoretically. Progress in experimental observation of cyclotron superradiance based on using a subnanosecond pulse generator with explosive electron emission is discussed.
1. Introduction Recently much attention has been given to superradiance (SR) in bunches of classical electron oscillating either in undulator field or in uniform magnetic field [l-8]. As a consequence of the development of nonthreshold SR instabilities, the energy of oscillatory motion is emitted in the form of a short electromagnetic pulse with the duration of about several periods of HF oscillations. This report is devoted to the cyclotron superradiance of electron bunches moving through waveguide systems. In Section 2 we study theoretically specific regimes of SR which may occur due to peculiarities of waveguide dispersion. Among them there are regimes of radiation near the cut-off frequency as well as regimes of group synchronism. At the last operating regimes the electron bunch longitudinal velocity coincides with the group velocity of the e.m. wave. It is found the increasing of the SR instability growth rate and energy extraction efficiency in such regimes. In Section 3 we describe experimental set up based on subnanosecond pulser with explosive electron emission which we intend to use for observation of cyclotron SR.
2. Superradiance
under group synchronism
condition
e.m. radiation when the dispersion curves of electromagnetic wave, h = L yw, and electron beam, w hy, = wH. are tangent (see Fig. la). In this case the cut-off frequency q. relativistic gyrofrequency wH = eH,,lmcy and radiation frequency w satisfy
where
y, = (I -vi/‘-)-
y = (I - QIcZ
~ vt
I
is the electron transverse velocity. Note that for ultrarelativistic electrons this frequency may be substantially higher than the electron oscillation frequency. In the analysis below we work in a comoving frame of reference K’, which is moving at the translational velocity of the electrons. Using Lorentz transformations, we easily find that the longitudinal wave number h’ and the transverse component of the magnetic field H ’ in the K’ frame tend to zero, and this process reduces to the radiation of an immovable (V,; = 0) ensemble of cyclotron oscillators at a quasicritical frequency (Fig. I b). Representing the radiation field in the form E’ = Re[E:(rJ )A’(z’. t’) exp(iqt’)] where the function E:(r:) characterizes the transverse structure of the waveguide mode, we will describe the evolution of the longitudinal cY”z.
and V_ = pIc
Let us analyze cyclotron SR under the group synchronism condition, when the translation velocity of the electron bunch is equal to the group velocity of an e.m. wave in the waveguide:
(1)
VI,= vGr This regime is realized during waveguide
propagation
*Corresponding author. Tel. +7 8312 365921, 362061, e-mail [email protected]. 016%9002/96/$15.00 Copyright PI/ SO168-900’(96)00062-9
0 1996 Published
of
fax +7 8312
Fig. I. Dispersion diagram of the group synchronism regime in the lab frame of reference (a) and in the comoving frame (b).
by Elsevier Science B.V. All rights reserved VIII. NEW DIRECTIONS
554
N.S.
Gkhurg
et al.
I Nucl. Instr.
and Meth.
field distribution A’(z’, t’). in accordance with the dispersion relation, by the inhomogeneous parabolic equation 7
i2
+ g
= 3if(Z)G( p+ ) (+,
The azimuthal self-bunching of the electrons is caused by the dependence of the gyrofrequency on the energy of the particles. It is described by the equations of a nonisochronous oscillator
Under the assumption that in the initial state the electrons are distributed uniformly in cyclotron-rotation phase, aside from fluctuations stemming the small parameter r, we can write the initial conditions on system (3), (4) as follows: ~+I~_,,=expi(~~),,+vcos0,,),
@,E[0.2~],
nI7=,, = 0. Here we are using dimensionless variables: 6, = (/3: + is the normalized transverse electron velocity: MYPI,, Ll =
2eA’ mcqp:;,
T Jm_,(R,,q)/c),
Z=,_‘p;,,qlc,
A = 2(w;, - w,)q& ;, is the detuning frequency from the cut-off frequency:
in Phys. Res. A 375 (1996)
S_T-SS7
determining the complex eigenfrequency. At the sufficiently small particle density (6 e I ) in the case of exact group synchronism (A = 0) the growth rate in Im R = (26)“’ sin(n/5). Correspondingly. the growth rate of the SR instability is given in dimensional variables by
(7) Note that the SR instability does not involve a threshold. This is a consequence of the infinite lifetime of the electron oscillators in the region of the interaction with the e.m. field. Because of the electron shift, the radiation frequency is above the cut-off Re R > 0 and there are fluxes of e.m. energy in both directions away from the electron bunch Re !l < 0. The dependence of the gain Im R, the frequency detuning Re 0 and the real and imaginery part of longitudinal wave number 1; on the parameter A are shown in Fig. 2. We see that a detuning from the grazing regime leads to a decrease in the growth rates. While the instability is cut off at a large negative detuning (w,‘, < w,). the instability persists at arbitrary large values of A in the region of positive detuning (WC,> w,). Under the condition A + I, the following asymptotic expressions hold:
of the cyclotron
is a form-factor written under the assumption that the electron bunch is hollow with an injection radius R,; I,, is the total current in the lab frame; A = 27rclq = 27rRly,; R is the radius of the waveguide, m is the azimutal index of the waveguide mode: and z+,is the nth root of the equation J,,(v) = 0. The function f(Z) describes the distribution of the electron density. Below we consider the case in which the electron bunch is relatively short, and the condition
holds; here b’ = by, is the length of the bunch, T’ is the time of the process development (the reciprocal growth rate: see Eq. (7)). Under condition (5) we can set f’(Z) = B&Z). where B = /3~&‘qlc and 6(Z) is the Dirac deltafunction. To describe the initial linear stage of the SR, we write the radiate field in the form a(Z, 7) = a(O) exp(-ih^lZI + iA + iRr) and linearizing the equations (3), (4). We find the characteristic equation (6 = GB)
Fig. 2. Real and imaginary part of the longitudinal wave number (a) and the growth rate and electron frequency shift (b) versus the detuning parameter A, G = 0.05.
N.S. Ginsburg
lx
la
555
et al. I Nuci. Instr. and Meth. in Phys. Res. A 375 (1996) 553-557
0.000
Lii:-
field times the reciprocal growth rate. The maximum amplitude has reached the case of exact group synchronism. Let us look at the basic characteristics of the SR in the lab frame of reference. In the group synchronism regime, the frequencies of the radiation in the positive and negative directions along the z axis are approximately equal and given by Eq. (2). The peak power of the SR passing through a fixed area outside the bunch is given by
77 0.8 0.5
2
0.3
0.0
(9)
l-3
b)
0
20
40
The average electron efficiency in the lab frame can be found with the help of the formula
7 60
Fig. 3. Time evolution of (a) the square modulus of the amplitude and (b) the electron efficiency. 1 -Group synchronism regime (A = 0). 2 - deviation from the group synchronism regime (A = I ). e = 0.05.
(8) These expressions correspond to a transition to a region of an intersection of the dispersion characteristics, in which there is no group synchronism [6]. Fig. 3 shows results of a numerical simulation of the nonlinear stage of the SR according to Eqs. (3) and (4). Shown here are plots of the time dependence of the square amplitude ]a(’ and the electron efficiency 77: = 1 - (I/ 27~)J,fm j/3: 1’ d@,,. We see that the bulk of the transverse oscillation energy of the electrons is transformed into the energy of e.m. radiation over a time on the order of a few
In the ultrarelativistic case the em high efficiency can be achieved under rather small transverse velocities p,, - yi),‘, because the energy of both the transverse and longitudinal motions of electrons is converted into the energy of e.m. oscillations in this frame.
3. The experimental
facilities and preliminary
tests
For experimental observation of cyclotron SR in millimeter waveband we intend to use subnanosecond pulse generator with explosive electron emission. The scheme of the experimental set up is shown in Fig. 4. It consists of 4 main units: a) a nanosecond, driver, b) pulse slicer and transmitting line, c) magnetically insulated coaxial vacuum diode (MICD) and d) microwave unit. The nanosecond pulse-repetitive driver used was a compact top-table RADAN-303 generator [9], whose basic component represented a 4-nanosecond double forming
Fig. 4. Experimental setup for investigation of the cyclotron superradiance of the subnanosecond electron bunch. 2 - double forming line; 3 - peaking spark gap; 4 -chopping spark gap; 5 - nonuniform transmitting line; 6 - thin-edge emitting cathode; 7 - kicker; 8 - guiding solenoid; 9 - circular waveguide: IO- 14 - microwave horn antenna.
1-gas spark gap: tubular explosive-
VIII. NEW DIRECTIONS
line. With a matched 50n load, the driver permitted generation of adjustable-amplitude pulses with II,.,< ranging between 150 and 200 kV according to the repetition frequency, which ran to 100 Hz. As our case required generating high-power pulses with durations under I ns, a special subnanosecond former ( “slicer” ) was designed [IO], Fig. 4. This former based on the cutting the subnanosecond pulse out of the nanosecond pulse and involved a peaking and a chopping gas spark gaps. Such a slicer depends for its operation on the subnanosecond time delay between the switching of the peaking spark gap and that of the chopping spark gap. This delay determines output pulse duration. A single-gap peaking-spark-gap slicer yielded a - 150 kV pulse with a minimum half-height duration of -300~s. The rate of voltage rise and fall for such a subnanosecond pulse was at a level of -(5-IO) X IO"V/s [I I]. a value which was approximately an order of magnitude higher than the corresponding characteristic of a nanosecond driver. The subnanosecond slicer does not permit to multiply the output voltage of the nanosecond driver. However, while the slicer output impedance is essentially less than impedance of the magnetically insulated coaxial vacuum diode (MICD), some increasing of the voltage amplitude across the cathode becomes possible. To provide the voltage amplitude gain and to match the 50R pulser and high-ohmic ( 150-200 0) MICD the output nonuniform adiabatic transmitting line is installed between these two units. Our preliminary tests have shown that the accelerating voltage of 200 kV is available for the device (Fig. 5a) when the subnanosecond slicer forms the original l50-kV pulses. Such accelerating pulse of minimum duration of 300 ps was applied in the initial tests of the subnanosecond electron accelerator produced a rectilinear hollow beam. The tubular thin-edge graphite cathode has an external diameter of 4 mm while its edge thickness does not exceed of 0.1 mm. The last circumstance is essential in the terms of decreasing the position spread of the electrons emitted. The external fraction of the beam electrons possesses an increased initial transverse velocities due to presence in MICD crossed E and H fields [ 121. As the experimentally-
I’
-.-._
-
1
1 ns/division Fig. S. Oscillogram
of the accelerating
I
I
Table I Main parameters pulse
of acceleration
and results of simulation
of SR
No ps 100 kV 0.1 kA
Electron pulse duration Voltage Peak current Pitch-factor Guiding magnetic tield Wavelength Wavrgmde radius Operating mode SR peak power SR pulse duration
I 1.5 kOe
9.3 mm 5.5 mm TEz, 2.1 MW 360 ps
-
measured e-beam current was as high as I kA (Fig. 5b), and as only -O.l-kA operating current is needed for the experimental study of cyclotron SR, so there is an essential margin to increase the beam quality. It may be done with the use of space-extended collimator installed in the drift tube close to the cathode. Even a weakly-collimated, 0.9kA subnanosecond e-beam (the diameters of the cathode and the collimator were 4 and 5 mm, respectively) had a thin “wall” (about 0.4 mm) that was checked from the beam imprint on the dosimetric film positioned at drift chamber. We hope that such ‘*cooled” e-beam could be acceptable to perform the pumping of the electrons transverse velocities and to obtain the electrons pitch angle of about I. To pump the beam transverse velocity a short active undulator (kicker) will be installed between the drift chamber and the guiding solenoid, as it shown in Fig. 4. The main parameters of the electron bunch and an estimation of the parameters of the SR pulse based on numerical simulation are given in Table I.
References V. Zheleanyakov. W. Kocharovsky and V1.V. Kochrovsky, Izv. Vuzov. Radiofiz. 29 ( 1986) 1095. R. Bonifacio, C. Maroli and N. Piovella. Opt. Commun. 68 (1988) 369.
I
1 ns/division
voltage pulse applied to the cathode (a), and the oscillogram
of subnanosecond
e-beam current (b).
N.S. Gkburg
et al. I NW!. Instr. und Mrth. in Phw
[3] R. Bonifacio. B.W.J. McNeil and P. Pierini. Phys. Rev. A 40 ( 1989) 4467. [4] R.H. Bonifacio, W.M. Sharp and W.M. Fawley. Nucl. Instr. and Meth. A 285 (1989) 217. [S] N.S. Ginzburg, Sov. JTP Lett. 14 ( 1988) 440. 161 N.S. Ginzburg. IV. Zotova, Sov. JTP Lett. 15 ( 1989) 83. [7] N.S. Ginzburg and AS. Sergeev, Sov. JETP Lett. 54 (1991) 44.5. [8] N.S. Ginzburg and A.S. Sergeev, Sov. JETP 99 (1991) 43X.
Res. A .?75 (1996) 5L-557
551
[9] B.M. Kovalchuk. G..&. Mesyats and V.G. Shpak. Proc. Int. Pulsed Power Conf., P.lD5, Lubbok, TX, 1976. [IO] G.A. Mesyats. V.G. Shpak. M.I. Yalandin and S.A. Shunailov. IEEE Proc. 9th Int. Pulsed Power Conf.. Albuquerque, NM, 1993, p. 835. [II] G.A. Mesyats, V. G. Shpak, S.A. Shunailov and M.I. Yalandin. Proc. SPIE Int. Symp. Intense Microwave Pulses. Vol. 2154 CA 1994 p. 262. 1121 S.D. ‘Koroiin an> I.V. Pegel. Sov. TP 62 (1992) 139.
VIII. NEW DIRECTIONS