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Millimeter wave radiation from a rotating electron ring subjected to an azimuthally periodic wiggler magnetic field
352
Nuclear Instruments and Methods in Physics Research A250 (1986) 352-356 North-Holland, Amsterdam
MILLIMETER WAVE RADIATION FROM A ROTATING ELECTRON RING SUBJECTED TO AN AZIMUTHALLY PERIODIC WIGGLER MAGNETIC FIELD G. BEKEFI and R.E. SHEFER **
Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of TechnoloU, Cambridge, Massachusetts 02139, USA
W.W. DESTLER
University of Maryland, College Park, Maryland 20742, USA
The generation of millimeter wave radiation (80-180 GHz) caused by the interaction of a rotating electron ring (2 MV, 1.4-3.6 kA, 5 ns) with an azimuthally periodic wiggler magnetic field has been studied experimentally and theoretically, and by computer simulations. Narrow band radiation is observed at power levels exceeding several megawatts.
1. Introduction We report studies of a free electron laser oscillator comprised of a rotating, relativistic electron ring subjected to an azimuthally periodic wiggler magnetic field. We observe narrow band radiation at 88 and 175 GHz for wiggler field periodicities 1. of 6.28 and 3.14 cm, respectively . The results are compared with theoretical predictions and computer simulations . In the experiment [1,2] illustrated in fig. 1 a high quality (energy spread < 1%) rotating electron ring is produced by injecting a hollow nonrotating beam into a narrow magnetic cusp . The hollow beam is generated by field emission from an annular cathode energized by a pulsed, high voltage, high current accelerator (2 MV, 20 kA, 30 ns). The resulting rotating electron ring is guided downstream from the cusp by a uniform axial magnetic field of -- 1.4 kG . The ring is 6 cm in radius, has a duration of - 5 ns, and carries an axial current of 1 .4-3 .6 kA. The electron rotation velocity ve = 0.96 c, and the elec-
Embedded Permanent Magnets
tron axial velocity vz = 0.2c . Thus, in the absence of the wiggler magnetic field, the electron orbits form fairly tight helices. The electron ring propagates within the gap formed by two stainless steel cylinders 5.398 and 6.509 cm in radius . Superimposed on the axial guiding magnetic field is an azimuthally periodic magnetic wiggler field B,, which, near the center of the gap, is primarily radial * This work was supported by the US Department of Energy, the Air Force Office of Scientific Research, and the National Science Foundation . ** Present address : Science Research Laboratory, Inc ., 15 Ward St ., Somerville, Massachusetts 02143, USA
0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Diode Coils Fig. 1 . Experimental arrangement
Wave Guide
G. Bekefi et al. / A rotating electron ring
and is thus transverse to the electron flow velocity, as is the case in conventional linear free electron lasers . The wiggler magnetic field is produced by an assembly of 384 samarium-cobalt bar magnets 0.40 x 0.40 x 4.8 cm3, each having a residual induction of - 9.0 kG . The magnets are positioned behind the grounded stainless steel cylinders and held in place in grooved aluminum holders. To achieve a given periodicity IW , the dipole axes of the magnets are arranged in the Halbach configuration [3]. The axial length of the wiggler is 20 cm . This is achieved by stacking rows of the bar magnets end-to-end . For a wiggler periodicity 1W of 6.28 cm (corresponding to N = 6 periods around the azimuth) the wiggler amplitude BW at the position of the electron ring Ro = 6 cm equals 1300 G. For a periodicity 1. = 3.14 cm (N =12), BW =1000 G. In section 2 of this paper we summarize some of the theoretical considerations and computer simulations . Section 3 gives a brief discription of the experimental results. Conclusions are drawn in section 4.
353
1,5x10 9
0 Fig.
2.
15'
20
25
30
160
150
Growth rate of the FEL instability as a function of 1;
current density = 3.23 A/cm2. Axial beam current density = 0. radiation frequencies :
2. Theory and computer simulations
we (l,m)
= [MIrc/ri (g-1)][1+al2 ] 1/2
X(aA-1)-1},
,
where g = ro/r with r,, as the outer and ri as the inner radius, and a=[2(g-1)/vrm(g+1)]2 . Solving for the crossing points yields the following expression for the
180
m =1 ; ro = 6 .51 cm ; r, = 5 .40 cm ; R o = 5 .84 cm ; v, 1c = 0.95 ; x BW = 750 G; azimuthal beam 92 11 = 4.88 10 9 rad/s; N = 6 ;
w=92 11 {N+[N±(A+aAN 2 -aA2 )
In the theoretical model [4] we assume a thin, tenuous electron ring undergoing pure rotation (the axial velocity is zero) and comprised of monoenergetic electrons with zero energy spread. The rotational velocity vB = d2 1 Ro is perturbed by a radially directed, azimuthally periodic wiggler magnetic field, as a result of which growing electromagnetic modes are excited. (9211 is the relativistic electron cyclotron frequency.) The excitation frequencies and temporal growth rates are derived for the TM I, . family of modes that can be supported in a coaxial waveguide with radii ro and ri. The appropriate dispersion equation is derived for complex frequencies w under the assumption that the axial wave vector k1l of the electromagnetic fields is zero (cutoff condition) . It is found that radiation growth occurs near frequencies corresponding to the crossing point of the cutoff waveguide modes w = wß(1, m) (wc is the cutoff frequency) and the beam modes w = (l + N)011 upshifted by the wiggler periodicity N. This coupling is similar in nature to that which occurs in conventional, linear free electron lasers. For given fixed values of l and m two crossing points occur, one at low frequency, and the other at high frequency. For a narrow gap coaxial waveguide such that (r,, ri )/ro << 1, the cutoff frequency w. for the lth azimuthal and mth radial mode can be approximated by
170
AZIMUTHAL MODE NUMBER
1/21 (2)
where A = [(7rmc)/rl (g -1)
9211)12
.
To obtain the growth
PARTICLE DENSITY 0
x
>N
+9
-9
0 x
0.524 1.047 8 (radians) Fig. 3 . Simulation of the electron density distribution, and of the axial and azimuthal momenta 6 ns after start-up ; ro = 6.509 cm ; r, = 5 .398 cm ; 1 , = 6 .28 cm (N = 6) ; Bw = 750 G~ ; B~ = 1100 G; ve/c = 0 .968 ; azimuthal circulating current density Ja =1 .1 A/cm2. Axial beam current density = 0. IX. RAMAN/GUIDE FIELD FELS
354
G. Bekefi et al. / A rotating electron ring
and the beam mode given by w=kllvll+ (1+N)S2I1 .
w 0
a a 6
9 TIME (ns)
__12
w
(4)
Detailed dispersion equations giving the radiation frequencies and growth rates as a function of v ll and kll have been derived [6]. Maximum growth rate is expected to occur at the tangential intersection of the above two waves, at which point the low and high frequency brandhes merge into a single mode. This takes place when the wave group velocities aw/8k l are equal to v ll , with the result that w-Yllwc(1, m)=YIÎ(1+N)Slll,
0
where yll=[1-(VIIIC)z]-t12 .
a a co
3. Experiments
0
720
Fig. 4. Simulations of the temporal growth, wave number, and frequency spectrum for the z component of the RF electric field . TM family of coaxial waveguide modes 6 ns after start-up. The remaining parameters are the same as those given in the caption to fig. 3. rate of the instability (that is, the imaginary part of w) one must solve the complete dispersion equation [4]. Fig. 2 illustrates the growth rates of the low and high frequency branches as a function of 1, for a fixed value of m =1 . Each point indicates the growth rate of a discrete mode 1. The solid lines merely connect the points . We have also performed a series of computer simulations using MASK, a 2-', -dimensional, fully relativistic particle-in-cell code [5]. In the code a 60° sector of the circular FEL structure is represented by a 15 X 256 mesh and the fields and particle positions are integrated forward in time with successive time steps of 5 X 10 -13 s; 11000 simulation particles have been used. Fig. 3 shows the beam density distribution and particle momenta pZ and pe 6 ns (12000 time steps) after start-up . Fig. 4 illustrates the RF characteristics. The large resonant peaks in the wavenumber and frequency spectra corresponds to the low frequency branch of the FEL instability as given by eq . (2). The high frequency branch has as yet not been identified. Because the growth rate of this branch is expected to be small, many more time steps will probably be required. Hitherto we assumed that the axial electron velocity v 11 and the axial wavenumber k 1l are identically zero . When these conditions are relaxed, one finds from theory that now radiation growth occurs near the crossing points of the waveguide mode given by w2 =k~c Z +wC(1, m)
The radiation generated in the experiments is picked up with a small RF probe in the form of a horn antenna located immediately downstream from the magnetic wiggler (see fig. 1) . A section of waveguide acting as a high pass filter cuts off all radiation below 74 GHz. When the wiggler magnets are removed there is no measurable radiation at frequencies above 74 GHz. With the wiggler magnets in place, strong emission is observed . The radiation intensity is found to be a sensitive function of the current injected into the wiggler . This is illustrated in fig. 5 in which we plot the total RF power detected above 74 GHz, as a function of the axial electron current (this is the current downstream from
F_ 2
3
w
Fa W N
2
x v ti w
0 m a
w 3
0a 0 w Fa a s
0
0
I 2 3 INJECTED AXIAL CURRENT (kA)
4
Fig. 5. Radiated RF power above 74 GHz as a function of injected axial current; 1, = 6.28 m (N = 6) ; Br =1325 G.
G. Bekefi et al. / A rotating electron ring
RF probe through the 20 cm long magnetic wiggler . Fig . 6 shows that the radiation intensity grows quite rapidly with z and reaches a plateau in a distance of - 5 cm . The radiated power spectra for various configurations have been measured using a sensitive grating spectrometer [7], with gratings available in the range 70-200 GHz. The frequency resolution of the spectrometer is typically dw/w = 0 .02, and the insertion loss is in the range 3-5 dB. Fig. 7 shows the measured spectral characteristics for the two wiggler periodicities lw = 6 .28 cm (N = 6) and l w = 3 .14 cm (N = 12). The vertical arrows give the emission frequencies as predicted from eq. (2) . However, we note that the emission frequency is a sensitive function of the various experimental parameters (12~~, r ro , R o ) and the very good agreement between experiment and theory seen in fig . 7 may be somewhat fortuitous .
F z w a w N w 0 m a w 3
0 a
0 w
á a o:
AXIAL DISTANCE Z(cm)
Fig. 6 . Radiated power above 74 GHz, and the spatial wiggler amplitude distribution as a function of axial position ; l w = 6.28 cm (N = 6). Injected axial current =1 .4 kA .
the interaction region as measured in the absence of the wiggler magnets) . We see from fig. 5 that by increasing the current by a factor of approximately 2 .5, the radiation intensity increases by about a factor of one hundred . We estimate that at the injected current of 3 .6 kA, the RF power is in excess of several megawatts, and may be as high as several tens of megawatts . The rapid increase in RF power with current suggests that we are witnessing phenomena associated with oscillation onset, and that the threshold injection current is in the vicinity of 1 kA . The growth of the radiated power (at constant injection current), as a function of the axial position z within the interaction region is measured by moving our 200
w á
4 . Conclusions In this paper we have presented a summary of recent measurements, theoretical studies and computer simulations of the circular free electron laser employing a rotating, relativistic electron ring subjected to an azimuthally periodic wiggler magnetic field . The studies indicate that the production of millimeter wave radiation is consistent with theoretical expectations . Although the efficiency of conversion of electron beam energy to radiation is currently low (less than 1%), it is not at all clear how efficiently the radiation is being coupled out of the interaction region . This region represents a highly overmoded, quasi-optical coaxial waveguide, and when the azimuthal wavenumber 1 is large, as it is in our experiments (see fig . 2), one is dealing with RF modes of the "whispering gallery" type. Coupling energy out of such a mode configuration has received some attention [8]. The issues are similar to those encountered in coupling energy from an overmoded millimeter wave gyrotron [8].
References
E a
Z 0
35 5
100
3
0 U
0 70
90
110 170 130 150 RADIATION FREQUENCY w/2V (GHZ)
190
Fig. 7 . Radiated power spectra for two wiggler periodicities N = 6 and 12. The vertical arrows are predictions from eq . (2). Injected axial current =1.4 kA.
[1] G . Bekefi, R .E . Shefer and W.W . Destler, Appl. Phys . Lett . 44 (1984) 280 . [2] W .W. Destler, F.M . Aghamir, D.A. Boyd, G . Bekefi, R.E. Shefer and Y .Z . Yin, Phys . Fluids 28 (1985) 1962. [3] K. Halbach, Lawrence Berkeley Laboratory, University of California Accelerator and Fusion Research Division Report No. í,)3L11393 (August 1980) ; IEEE Trans . Nucl . Sci. NS-26 (1979) 3882 . [4] Y .Z . Yin and G. Bekefi, Phys. Fluids 28 (1985) 1186. [5] A . Palevsky, G. Bekefi and A .T. Drobot, J . Appl . Phys . 52 (1981) 4938 ; J .P. Boris, in : Proc . Fourth Conf . on Numerical Simulation of Plasmas, eds ., J .P. Boris and R .A . Shanny (Stock 08510059, US GPO, Washington, D .C., 1971) p . 3; IX. RAMAN/GUIDE FIELD FELS
356
G. Bekefi et al. / A rotating electron ring
A.B. Langdon and B.F . Lasinski, in : Methods of Computational Physics, Vol. 16, ids ., B. Adler, S . Fernbach and M . Rotenberg (Academic, New York, 1976) p . 327. [6] Y .Z. Yin, R.J. Ying and G. Bekefi, to be published . [7] J . Fischer, D.A. Boyd, A. Cavallo and J. Benson, Rev . Sci . Instr. 54 (1983) 1085 .
[8] B.G . Danly, K.E. Kreischer, W.J . Mulligan and R.J. Temkin, Massachusetts Institute of Technology, Cambridge, Massachusetts, Plasma Fusion Center Report No. PFC/JA-85-9 (1985) ; S.N . Vlasov, L .I . Zagryadskaya and M .I . Petelin, Radio Eng. Electron. Phys. 20 (1975) 14 .
Nuclear Instruments and Methods in Physics Research A250 (1986) 352-356 North-Holland, Amsterdam
MILLIMETER WAVE RADIATION FROM A ROTATING ELECTRON RING SUBJECTED TO AN AZIMUTHALLY PERIODIC WIGGLER MAGNETIC FIELD G. BEKEFI and R.E. SHEFER **
Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of TechnoloU, Cambridge, Massachusetts 02139, USA
W.W. DESTLER
University of Maryland, College Park, Maryland 20742, USA
The generation of millimeter wave radiation (80-180 GHz) caused by the interaction of a rotating electron ring (2 MV, 1.4-3.6 kA, 5 ns) with an azimuthally periodic wiggler magnetic field has been studied experimentally and theoretically, and by computer simulations. Narrow band radiation is observed at power levels exceeding several megawatts.
1. Introduction We report studies of a free electron laser oscillator comprised of a rotating, relativistic electron ring subjected to an azimuthally periodic wiggler magnetic field. We observe narrow band radiation at 88 and 175 GHz for wiggler field periodicities 1. of 6.28 and 3.14 cm, respectively . The results are compared with theoretical predictions and computer simulations . In the experiment [1,2] illustrated in fig. 1 a high quality (energy spread < 1%) rotating electron ring is produced by injecting a hollow nonrotating beam into a narrow magnetic cusp . The hollow beam is generated by field emission from an annular cathode energized by a pulsed, high voltage, high current accelerator (2 MV, 20 kA, 30 ns). The resulting rotating electron ring is guided downstream from the cusp by a uniform axial magnetic field of -- 1.4 kG . The ring is 6 cm in radius, has a duration of - 5 ns, and carries an axial current of 1 .4-3 .6 kA. The electron rotation velocity ve = 0.96 c, and the elec-
Embedded Permanent Magnets
tron axial velocity vz = 0.2c . Thus, in the absence of the wiggler magnetic field, the electron orbits form fairly tight helices. The electron ring propagates within the gap formed by two stainless steel cylinders 5.398 and 6.509 cm in radius . Superimposed on the axial guiding magnetic field is an azimuthally periodic magnetic wiggler field B,, which, near the center of the gap, is primarily radial * This work was supported by the US Department of Energy, the Air Force Office of Scientific Research, and the National Science Foundation . ** Present address : Science Research Laboratory, Inc ., 15 Ward St ., Somerville, Massachusetts 02143, USA
0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Diode Coils Fig. 1 . Experimental arrangement
Wave Guide
G. Bekefi et al. / A rotating electron ring
and is thus transverse to the electron flow velocity, as is the case in conventional linear free electron lasers . The wiggler magnetic field is produced by an assembly of 384 samarium-cobalt bar magnets 0.40 x 0.40 x 4.8 cm3, each having a residual induction of - 9.0 kG . The magnets are positioned behind the grounded stainless steel cylinders and held in place in grooved aluminum holders. To achieve a given periodicity IW , the dipole axes of the magnets are arranged in the Halbach configuration [3]. The axial length of the wiggler is 20 cm . This is achieved by stacking rows of the bar magnets end-to-end . For a wiggler periodicity 1W of 6.28 cm (corresponding to N = 6 periods around the azimuth) the wiggler amplitude BW at the position of the electron ring Ro = 6 cm equals 1300 G. For a periodicity 1. = 3.14 cm (N =12), BW =1000 G. In section 2 of this paper we summarize some of the theoretical considerations and computer simulations . Section 3 gives a brief discription of the experimental results. Conclusions are drawn in section 4.
353
1,5x10 9
0 Fig.
2.
15'
20
25
30
160
150
Growth rate of the FEL instability as a function of 1;
current density = 3.23 A/cm2. Axial beam current density = 0. radiation frequencies :
2. Theory and computer simulations
we (l,m)
= [MIrc/ri (g-1)][1+al2 ] 1/2
X(aA-1)-1},
,
where g = ro/r with r,, as the outer and ri as the inner radius, and a=[2(g-1)/vrm(g+1)]2 . Solving for the crossing points yields the following expression for the
180
m =1 ; ro = 6 .51 cm ; r, = 5 .40 cm ; R o = 5 .84 cm ; v, 1c = 0.95 ; x BW = 750 G; azimuthal beam 92 11 = 4.88 10 9 rad/s; N = 6 ;
w=92 11 {N+[N±(A+aAN 2 -aA2 )
In the theoretical model [4] we assume a thin, tenuous electron ring undergoing pure rotation (the axial velocity is zero) and comprised of monoenergetic electrons with zero energy spread. The rotational velocity vB = d2 1 Ro is perturbed by a radially directed, azimuthally periodic wiggler magnetic field, as a result of which growing electromagnetic modes are excited. (9211 is the relativistic electron cyclotron frequency.) The excitation frequencies and temporal growth rates are derived for the TM I, . family of modes that can be supported in a coaxial waveguide with radii ro and ri. The appropriate dispersion equation is derived for complex frequencies w under the assumption that the axial wave vector k1l of the electromagnetic fields is zero (cutoff condition) . It is found that radiation growth occurs near frequencies corresponding to the crossing point of the cutoff waveguide modes w = wß(1, m) (wc is the cutoff frequency) and the beam modes w = (l + N)011 upshifted by the wiggler periodicity N. This coupling is similar in nature to that which occurs in conventional, linear free electron lasers. For given fixed values of l and m two crossing points occur, one at low frequency, and the other at high frequency. For a narrow gap coaxial waveguide such that (r,, ri )/ro << 1, the cutoff frequency w. for the lth azimuthal and mth radial mode can be approximated by
170
AZIMUTHAL MODE NUMBER
1/21 (2)
where A = [(7rmc)/rl (g -1)
9211)12
.
To obtain the growth
PARTICLE DENSITY 0
x
>N
+9
-9
0 x
0.524 1.047 8 (radians) Fig. 3 . Simulation of the electron density distribution, and of the axial and azimuthal momenta 6 ns after start-up ; ro = 6.509 cm ; r, = 5 .398 cm ; 1 , = 6 .28 cm (N = 6) ; Bw = 750 G~ ; B~ = 1100 G; ve/c = 0 .968 ; azimuthal circulating current density Ja =1 .1 A/cm2. Axial beam current density = 0. IX. RAMAN/GUIDE FIELD FELS
354
G. Bekefi et al. / A rotating electron ring
and the beam mode given by w=kllvll+ (1+N)S2I1 .
w 0
a a 6
9 TIME (ns)
__12
w
(4)
Detailed dispersion equations giving the radiation frequencies and growth rates as a function of v ll and kll have been derived [6]. Maximum growth rate is expected to occur at the tangential intersection of the above two waves, at which point the low and high frequency brandhes merge into a single mode. This takes place when the wave group velocities aw/8k l are equal to v ll , with the result that w-Yllwc(1, m)=YIÎ(1+N)Slll,
0
where yll=[1-(VIIIC)z]-t12 .
a a co
3. Experiments
0
720
Fig. 4. Simulations of the temporal growth, wave number, and frequency spectrum for the z component of the RF electric field . TM family of coaxial waveguide modes 6 ns after start-up. The remaining parameters are the same as those given in the caption to fig. 3. rate of the instability (that is, the imaginary part of w) one must solve the complete dispersion equation [4]. Fig. 2 illustrates the growth rates of the low and high frequency branches as a function of 1, for a fixed value of m =1 . Each point indicates the growth rate of a discrete mode 1. The solid lines merely connect the points . We have also performed a series of computer simulations using MASK, a 2-', -dimensional, fully relativistic particle-in-cell code [5]. In the code a 60° sector of the circular FEL structure is represented by a 15 X 256 mesh and the fields and particle positions are integrated forward in time with successive time steps of 5 X 10 -13 s; 11000 simulation particles have been used. Fig. 3 shows the beam density distribution and particle momenta pZ and pe 6 ns (12000 time steps) after start-up . Fig. 4 illustrates the RF characteristics. The large resonant peaks in the wavenumber and frequency spectra corresponds to the low frequency branch of the FEL instability as given by eq . (2). The high frequency branch has as yet not been identified. Because the growth rate of this branch is expected to be small, many more time steps will probably be required. Hitherto we assumed that the axial electron velocity v 11 and the axial wavenumber k 1l are identically zero . When these conditions are relaxed, one finds from theory that now radiation growth occurs near the crossing points of the waveguide mode given by w2 =k~c Z +wC(1, m)
The radiation generated in the experiments is picked up with a small RF probe in the form of a horn antenna located immediately downstream from the magnetic wiggler (see fig. 1) . A section of waveguide acting as a high pass filter cuts off all radiation below 74 GHz. When the wiggler magnets are removed there is no measurable radiation at frequencies above 74 GHz. With the wiggler magnets in place, strong emission is observed . The radiation intensity is found to be a sensitive function of the current injected into the wiggler . This is illustrated in fig. 5 in which we plot the total RF power detected above 74 GHz, as a function of the axial electron current (this is the current downstream from
F_ 2
3
w
Fa W N
2
x v ti w
0 m a
w 3
0a 0 w Fa a s
0
0
I 2 3 INJECTED AXIAL CURRENT (kA)
4
Fig. 5. Radiated RF power above 74 GHz as a function of injected axial current; 1, = 6.28 m (N = 6) ; Br =1325 G.
G. Bekefi et al. / A rotating electron ring
RF probe through the 20 cm long magnetic wiggler . Fig . 6 shows that the radiation intensity grows quite rapidly with z and reaches a plateau in a distance of - 5 cm . The radiated power spectra for various configurations have been measured using a sensitive grating spectrometer [7], with gratings available in the range 70-200 GHz. The frequency resolution of the spectrometer is typically dw/w = 0 .02, and the insertion loss is in the range 3-5 dB. Fig. 7 shows the measured spectral characteristics for the two wiggler periodicities lw = 6 .28 cm (N = 6) and l w = 3 .14 cm (N = 12). The vertical arrows give the emission frequencies as predicted from eq. (2) . However, we note that the emission frequency is a sensitive function of the various experimental parameters (12~~, r ro , R o ) and the very good agreement between experiment and theory seen in fig . 7 may be somewhat fortuitous .
F z w a w N w 0 m a w 3
0 a
0 w
á a o:
AXIAL DISTANCE Z(cm)
Fig. 6 . Radiated power above 74 GHz, and the spatial wiggler amplitude distribution as a function of axial position ; l w = 6.28 cm (N = 6). Injected axial current =1 .4 kA .
the interaction region as measured in the absence of the wiggler magnets) . We see from fig. 5 that by increasing the current by a factor of approximately 2 .5, the radiation intensity increases by about a factor of one hundred . We estimate that at the injected current of 3 .6 kA, the RF power is in excess of several megawatts, and may be as high as several tens of megawatts . The rapid increase in RF power with current suggests that we are witnessing phenomena associated with oscillation onset, and that the threshold injection current is in the vicinity of 1 kA . The growth of the radiated power (at constant injection current), as a function of the axial position z within the interaction region is measured by moving our 200
w á
4 . Conclusions In this paper we have presented a summary of recent measurements, theoretical studies and computer simulations of the circular free electron laser employing a rotating, relativistic electron ring subjected to an azimuthally periodic wiggler magnetic field . The studies indicate that the production of millimeter wave radiation is consistent with theoretical expectations . Although the efficiency of conversion of electron beam energy to radiation is currently low (less than 1%), it is not at all clear how efficiently the radiation is being coupled out of the interaction region . This region represents a highly overmoded, quasi-optical coaxial waveguide, and when the azimuthal wavenumber 1 is large, as it is in our experiments (see fig . 2), one is dealing with RF modes of the "whispering gallery" type. Coupling energy out of such a mode configuration has received some attention [8]. The issues are similar to those encountered in coupling energy from an overmoded millimeter wave gyrotron [8].
References
E a
Z 0
35 5
100
3
0 U
0 70
90
110 170 130 150 RADIATION FREQUENCY w/2V (GHZ)
190
Fig. 7 . Radiated power spectra for two wiggler periodicities N = 6 and 12. The vertical arrows are predictions from eq . (2). Injected axial current =1.4 kA.
[1] G . Bekefi, R .E . Shefer and W.W . Destler, Appl. Phys . Lett . 44 (1984) 280 . [2] W .W. Destler, F.M . Aghamir, D.A. Boyd, G . Bekefi, R.E. Shefer and Y .Z . Yin, Phys . Fluids 28 (1985) 1962. [3] K. Halbach, Lawrence Berkeley Laboratory, University of California Accelerator and Fusion Research Division Report No. í,)3L11393 (August 1980) ; IEEE Trans . Nucl . Sci. NS-26 (1979) 3882 . [4] Y .Z . Yin and G. Bekefi, Phys. Fluids 28 (1985) 1186. [5] A . Palevsky, G. Bekefi and A .T. Drobot, J . Appl . Phys . 52 (1981) 4938 ; J .P. Boris, in : Proc . Fourth Conf . on Numerical Simulation of Plasmas, eds ., J .P. Boris and R .A . Shanny (Stock 08510059, US GPO, Washington, D .C., 1971) p . 3; IX. RAMAN/GUIDE FIELD FELS
356
G. Bekefi et al. / A rotating electron ring
A.B. Langdon and B.F . Lasinski, in : Methods of Computational Physics, Vol. 16, ids ., B. Adler, S . Fernbach and M . Rotenberg (Academic, New York, 1976) p . 327. [6] Y .Z. Yin, R.J. Ying and G. Bekefi, to be published . [7] J . Fischer, D.A. Boyd, A. Cavallo and J. Benson, Rev . Sci . Instr. 54 (1983) 1085 .
[8] B.G . Danly, K.E. Kreischer, W.J . Mulligan and R.J. Temkin, Massachusetts Institute of Technology, Cambridge, Massachusetts, Plasma Fusion Center Report No. PFC/JA-85-9 (1985) ; S.N . Vlasov, L .I . Zagryadskaya and M .I . Petelin, Radio Eng. Electron. Phys. 20 (1975) 14 .