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High-power two-stage FEL oscillator operating in the trapped particle mode
154
Nuclear Instruments and Methods m Physics Research A237 (1985) 154-157 North-Holland, Amsterdam
HIGH-POWER TWO-STAGE FEL OSCILLATOR OPERATING IN THE TRAPPED PARTICLE MODE J.A . PASOUR, P. SPRANGLE, C.M . TANG and C.A . KAPETANAKOS Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA
A two-stage FEL oscillator is proposed as a high-power source of infrared radiation Such a device is attractive because it employs a relatively low-energy electron beam, which can significantly reduce the size and cost of the system . The steady-state parameters for a 10-pin, 750-MW FEL are presented, and the start-up, resonator configuration and electron beam requirements are discussed . Although there are several significant technical issues and further analysis is required, it appears as if the approach is feasible . 1 . Introduction A two-stage free electron laser (FEL) uses the output of a conventional FEL, which comprises the first stage, as an electromagnetic wiggler for the second stage [1,2]. The major advantage of such a device is the additional Doppler frequency shift that is obtained . Since the same electron beam is used for both stages, the second stage radiation wavelength is A2 = X w /8y°, where X, is the first stage wiggler period and y is the usual relativistic factor. Consequently, a relatively low-energy electron beam can be used to generate infrared (IR) or even shorter wavelength radiation. In this paper, we will examine the feasibility of using a two-stage FEL oscillator to generate high power (> 100 MW) IR radiation. The first stage of such a device can initially operate in the high-gain collective (Raman) regime. Consequently, the pump field for the second stage is established very quickly . The second stage is designed for steady-state operation in the trapped particle mode . An axial electric field is applied over the interaction length of the second stage for efficiency enhancement [3,4]. With a 1-m-long first and second stage and an accelerating electric field of 2 .5 kV/cm in the second stage, a 10-um FEL having an output power of 0.75 GW can be designed . The stored power to each of the stages is in excess of 10 GW, and the trapping potential m the second stage is 4% of the beam energy . The development of a two-stage FEL oscillator requires careful consideration of some important technical issues . First, to achieve such high radiation power with a relatively low energy electron beam, a large beam current is required . Thus, the generation and transport of a sufficiently high quality beam are somewhat more difficult than in existing FEL sources. In addition, the resonator must be carefully designed in order to avoid mirror damage and still maintain a suitably short light path . Finally, the start-up time needed to reach the 0168-9002/85/$03 .30 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
steady-state in the second stage must be kept to a minimum. Although these problems are significant, they are probably not insurmountable. 2. Steady-state operation Assuming for the moment that the beam pulse is long enough to reach a steady-state, we begin by establishing the parameters associated with steady-state operation. The beating of the first and second stage radiation fields creates a trapping potential 0,2 in the second stage. Denoting first or second stage parameters with a subscript 1 or 2, respectively, the relative depth of this potential is [5] eoc~ -_ ymc`
DE)2-4iata2/(1+a~+a2)11
/2,
where a,= eA,/mc 2 and A, is the amplitude of the vector potential of the radiation fields . The transverse velocity induced by these fields is ß, = a,/y, so we may write 4E ] ( E ) =4 Y~2(Plß2) /2, 2 and in order to trap the beam electrons we must have ('~"E/E)2 > ,~"y/Y, where dy/y is the fractional beam energy spread. In terms of the steady-state power P5, stored in the resonator 2eX, Pg, 1/2 aymc 2w, ( c )
where a, is the radiation wavelength and w, is the radiation spot size assuming a Gaussian beam with intensity I,=I., exp(-2r,2 /w,2 ). The phase at which the particles are in resonance with the trapping potential well is determined by the radiation power density and the accelerating electric
15 5
J . A Pasour et al / High -power two-stage FEL oscillator
field used for efficiency enhancement. The resonant phase 4 is given by [4] cos
ymc3 mc 3 R- 2eX, awlw2(PS1PSz)
1/23 4 az
az
where 0a2 is the potential of the accelerating electric field. The second stage efficiency is 112 = Pot/Pb, where Pot = (1 - R 2 ) P52 is the output power, Pb is the input beam power, and R 2 is the second stage output mirror reflectivity . In the steady-state the accelerating potential resupplies energy to the electrons equal to that lost to the radiation field. Therefore, rl 2 is Simply e 112 - ymc 2 [ ' pa2 ( L2) - Oa2 ( 0 )l f2 , where f2 is the fraction of the electrons trapped in the potential well and L2 is the length of the second stage interaction region . From eqs. (2)-(5) we can write 112
2L2z
f192f2 COS Y'R,
or m terms of the trapping potential 712
7rL2 f2 32~ zY
2
COS 'PR
( AE E
I2 . )2 *
Table 1 Steady-state parameters of a two-stage FEL oscillator operating at 10 lam Parameter
Electron beam Electron energy Beam current /,, Beam radius r h First stage FEL Wiggler period a w Wiggler field B, Interaction length L, Radiation wavelength Radiation waist wo , Efficiency il, Effective mirror reflectively R, Stored power P,, Second stage FEL Interaction length L 2 Accelerating electric field Eat Radiation waist woe Fractional trapping potential ("E /02 at entrance Fractional trapping potential (~E/02 at exit Efficiency 112 Effective mirror reflectivity R 2 Stored power P,2 Output power P.2
Value 2 .5 MeV 3 kA 0 25 cm 5 cm 1 .4 kG
1 .0 m 1 .4 mm 1.1 cm
26% 0 .95 30 GW
lm 2.5 kV/cm 0 .4 cm 3 .8% 7 .0% 8 .3% 0 .95 15 GW 0 .75 GW
The first stage stored power is Psi =711Pb/(1 - R1), where rl l is the efficiency and (1 - R 1 ) the net resonator loss, i.e., R 1 is the effective mirror reflectivity. Since the first stage operates in the Raman regime, the intrinsic efficiency is [6] l
W
t/2
gyZ1rb(YI
The electron beam power is Pb = vym 2 c 5/e 2 , where v = I (kA)/17 is the Budker parameter, so from eqs. (2), (3) and (7) we can write _ 64vy 2 (
AE E
2
wlw 2
L2?2f2 COS 9'R
1, 1
)1/2
27r 3 /2
x [( 1- R1)( 1- R2)1 In eq . (9) we have made the approximations yr = y and 2 X1 = 4Y ~z . The above equations can now be used to generate a set of design parameters, listed in table 1, for a highpower 10-p.m FEL. A 2.5 MeV electron beam is required to obtain a sufficiently large Doppler upshift, and we have chosen a current of 3 kA in order to have sufficiently large beam power. We will discuss later the resonator and beam quality requirements imposed by these parameters . 3. Start-up Because the first stage of the device will initially operate in the high gain, cold beam, collective regime, Psl increases rapidly and reaches saturation within a few passes . The growth rate for this regime is [6] ) 1/a (10) FI = (iryz1Ft)1/2( Bw/(rb~w)1/2, Y~ where Fl is the filling factor associated with the first stage, /3w, is the perpendicular velocity due to the wiggler, and r b is the electron beam radius. Denoting the minimum radiation spot radius by woe and the radius at the end of the interaction region by w, l , the filling factor can be approximated by F1 =0 .5I( rb
w01
2
)
+( rb
wLl )21
.
The first stage can operate in the trapped particle mode after P51 becomes large enough to trap the electrons; i.e ., when evil /ymc 2 > AY/y . For the parameters in table 1, e¢i,l/ymc 2 > 20% when P51 = 1 GW. Also, Fl = 0.03 and the power gain per gas is Gl = 220. The second stage start-up is a more serious issue. The initial second stage gain is much smaller than that of the first stage, so resonator losses and spontaneous emission power must be accurately known in order to I. THEORY
15 6
JA Pasour et al / High-power two-stage FEL oscillator
calculate a realistic start-up time. In order to get an estimate of this time, we will make some assumptions which will later have to be verified numerically . First, we assume that the second stage initially operates in the high-gain Compton regime . This regime [6] is characterized by a thermal beam having an energy spread 4 113 . 2 d 7 F1711 v »7 .6x10 (12) Y 2 ~(Y) ( rh ) I-R1 , The spatial growth rate can be written as [6] v 24X2 711 3-y -2 . (13) Y r 4 1 - RI ( y ) For the parameters given in table 1 and assuming a total beam energy spread of 2%, F2 = 0.4 and the power gain per pass G2 = exp(2 F2 L2) = 1 .5 . A large number of passes will be required to build up the radiation to a level at which significant trapping will occur. If we also assume that the spontaneous emission power is 10 mW and the total resonator losses are 5%, we require 56 passes to increase Ps2 to 10 MW . If in fact the turn-on time is too long for the available electron pulse duration, it can be reduced to an acceptable level by seeding the resonator with a modest quantity of 10 p,m radiation . FIF2
Fig. 1 . Schematic of two-stage FEL oscillator using grazing incidence mirrors. employing a long pulse intense e-beam .
I"=5 .5
4. Resonator requirements At the large stored power levels given in table 1, mirror damage is a mayor issue. The damage threshold for multiple shots of 10 .6 pin radiation on normal incidence copper mirrors is [7] Im - 150/ Jt p (Its)
MW/cm' .
The Rayleigh lengths of the radiation envelopes are ZRi = 27 cm and ZR2 = 5 m, so in order for the radiation to expand to an acceptably low power density for normal incidence mirrors and a 1 Its pulse, resonator lengths Hl = 4 m and H2 = 140 m are required. Obviously, such a large value of H2 is not acceptable given the few ,us pulse duration of the electron beam. An attractive alternative is to use a ring resonator for the second stage, as shown in fig. 1 . The grazing incidence mirrors in the resonator present a larger surface area to the radiation beam . In addition, the damage threshold for radiation polarized perpendicular to the plane of incidence increases dramatically at grazing incidence [8]. Therefore, a relatively compact resonator can be designed. The resonator parameters for the design shown in fig. 1 are given in table 2. Radiation can be coupled out of the resonator through a hole in one of the larger mirrors. If it is necessary to seed the resonator, the seed radiation can be introduced through a hole in the other large mirror without significantly increasing the resonator losses .
Table 2 Ring resonator parameters Parameter
First stage Cavity length Rayleigh length ZRi Spot size at mirror w Li Power flux on mirror Second stage Rayleigh length ZR2 Glancing incidence mirror spacing Total resonator light path length Angle of incidence Spot size at glancing incidence rrurror Power flux on rrurror Damage threshold [81
Value 4.4 m
27 cm 92 cm
110 MW/cm Z 5m 55m 15 m 80 , 0.5 cm
2.6 GW/cmZ 4 .5 GW/cmZ
5. Electron beam requirements The most stringent requirement on beam quality arises from the 4% trapping potential in the second stage . The axial beam energy spread must be kept smaller than this value in order to trap a large fraction of the beam electrons. The beam energy spread Ay/y consists of various contributions, but we will primarily address those associated with the beam emittance and space charge . The contribution from wiggler field gradients is not as important in the second stage where the wiggler field is the first stage radiation field, which has a cross section large compared to the electron beam . The total energy spread due to emittance and space charge is z 2 _ (14) 2 ~ (~rrb/ J 2+ 1Y/ ' where c n =ßyr h(0)7r is the normalized emittance. The space charge term represents the radial potential variation across the beam . For the parameters in table 1, v/y = 3% . However, the axial energy spread due to space charge can in principal be eliminated by propa-
J.A Pasour et al / High-power two-stage FEL oscillator
gating the beam m a Brillouin flow configuration, in which case the axial velocity is constant across the beam . Assuming the electron beam is born in a magnetic field free region, the axial magnetic field required to establish Brillouin flow is _ 2~ inc2 ( u i/2 15 rb 2 e \y) -
For the parameters of table 1, Bz = 3.4 kG . Even if true Brillouin flow cannot be realized, the variation in axial velocity can be kept much smaller than the total spread by applying this axial field. The emittance term represents an inherent beam divergence and cannot be eliminated . An empirical expression relating emittance to beam current t b is the Lawson-Penner condition [9], which is EnP=
aiJb (kA)
7r
rad cm .
For thermionic cathodes operating at current densities of < 10 A/cmZ, a = 0.1-0.3 . For the beam parameters in table 1, we must have E n = 0.05 rad cm, or a = 0.03, in order to achieve (Dy/y)E=2% . Consequently, we must reduce the emittance by a factor of 3-10 below the Lawson-Penner value. Recent experimental work at several laboratories has produced beams with E n << ELP . These results have been obtained using higher current density cathodes which are usually immersed in an axial magnetic field. The beam diodes or electron guns are computer designed for optimum beam quality, and good agreement between experimental and numerical results has been achieved . In particular, recent experiments at the Naval Research Laboratory [10] and at Los Alamos National Laboratory [111 have achieved a < 0.03. These experiments use high-current-density, field-emission cathodes and operate at 5 kA/cmZ and 400 kA/cmZ, respectively . The NRL beam has y = 4 and the LANL beam has y = 8. (The LANL beam is annular, hence the large current density.) Thus, high current beams with quality in excess of our requirements have already been generated. Although field emission cathodes work well at these high current densities for short pulses ( < 100 ns), a different cathode type will probably be required for multi-ps operation. There is currently a great deal of interest m developing such cathodes, because several applications (including other FEL proposals) require
15 7
the same high beam quality needed for the two-stage FEL. Advanced thermionic and photoemissive cathodes have recently been proposed as a means of achieving the required beam quality. These cathodes will furthermore be capable of long pulse operation. 6. Conclusion A two-stage FEL oscillator has several very attractive features which result from the relatively low energy electron beam . The device is compact and would be considerably less expensive than a comparable single-stage FEL employing a high-energy beam . Although several important technical issues must be resolved, it appears that the two-stage FEL is a feasible high-power IR source . It should be noted that the parameters in table 1 are not optinuzed and should not be regarded as a firm design . In order to carefully design an actual experiment and to determine the limitations of the device, more detailed analytical and numerical work is required . Based on the positive conclusions of this preliminary work, we are extending our analysis . References [1] [2] [31 [4] [5] [6] [7] [8] [91 [10] [II]
L R. Elias, Phys. Rev. Lett. 42 (1979) 977. P. Sprangle and R A. Smith, Phys . Rev. A21 (1980) 293. A.T . Lm, Phys . Fluids 24 (1981) 316 P. Sprangle and C M. Tang, AIAA Journal 19 (1981) 1164. N.M . Kroll, P L Morton and M.N Rosenbluth, IEEE J. Quantum Electron . QE-17 (1981) 1436. P. Sprangle, R.A . Smith and V.L . Granatstem, m- Infrared and Millimeter Waves, vol . 1, ed ., K.J Button (Acaderruc Press, New York, London, 1979) p. 279. Laser Induced Damage in Optical Materials, Proc . of the Boulder Damage Symposium, Boulder, CO, 1981 (NBS Special Publication 638, 1983). P.B. Mumola and D.C Jordan, Proc . of Los Alamos Conf. on Optics, 1981, SPIE 288 (1982) p. 54 . V.K. Neil, Jason Tech Rep. JSR-79-10, SRI International, Arlington, VA (1979) . R.H . Jackson et al ., IEEE J. Quantum Electron. QE-19 (1983) 346. R.L Sheffield, M.D . Montgomery, J.V Parker, K.B . Riepe and S. Singer, J. Appl . Phys 53 (1982) 5408 .
I. THEORY
Nuclear Instruments and Methods m Physics Research A237 (1985) 154-157 North-Holland, Amsterdam
HIGH-POWER TWO-STAGE FEL OSCILLATOR OPERATING IN THE TRAPPED PARTICLE MODE J.A . PASOUR, P. SPRANGLE, C.M . TANG and C.A . KAPETANAKOS Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375, USA
A two-stage FEL oscillator is proposed as a high-power source of infrared radiation Such a device is attractive because it employs a relatively low-energy electron beam, which can significantly reduce the size and cost of the system . The steady-state parameters for a 10-pin, 750-MW FEL are presented, and the start-up, resonator configuration and electron beam requirements are discussed . Although there are several significant technical issues and further analysis is required, it appears as if the approach is feasible . 1 . Introduction A two-stage free electron laser (FEL) uses the output of a conventional FEL, which comprises the first stage, as an electromagnetic wiggler for the second stage [1,2]. The major advantage of such a device is the additional Doppler frequency shift that is obtained . Since the same electron beam is used for both stages, the second stage radiation wavelength is A2 = X w /8y°, where X, is the first stage wiggler period and y is the usual relativistic factor. Consequently, a relatively low-energy electron beam can be used to generate infrared (IR) or even shorter wavelength radiation. In this paper, we will examine the feasibility of using a two-stage FEL oscillator to generate high power (> 100 MW) IR radiation. The first stage of such a device can initially operate in the high-gain collective (Raman) regime. Consequently, the pump field for the second stage is established very quickly . The second stage is designed for steady-state operation in the trapped particle mode . An axial electric field is applied over the interaction length of the second stage for efficiency enhancement [3,4]. With a 1-m-long first and second stage and an accelerating electric field of 2 .5 kV/cm in the second stage, a 10-um FEL having an output power of 0.75 GW can be designed . The stored power to each of the stages is in excess of 10 GW, and the trapping potential m the second stage is 4% of the beam energy . The development of a two-stage FEL oscillator requires careful consideration of some important technical issues . First, to achieve such high radiation power with a relatively low energy electron beam, a large beam current is required . Thus, the generation and transport of a sufficiently high quality beam are somewhat more difficult than in existing FEL sources. In addition, the resonator must be carefully designed in order to avoid mirror damage and still maintain a suitably short light path . Finally, the start-up time needed to reach the 0168-9002/85/$03 .30 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
steady-state in the second stage must be kept to a minimum. Although these problems are significant, they are probably not insurmountable. 2. Steady-state operation Assuming for the moment that the beam pulse is long enough to reach a steady-state, we begin by establishing the parameters associated with steady-state operation. The beating of the first and second stage radiation fields creates a trapping potential 0,2 in the second stage. Denoting first or second stage parameters with a subscript 1 or 2, respectively, the relative depth of this potential is [5] eoc~ -_ ymc`
DE)2-4iata2/(1+a~+a2)11
/2,
where a,= eA,/mc 2 and A, is the amplitude of the vector potential of the radiation fields . The transverse velocity induced by these fields is ß, = a,/y, so we may write 4E ] ( E ) =4 Y~2(Plß2) /2, 2 and in order to trap the beam electrons we must have ('~"E/E)2 > ,~"y/Y, where dy/y is the fractional beam energy spread. In terms of the steady-state power P5, stored in the resonator 2eX, Pg, 1/2 aymc 2w, ( c )
where a, is the radiation wavelength and w, is the radiation spot size assuming a Gaussian beam with intensity I,=I., exp(-2r,2 /w,2 ). The phase at which the particles are in resonance with the trapping potential well is determined by the radiation power density and the accelerating electric
15 5
J . A Pasour et al / High -power two-stage FEL oscillator
field used for efficiency enhancement. The resonant phase 4 is given by [4] cos
ymc3 mc 3 R- 2eX, awlw2(PS1PSz)
1/23 4 az
az
where 0a2 is the potential of the accelerating electric field. The second stage efficiency is 112 = Pot/Pb, where Pot = (1 - R 2 ) P52 is the output power, Pb is the input beam power, and R 2 is the second stage output mirror reflectivity . In the steady-state the accelerating potential resupplies energy to the electrons equal to that lost to the radiation field. Therefore, rl 2 is Simply e 112 - ymc 2 [ ' pa2 ( L2) - Oa2 ( 0 )l f2 , where f2 is the fraction of the electrons trapped in the potential well and L2 is the length of the second stage interaction region . From eqs. (2)-(5) we can write 112
2L2z
f192f2 COS Y'R,
or m terms of the trapping potential 712
7rL2 f2 32~ zY
2
COS 'PR
( AE E
I2 . )2 *
Table 1 Steady-state parameters of a two-stage FEL oscillator operating at 10 lam Parameter
Electron beam Electron energy Beam current /,, Beam radius r h First stage FEL Wiggler period a w Wiggler field B, Interaction length L, Radiation wavelength Radiation waist wo , Efficiency il, Effective mirror reflectively R, Stored power P,, Second stage FEL Interaction length L 2 Accelerating electric field Eat Radiation waist woe Fractional trapping potential ("E /02 at entrance Fractional trapping potential (~E/02 at exit Efficiency 112 Effective mirror reflectivity R 2 Stored power P,2 Output power P.2
Value 2 .5 MeV 3 kA 0 25 cm 5 cm 1 .4 kG
1 .0 m 1 .4 mm 1.1 cm
26% 0 .95 30 GW
lm 2.5 kV/cm 0 .4 cm 3 .8% 7 .0% 8 .3% 0 .95 15 GW 0 .75 GW
The first stage stored power is Psi =711Pb/(1 - R1), where rl l is the efficiency and (1 - R 1 ) the net resonator loss, i.e., R 1 is the effective mirror reflectivity. Since the first stage operates in the Raman regime, the intrinsic efficiency is [6] l
W
t/2
gyZ1rb(YI
The electron beam power is Pb = vym 2 c 5/e 2 , where v = I (kA)/17 is the Budker parameter, so from eqs. (2), (3) and (7) we can write _ 64vy 2 (
AE E
2
wlw 2
L2?2f2 COS 9'R
1, 1
)1/2
27r 3 /2
x [( 1- R1)( 1- R2)1 In eq . (9) we have made the approximations yr = y and 2 X1 = 4Y ~z . The above equations can now be used to generate a set of design parameters, listed in table 1, for a highpower 10-p.m FEL. A 2.5 MeV electron beam is required to obtain a sufficiently large Doppler upshift, and we have chosen a current of 3 kA in order to have sufficiently large beam power. We will discuss later the resonator and beam quality requirements imposed by these parameters . 3. Start-up Because the first stage of the device will initially operate in the high gain, cold beam, collective regime, Psl increases rapidly and reaches saturation within a few passes . The growth rate for this regime is [6] ) 1/a (10) FI = (iryz1Ft)1/2( Bw/(rb~w)1/2, Y~ where Fl is the filling factor associated with the first stage, /3w, is the perpendicular velocity due to the wiggler, and r b is the electron beam radius. Denoting the minimum radiation spot radius by woe and the radius at the end of the interaction region by w, l , the filling factor can be approximated by F1 =0 .5I( rb
w01
2
)
+( rb
wLl )21
.
The first stage can operate in the trapped particle mode after P51 becomes large enough to trap the electrons; i.e ., when evil /ymc 2 > AY/y . For the parameters in table 1, e¢i,l/ymc 2 > 20% when P51 = 1 GW. Also, Fl = 0.03 and the power gain per gas is Gl = 220. The second stage start-up is a more serious issue. The initial second stage gain is much smaller than that of the first stage, so resonator losses and spontaneous emission power must be accurately known in order to I. THEORY
15 6
JA Pasour et al / High-power two-stage FEL oscillator
calculate a realistic start-up time. In order to get an estimate of this time, we will make some assumptions which will later have to be verified numerically . First, we assume that the second stage initially operates in the high-gain Compton regime . This regime [6] is characterized by a thermal beam having an energy spread 4 113 . 2 d 7 F1711 v »7 .6x10 (12) Y 2 ~(Y) ( rh ) I-R1 , The spatial growth rate can be written as [6] v 24X2 711 3-y -2 . (13) Y r 4 1 - RI ( y ) For the parameters given in table 1 and assuming a total beam energy spread of 2%, F2 = 0.4 and the power gain per pass G2 = exp(2 F2 L2) = 1 .5 . A large number of passes will be required to build up the radiation to a level at which significant trapping will occur. If we also assume that the spontaneous emission power is 10 mW and the total resonator losses are 5%, we require 56 passes to increase Ps2 to 10 MW . If in fact the turn-on time is too long for the available electron pulse duration, it can be reduced to an acceptable level by seeding the resonator with a modest quantity of 10 p,m radiation . FIF2
Fig. 1 . Schematic of two-stage FEL oscillator using grazing incidence mirrors. employing a long pulse intense e-beam .
I"=5 .5
4. Resonator requirements At the large stored power levels given in table 1, mirror damage is a mayor issue. The damage threshold for multiple shots of 10 .6 pin radiation on normal incidence copper mirrors is [7] Im - 150/ Jt p (Its)
MW/cm' .
The Rayleigh lengths of the radiation envelopes are ZRi = 27 cm and ZR2 = 5 m, so in order for the radiation to expand to an acceptably low power density for normal incidence mirrors and a 1 Its pulse, resonator lengths Hl = 4 m and H2 = 140 m are required. Obviously, such a large value of H2 is not acceptable given the few ,us pulse duration of the electron beam. An attractive alternative is to use a ring resonator for the second stage, as shown in fig. 1 . The grazing incidence mirrors in the resonator present a larger surface area to the radiation beam . In addition, the damage threshold for radiation polarized perpendicular to the plane of incidence increases dramatically at grazing incidence [8]. Therefore, a relatively compact resonator can be designed. The resonator parameters for the design shown in fig. 1 are given in table 2. Radiation can be coupled out of the resonator through a hole in one of the larger mirrors. If it is necessary to seed the resonator, the seed radiation can be introduced through a hole in the other large mirror without significantly increasing the resonator losses .
Table 2 Ring resonator parameters Parameter
First stage Cavity length Rayleigh length ZRi Spot size at mirror w Li Power flux on mirror Second stage Rayleigh length ZR2 Glancing incidence mirror spacing Total resonator light path length Angle of incidence Spot size at glancing incidence rrurror Power flux on rrurror Damage threshold [81
Value 4.4 m
27 cm 92 cm
110 MW/cm Z 5m 55m 15 m 80 , 0.5 cm
2.6 GW/cmZ 4 .5 GW/cmZ
5. Electron beam requirements The most stringent requirement on beam quality arises from the 4% trapping potential in the second stage . The axial beam energy spread must be kept smaller than this value in order to trap a large fraction of the beam electrons. The beam energy spread Ay/y consists of various contributions, but we will primarily address those associated with the beam emittance and space charge . The contribution from wiggler field gradients is not as important in the second stage where the wiggler field is the first stage radiation field, which has a cross section large compared to the electron beam . The total energy spread due to emittance and space charge is z 2 _ (14) 2 ~ (~rrb/ J 2+ 1Y/ ' where c n =ßyr h(0)7r is the normalized emittance. The space charge term represents the radial potential variation across the beam . For the parameters in table 1, v/y = 3% . However, the axial energy spread due to space charge can in principal be eliminated by propa-
J.A Pasour et al / High-power two-stage FEL oscillator
gating the beam m a Brillouin flow configuration, in which case the axial velocity is constant across the beam . Assuming the electron beam is born in a magnetic field free region, the axial magnetic field required to establish Brillouin flow is _ 2~ inc2 ( u i/2 15 rb 2 e \y) -
For the parameters of table 1, Bz = 3.4 kG . Even if true Brillouin flow cannot be realized, the variation in axial velocity can be kept much smaller than the total spread by applying this axial field. The emittance term represents an inherent beam divergence and cannot be eliminated . An empirical expression relating emittance to beam current t b is the Lawson-Penner condition [9], which is EnP=
aiJb (kA)
7r
rad cm .
For thermionic cathodes operating at current densities of < 10 A/cmZ, a = 0.1-0.3 . For the beam parameters in table 1, we must have E n = 0.05 rad cm, or a = 0.03, in order to achieve (Dy/y)E=2% . Consequently, we must reduce the emittance by a factor of 3-10 below the Lawson-Penner value. Recent experimental work at several laboratories has produced beams with E n << ELP . These results have been obtained using higher current density cathodes which are usually immersed in an axial magnetic field. The beam diodes or electron guns are computer designed for optimum beam quality, and good agreement between experimental and numerical results has been achieved . In particular, recent experiments at the Naval Research Laboratory [10] and at Los Alamos National Laboratory [111 have achieved a < 0.03. These experiments use high-current-density, field-emission cathodes and operate at 5 kA/cmZ and 400 kA/cmZ, respectively . The NRL beam has y = 4 and the LANL beam has y = 8. (The LANL beam is annular, hence the large current density.) Thus, high current beams with quality in excess of our requirements have already been generated. Although field emission cathodes work well at these high current densities for short pulses ( < 100 ns), a different cathode type will probably be required for multi-ps operation. There is currently a great deal of interest m developing such cathodes, because several applications (including other FEL proposals) require
15 7
the same high beam quality needed for the two-stage FEL. Advanced thermionic and photoemissive cathodes have recently been proposed as a means of achieving the required beam quality. These cathodes will furthermore be capable of long pulse operation. 6. Conclusion A two-stage FEL oscillator has several very attractive features which result from the relatively low energy electron beam . The device is compact and would be considerably less expensive than a comparable single-stage FEL employing a high-energy beam . Although several important technical issues must be resolved, it appears that the two-stage FEL is a feasible high-power IR source . It should be noted that the parameters in table 1 are not optinuzed and should not be regarded as a firm design . In order to carefully design an actual experiment and to determine the limitations of the device, more detailed analytical and numerical work is required . Based on the positive conclusions of this preliminary work, we are extending our analysis . References [1] [2] [31 [4] [5] [6] [7] [8] [91 [10] [II]
L R. Elias, Phys. Rev. Lett. 42 (1979) 977. P. Sprangle and R A. Smith, Phys . Rev. A21 (1980) 293. A.T . Lm, Phys . Fluids 24 (1981) 316 P. Sprangle and C M. Tang, AIAA Journal 19 (1981) 1164. N.M . Kroll, P L Morton and M.N Rosenbluth, IEEE J. Quantum Electron . QE-17 (1981) 1436. P. Sprangle, R.A . Smith and V.L . Granatstem, m- Infrared and Millimeter Waves, vol . 1, ed ., K.J Button (Acaderruc Press, New York, London, 1979) p. 279. Laser Induced Damage in Optical Materials, Proc . of the Boulder Damage Symposium, Boulder, CO, 1981 (NBS Special Publication 638, 1983). P.B. Mumola and D.C Jordan, Proc . of Los Alamos Conf. on Optics, 1981, SPIE 288 (1982) p. 54 . V.K. Neil, Jason Tech Rep. JSR-79-10, SRI International, Arlington, VA (1979) . R.H . Jackson et al ., IEEE J. Quantum Electron. QE-19 (1983) 346. R.L Sheffield, M.D . Montgomery, J.V Parker, K.B . Riepe and S. Singer, J. Appl . Phys 53 (1982) 5408 .
I. THEORY