- Email: [email protected]
What limits the wavelength of an FEL? Challenge at the shortest wavelength lasing limit of linac-based FELs using the FELI linac with a thermionic gun
Nuclear Instruments and Methods in Physics Research A 393 (1997)230-233
NUCLEAR
INSTRUMENTS & METHOOS IN PHYSICS RESEARCH
ELSEVIER
What limits the wavelength of an FEL? Challenge at the shortest wavelength lasing limit of linac-based FELs using the FELI linac with a thermionic gun Takio Tomimasu* Free Electron Laser Research Institute, Inc, (FELI)), 2-9-5, Tsuda-Yamate,
Hirakata,
Osaka 573-01, Japan
Abstract
We have demonstrated that a medium-emittance (26~1 mm mrad), medium-current (60A), 24 ps pulse 155 MeV electron beam from the FELI linac with a thermionic gun allows free electron laser (FEL) oscillations at 0.28-0.36 pm. The peak and average FEL powers are 1.8 MW and 4 mW at 0.35 lm. Gain estimation and effects of electron beam quality and filling factor on gain are also discussed. Experimental verification of gain estimates and the criteria on the electron beam quality and wavelength limit due to photon diffraction are tested with our data from visible- and ultraviolet-FEL oscillations.
1. Introduction
It has been said that lasing at ultraviolet frequencies cannot be achieved by using an electron linac with a thermionic gun, because of its large beam emittance which builds up in the bunching process from the thermionic gun to the linac. Theory can describe the effect which is caused by photon diffraction. It depends on the electron beam quality and leads to a wavelength limit for free electron laser operation [l-4]. The empirical Lawson-Penner expression gives the normalized beam emittance E, = 1.6 I(A) ‘I2 10m4m.rad for an RF-linac with a thermionic gun, where I(A) is the peak current of RF-linac [S]. However, the FELI linac with a thermionic gun was carefully designed to reduce the emittance growth in the bunching process from the thermionic gun to the buncher and achieved first lasing at 0.34-0.35 pm using a 144 MeV electron beam on 26 December 1995 and at 0.28-0.29 pm using a 155 MeV electron beam on 14 April 1996 [6], as predicted at the FEL ‘95 Conference
UI. This paper describes (1) how the available small signal gain depends on the electron beam quality, (2) effects of
the filling factor on gain reduction, (3) criteria for electron beam quality and FEL wavelength limit and (4) experimental verification of gain estimates and these criteria.
2. Small signal gain and electron beam quality The small signal gain is reviewed for an electron beam passing through a planar undulator with the period length A,, the period number N and the magnetic field Bo. When the beam is continuous and the beam emittance and energy spread are negligibly small, the gain GF” for such an ideal beam is given by the following equation [S]: G?’ = {J,(O - 31(5)}‘(Io/377)Jnn,N2 x (K2/2)/( 1 +
(1)
where I0 is the peak current of electron micropulses, 3, is the FEL wavelength and other parameters are defined as follows: 5 = (l/4)K2/(1 + K2/2), K = 93.4&(T) n,(m). A gain reduction factor C = C,C,C,C, was estimated for pulse length effect C,, for energy spread C, and for the beam emittance C,, C’,,by many workers, for the electron beam with a normalized beam emittance E. and an energy spread cer where oe is the standard deviation [9]. The GF” for the practical electron beam is given as follows:
*Tel.: + 81 720 96 0414; fax: [email protected].
+ 81 720 96 0421; e-mail:
0168-9002/97/$17.00 Copyright PII SO168-9002(97)00479-S
1997 Elsevier Science B.V. All rights reserved
0
P/2)3’2,
G;“=G:“CCCC. E e X i
(2)
231
T TomimasulNucl. Instr. and Meth. in Ph.vs. Rex A 393 (19971 230-233
Table 1 Main parameters of optical cavity for the FEL laciliry 3 Type
Optical Mode
Length Rayleigh length y parameter
6.718 m 2.0 m -0.44 - 0.49 4.656 m 4.500 m Multilayer of Ta,0,/Si02 99.6% at 0.6 pm 0.4”/0
Mirror curvature
0
0.2
0.4
0.6
ENERGY SPREAD
0.8
1
1.2
Mirror type Reflection rate Transmission rate
oe (%)
Fig. I. N versus 6, for four different normalized emittance of (a) Orr,(b) 10% (c) 20x, and (d) 50~mm mrad.
A calculation was carried out to estimate two parameters N and oc giving a maximum corrected gain for 0.281 pm FEL generation for four different normalized beam emittances for a 165.6 MeV, 100 A electron beam and an undulator with &, = 30 mm and K = 1.4, using the gain reduction factor. Fig. 1 shows N versus Q, for four different normalized emittance of (a) OX, (b) 10x. (c) 20x, (d) 50~ mm mrad. The curves show that the gain increment with the decrease of the energy spread is fairly good for a beam with an emittance less than E, = 2071mm mrad and with an energy spread less than (T, = 0.5%. On the contrary, the gain increment with the decrease of the emittance becomes small for a beam with an emittance less than E, = 10nmm mrad and with an energy spread larger than oe = 0.5%. It is not so effective to increase the gain to decrease the emittance of a beam with an energy spread larger than 6, = 1%.
3. Effects of filling factor on gain The FELI FEL facility 3 consists of a 6.72 m long optical cavity and a 2.68 m long undulator [lo]. The optical cavity 3 is of the Fabry-Perrot type which consists of two mirror chambers and a vacuum duct connecting them. A rotating-type mirror holder in each mirror chamber can accomodate eight mirrors. Each cavity mirror is a spherical and dielectric multilayer mirror of Ta205/Si02 or HfOz/SiOz. Table 1 shows the main parameters of the optical cavity for the FEL facility 3 [ll]. The dimensionless Rayleigh length Z,, = ZR/L, of the FEL facility 3 is 0.75 from Table 1. This length gives a 90% of the maximum normalized gain according to the report of Small et al. [12,13], although the average filling factor over the undulator drops to half of its peak value at Z0 = 0.75. The dimensionless electron beam waist
radius (T, = rb(7c/L, A)‘I2 of the FEL facility 3 is 0.8 for 0.3 pm FEL, where rb is the electron beam radius. This radius gives 90% of the maximum normalized gain [12] for a normalized emittance beam of 16 Kmm mrad. This good agreement shows that our parameters on the beam quality and the filling factor are reasonably selected.
4. Criteria for electron beam quality and FEL wavelength limit
In the previous paper [14], we reviewed and verified relations between the relative energy spread AE/E (FWHM) and the normalized emittance E, of accelerated beams from RF linacs and storage rings which have achieved lasing at visible and ultraviolet wavelengths. The emittance E varies inversely with the linac energy as E = E&J, where y is the Lorentz factor. The lower energy of linac beams provides a significant improvement in the normalized emittance with respect to storage rings. Up to three orders of magnitude may be gained by using a 200 MeV linac beam to drive a 0.3 pm FEL. Fig. 2 shows energy spread and emittance of the electron beams achieved FEL oscillations. Sprangle et al. gave a criterion for wavelength limit in FELs based on the relative energy spread and the normalized emittance of the electron beam from the resonance condition of free electron laser [ 1). Their inequality can be written as
/I > (2n)“2(L/z,)l’2f-
1’2 [ 1 + (y>;]‘/4,
(3)
where i, is the FEL wavelength, I!,is the undulator length, f= 2r$rg is the filling factor, i.e., two times the ratio of cross-sectional area of the electron beam to the optical beam, rb is the electron beam radius at the beam waist. However, the following simplified equality minimizes diffraction effects and maximizes gain for L N ZR
IV. LONG-WAVELENGTH
FELs
232
T Tomimasu/Nucl.
Instr. and Metit. in Phys. Rex A 393 (1997) 230-233
1o-1 o
RF LINAC
l
RING
o
OSCILLATION
\
e’ B
CLIO(Spm)
@
l.ANL(0.37jtm) Q
Super AC0
FELI-l(4.8pm)
FELIX(l.B&tm)
6’ “VSOR@
10‘4’ 10-g
”
“’
“““’
10%
1o-7
.’
““’
10-s
“’
A 10’s
& (x m - rad 1 Fig. 2. Energy spread versus emittance of the electron beam of the facilities achieved FEL oscillations.
andf-
1 [l]
l/Z [I I >(27K)
+
(zy)y4
(E,h+
The simplified inequality in Eq. (4) shows that the wavelength limit is strongly affected by the normalized emittance, the electron beam radius and the energy spread terms. The solid line shown in Fig. 2 indicates wavelength limits for our electron beam quality calculated by using Eq. (4). Roberson and Hafize [2] introduced another criterion as a condition to match the waist of a freely diffracting fundamental Gaussian optical beam with that of an unfocused electron beam in the same space. Their inequality is given by 3, > K &“/Y.
(5)
A well-known criterion written in the text book [3] is 1. > 271&&.
(6)
On the other hand, electron beam requirements for single-pass saturation in a short wavelength Linac Coherent Light Source (LCLS) include (1) a peak current in the 7 kA range, (2) a relative energy spread of t0.05%, and (3) an emittance criterion i = 471an/y as the diffraction-limit condition [4]. i > 47cE./Y.
(7)
These Eqs. (4)-(7) show four kinds of criteria on the wavelength limit. The simplified inequality shown in Eq. (4) shows that the wavelength limit is affected by the
normalized emittance, electron beam radius, and the energy spread terms. However, other criteria are limited by the emittance contribution only. The factor of 4 found in Eqs. (5) and (7) is a huge margin for the same kind of criterion on the wavelength limit and spoils its reliability.
5. Experimental varification of gain estimates and these criteria
The solid line in Fig. 2 indicating the wavelength limit shows that our electron beam quality (AE/E = OS%, E, = 26 n mm mrad, r,, = 0.4 mm, y = 312) is possible for 0.27 pm FEL oscillations with an undulator 1, = 4 cm and K = 0.95. The previous gain simulation [7] is as follows. A calculated small signal gain of this undulator is 7.8% per pass for 0.3 urn spontaneous radiation using a 160 MeV, 50 A electron beam with E, = 26 x mm mrad when the K parameter is 0.95. The net gain is estimated to be larger than 7.3%, considering that the extraction factor of a dielectric multilayer mirror is 0.4% and the mirror loss per roundtrip of the spontaneous radiation is 0.1%. The net gain is more than twice as much as that at the 0.63 urn FEL oscillation we have achieved on the third harmonic using a 68 MeV, 42 A electron beam with a normalized emittance E, of 26 x mmmrad on 27 February 1995. If the normalized emittance E, of a 68 MeV, 42 A electron beam is conserved at a 160 MeV, 50 A electron beam, the estimated 7.3% net gain and the 24 us electron beam duration [ 151 are large enough to excite of 0.3 urn FEL. Considering that the net gain is 7.3% and the previous
T. Tomimasu/Nucl.
26-DEC-1995
Instr. and Meth. in Phys. Rex A 393 (1997) 230-233
233
We can easily estimate the net gain of an FEL oscillation, considering that the extraction factor of dielectric multilayer mirrors is 0.4% and the mirror loss per round trip of the spontaneous radiation is 0.1%.
17: 13
6. Conclusions
Top
:
Bottom
0.353 pm FEL output
The normalized Rayleigh length Z,, of the 6.72 m long optical cavity gives 90% of the maximum normalized gain, although the average filling factor over the 2.68 m long undulator drops to half of its peak value at Z0 = 0.75. The dimensionless electron beam waist radius is 0.8 for the 0.27 pm FEL and gives 90% of the maximum normalized gain for a normalized beam emittance of 16n:mm mrad.
(macropulse)
: Electron beam current
Our
(macropulse)
electron
beam
quality
(AE/E
= 0.5%,
F., =
mm mrad, rb = 0.4 mm, y = 312) satisfies the simplified inequality showing that it is possible for 0.3 pm FEL operation with an undulator of 1, = 4 cm and K = 0.95. 26 a
Fig. 3. 0.35 km FEL macropulse
and current
macropulse
Our results are useful to verify criteria which relate an FEL wavelength i, and an electron beam emittance E = &,/‘I,because our beam emittance is close to threshold values of those criteria such as i, > c.
References
N 0.9 72 i
z kf 0.8
-
rz
0.7 t
I
1
I
J-l
0.3 Wavelength Fig. 4. Characteristic reflectance layer mirror (Ta,O,/SiOz).
squared
of dielectric
multi-
pm FEL macropulse peak rises upto 20 ps [7], a 0.3 pm FEL macropulse will rise up around 15 ps. Fig. 3 shows a 0.35 pm FEL macropulse shape measured on 26 December with a Si-photodetector and a 144 MeV electron beam macropulse shape measured with a button monitor [16]. The 0.35 pm macropulse rises up around 18 ps as predicted at the FEL ‘95 Conference. Fig. 4 shows the characteristic reflectance squared of a dielectric multilayer mirror (TazOS/Si02). 0.63
[1] P. Sprangle et al.. Nucl. Instr. and Meth. A 331 (1993) 6. [Z] C.W. Roberson et al., Nucl. Instr. and Meth. A 331 (1993) 365. [3] J.B. Murphy, C. Pellegrini, Laser Handbook, voi. 6, North-Holland, Amsterdam, 1990, p. 9. [4] R. Tatchyn et al., Nucl. Instr. and Meth. A 375 (1996) 274. [S] J.D. Lawson, S. Penner, IEEE J. Quantum Electron. QE21(2) (1985) 174. [6] T. Tomimasu et al., Nucl. lnstr. and Meth. A 383 (1996) 337. [7] T. Tomimasu et al., Nucl. Instr. and Meth. A 375 (1996) 626. [S] U. Bizzarri et al., The free electron laser: status and perspectives, ENEA Report RT/TIB/85/49. [9] G. Dattoli et al., IEFE 3. Quantum Electron. QE-20 (1984) 631. [lo] Y. Miyauchi et al., Nucl. Instr. and Meth. A 375 (1996) ABS42. [l l] S. Okuma et al., Presented at 18th FEL Cont. Rome, Italy. 1996. [12] D.W. Small et al., Nucl. Instr. and Meth. A 375 (1996~ ABS61. [13] W.B. Colson, Ref. [3], p. 180. [14] T. Tomimasu et al., Nucl. Instr. Meth. A 341 (1994) ABS33. [I51 E. Oshita et al.. IEEE PAC ‘95. Dallas, May l-5. 1995. pp. 1608. [16] A. Zako et al., Proc. 20th Linear Accelerator Meeting in Japan, FELI. 6-8 September 1995, Osaka, Japan, p. 260.
IV. LONG-WAVELENGTH
FELs
NUCLEAR
INSTRUMENTS & METHOOS IN PHYSICS RESEARCH
ELSEVIER
What limits the wavelength of an FEL? Challenge at the shortest wavelength lasing limit of linac-based FELs using the FELI linac with a thermionic gun Takio Tomimasu* Free Electron Laser Research Institute, Inc, (FELI)), 2-9-5, Tsuda-Yamate,
Hirakata,
Osaka 573-01, Japan
Abstract
We have demonstrated that a medium-emittance (26~1 mm mrad), medium-current (60A), 24 ps pulse 155 MeV electron beam from the FELI linac with a thermionic gun allows free electron laser (FEL) oscillations at 0.28-0.36 pm. The peak and average FEL powers are 1.8 MW and 4 mW at 0.35 lm. Gain estimation and effects of electron beam quality and filling factor on gain are also discussed. Experimental verification of gain estimates and the criteria on the electron beam quality and wavelength limit due to photon diffraction are tested with our data from visible- and ultraviolet-FEL oscillations.
1. Introduction
It has been said that lasing at ultraviolet frequencies cannot be achieved by using an electron linac with a thermionic gun, because of its large beam emittance which builds up in the bunching process from the thermionic gun to the linac. Theory can describe the effect which is caused by photon diffraction. It depends on the electron beam quality and leads to a wavelength limit for free electron laser operation [l-4]. The empirical Lawson-Penner expression gives the normalized beam emittance E, = 1.6 I(A) ‘I2 10m4m.rad for an RF-linac with a thermionic gun, where I(A) is the peak current of RF-linac [S]. However, the FELI linac with a thermionic gun was carefully designed to reduce the emittance growth in the bunching process from the thermionic gun to the buncher and achieved first lasing at 0.34-0.35 pm using a 144 MeV electron beam on 26 December 1995 and at 0.28-0.29 pm using a 155 MeV electron beam on 14 April 1996 [6], as predicted at the FEL ‘95 Conference
UI. This paper describes (1) how the available small signal gain depends on the electron beam quality, (2) effects of
the filling factor on gain reduction, (3) criteria for electron beam quality and FEL wavelength limit and (4) experimental verification of gain estimates and these criteria.
2. Small signal gain and electron beam quality The small signal gain is reviewed for an electron beam passing through a planar undulator with the period length A,, the period number N and the magnetic field Bo. When the beam is continuous and the beam emittance and energy spread are negligibly small, the gain GF” for such an ideal beam is given by the following equation [S]: G?’ = {J,(O - 31(5)}‘(Io/377)Jnn,N2 x (K2/2)/( 1 +
(1)
where I0 is the peak current of electron micropulses, 3, is the FEL wavelength and other parameters are defined as follows: 5 = (l/4)K2/(1 + K2/2), K = 93.4&(T) n,(m). A gain reduction factor C = C,C,C,C, was estimated for pulse length effect C,, for energy spread C, and for the beam emittance C,, C’,,by many workers, for the electron beam with a normalized beam emittance E. and an energy spread cer where oe is the standard deviation [9]. The GF” for the practical electron beam is given as follows:
*Tel.: + 81 720 96 0414; fax: [email protected].
+ 81 720 96 0421; e-mail:
0168-9002/97/$17.00 Copyright PII SO168-9002(97)00479-S
1997 Elsevier Science B.V. All rights reserved
0
P/2)3’2,
G;“=G:“CCCC. E e X i
(2)
231
T TomimasulNucl. Instr. and Meth. in Ph.vs. Rex A 393 (19971 230-233
Table 1 Main parameters of optical cavity for the FEL laciliry 3 Type
Optical Mode
Length Rayleigh length y parameter
6.718 m 2.0 m -0.44 - 0.49 4.656 m 4.500 m Multilayer of Ta,0,/Si02 99.6% at 0.6 pm 0.4”/0
Mirror curvature
0
0.2
0.4
0.6
ENERGY SPREAD
0.8
1
1.2
Mirror type Reflection rate Transmission rate
oe (%)
Fig. I. N versus 6, for four different normalized emittance of (a) Orr,(b) 10% (c) 20x, and (d) 50~mm mrad.
A calculation was carried out to estimate two parameters N and oc giving a maximum corrected gain for 0.281 pm FEL generation for four different normalized beam emittances for a 165.6 MeV, 100 A electron beam and an undulator with &, = 30 mm and K = 1.4, using the gain reduction factor. Fig. 1 shows N versus Q, for four different normalized emittance of (a) OX, (b) 10x. (c) 20x, (d) 50~ mm mrad. The curves show that the gain increment with the decrease of the energy spread is fairly good for a beam with an emittance less than E, = 2071mm mrad and with an energy spread less than (T, = 0.5%. On the contrary, the gain increment with the decrease of the emittance becomes small for a beam with an emittance less than E, = 10nmm mrad and with an energy spread larger than oe = 0.5%. It is not so effective to increase the gain to decrease the emittance of a beam with an energy spread larger than 6, = 1%.
3. Effects of filling factor on gain The FELI FEL facility 3 consists of a 6.72 m long optical cavity and a 2.68 m long undulator [lo]. The optical cavity 3 is of the Fabry-Perrot type which consists of two mirror chambers and a vacuum duct connecting them. A rotating-type mirror holder in each mirror chamber can accomodate eight mirrors. Each cavity mirror is a spherical and dielectric multilayer mirror of Ta205/Si02 or HfOz/SiOz. Table 1 shows the main parameters of the optical cavity for the FEL facility 3 [ll]. The dimensionless Rayleigh length Z,, = ZR/L, of the FEL facility 3 is 0.75 from Table 1. This length gives a 90% of the maximum normalized gain according to the report of Small et al. [12,13], although the average filling factor over the undulator drops to half of its peak value at Z0 = 0.75. The dimensionless electron beam waist
radius (T, = rb(7c/L, A)‘I2 of the FEL facility 3 is 0.8 for 0.3 pm FEL, where rb is the electron beam radius. This radius gives 90% of the maximum normalized gain [12] for a normalized emittance beam of 16 Kmm mrad. This good agreement shows that our parameters on the beam quality and the filling factor are reasonably selected.
4. Criteria for electron beam quality and FEL wavelength limit
In the previous paper [14], we reviewed and verified relations between the relative energy spread AE/E (FWHM) and the normalized emittance E, of accelerated beams from RF linacs and storage rings which have achieved lasing at visible and ultraviolet wavelengths. The emittance E varies inversely with the linac energy as E = E&J, where y is the Lorentz factor. The lower energy of linac beams provides a significant improvement in the normalized emittance with respect to storage rings. Up to three orders of magnitude may be gained by using a 200 MeV linac beam to drive a 0.3 pm FEL. Fig. 2 shows energy spread and emittance of the electron beams achieved FEL oscillations. Sprangle et al. gave a criterion for wavelength limit in FELs based on the relative energy spread and the normalized emittance of the electron beam from the resonance condition of free electron laser [ 1). Their inequality can be written as
/I > (2n)“2(L/z,)l’2f-
1’2 [ 1 + (y>;]‘/4,
(3)
where i, is the FEL wavelength, I!,is the undulator length, f= 2r$rg is the filling factor, i.e., two times the ratio of cross-sectional area of the electron beam to the optical beam, rb is the electron beam radius at the beam waist. However, the following simplified equality minimizes diffraction effects and maximizes gain for L N ZR
IV. LONG-WAVELENGTH
FELs
232
T Tomimasu/Nucl.
Instr. and Metit. in Phys. Rex A 393 (1997) 230-233
1o-1 o
RF LINAC
l
RING
o
OSCILLATION
\
e’ B
CLIO(Spm)
@
l.ANL(0.37jtm) Q
Super AC0
FELI-l(4.8pm)
FELIX(l.B&tm)
6’ “VSOR@
10‘4’ 10-g
”
“’
“““’
10%
1o-7
.’
““’
10-s
“’
A 10’s
& (x m - rad 1 Fig. 2. Energy spread versus emittance of the electron beam of the facilities achieved FEL oscillations.
andf-
1 [l]
l/Z [I I >(27K)
+
(zy)y4
(E,h+
The simplified inequality in Eq. (4) shows that the wavelength limit is strongly affected by the normalized emittance, the electron beam radius and the energy spread terms. The solid line shown in Fig. 2 indicates wavelength limits for our electron beam quality calculated by using Eq. (4). Roberson and Hafize [2] introduced another criterion as a condition to match the waist of a freely diffracting fundamental Gaussian optical beam with that of an unfocused electron beam in the same space. Their inequality is given by 3, > K &“/Y.
(5)
A well-known criterion written in the text book [3] is 1. > 271&&.
(6)
On the other hand, electron beam requirements for single-pass saturation in a short wavelength Linac Coherent Light Source (LCLS) include (1) a peak current in the 7 kA range, (2) a relative energy spread of t0.05%, and (3) an emittance criterion i = 471an/y as the diffraction-limit condition [4]. i > 47cE./Y.
(7)
These Eqs. (4)-(7) show four kinds of criteria on the wavelength limit. The simplified inequality shown in Eq. (4) shows that the wavelength limit is affected by the
normalized emittance, electron beam radius, and the energy spread terms. However, other criteria are limited by the emittance contribution only. The factor of 4 found in Eqs. (5) and (7) is a huge margin for the same kind of criterion on the wavelength limit and spoils its reliability.
5. Experimental varification of gain estimates and these criteria
The solid line in Fig. 2 indicating the wavelength limit shows that our electron beam quality (AE/E = OS%, E, = 26 n mm mrad, r,, = 0.4 mm, y = 312) is possible for 0.27 pm FEL oscillations with an undulator 1, = 4 cm and K = 0.95. The previous gain simulation [7] is as follows. A calculated small signal gain of this undulator is 7.8% per pass for 0.3 urn spontaneous radiation using a 160 MeV, 50 A electron beam with E, = 26 x mm mrad when the K parameter is 0.95. The net gain is estimated to be larger than 7.3%, considering that the extraction factor of a dielectric multilayer mirror is 0.4% and the mirror loss per roundtrip of the spontaneous radiation is 0.1%. The net gain is more than twice as much as that at the 0.63 urn FEL oscillation we have achieved on the third harmonic using a 68 MeV, 42 A electron beam with a normalized emittance E, of 26 x mmmrad on 27 February 1995. If the normalized emittance E, of a 68 MeV, 42 A electron beam is conserved at a 160 MeV, 50 A electron beam, the estimated 7.3% net gain and the 24 us electron beam duration [ 151 are large enough to excite of 0.3 urn FEL. Considering that the net gain is 7.3% and the previous
T. Tomimasu/Nucl.
26-DEC-1995
Instr. and Meth. in Phys. Rex A 393 (1997) 230-233
233
We can easily estimate the net gain of an FEL oscillation, considering that the extraction factor of dielectric multilayer mirrors is 0.4% and the mirror loss per round trip of the spontaneous radiation is 0.1%.
17: 13
6. Conclusions
Top
:
Bottom
0.353 pm FEL output
The normalized Rayleigh length Z,, of the 6.72 m long optical cavity gives 90% of the maximum normalized gain, although the average filling factor over the 2.68 m long undulator drops to half of its peak value at Z0 = 0.75. The dimensionless electron beam waist radius is 0.8 for the 0.27 pm FEL and gives 90% of the maximum normalized gain for a normalized beam emittance of 16n:mm mrad.
(macropulse)
: Electron beam current
Our
(macropulse)
electron
beam
quality
(AE/E
= 0.5%,
F., =
mm mrad, rb = 0.4 mm, y = 312) satisfies the simplified inequality showing that it is possible for 0.3 pm FEL operation with an undulator of 1, = 4 cm and K = 0.95. 26 a
Fig. 3. 0.35 km FEL macropulse
and current
macropulse
Our results are useful to verify criteria which relate an FEL wavelength i, and an electron beam emittance E = &,/‘I,because our beam emittance is close to threshold values of those criteria such as i, > c.
References
N 0.9 72 i
z kf 0.8
-
rz
0.7 t
I
1
I
J-l
0.3 Wavelength Fig. 4. Characteristic reflectance layer mirror (Ta,O,/SiOz).
squared
of dielectric
multi-
pm FEL macropulse peak rises upto 20 ps [7], a 0.3 pm FEL macropulse will rise up around 15 ps. Fig. 3 shows a 0.35 pm FEL macropulse shape measured on 26 December with a Si-photodetector and a 144 MeV electron beam macropulse shape measured with a button monitor [16]. The 0.35 pm macropulse rises up around 18 ps as predicted at the FEL ‘95 Conference. Fig. 4 shows the characteristic reflectance squared of a dielectric multilayer mirror (TazOS/Si02). 0.63
[1] P. Sprangle et al.. Nucl. Instr. and Meth. A 331 (1993) 6. [Z] C.W. Roberson et al., Nucl. Instr. and Meth. A 331 (1993) 365. [3] J.B. Murphy, C. Pellegrini, Laser Handbook, voi. 6, North-Holland, Amsterdam, 1990, p. 9. [4] R. Tatchyn et al., Nucl. Instr. and Meth. A 375 (1996) 274. [S] J.D. Lawson, S. Penner, IEEE J. Quantum Electron. QE21(2) (1985) 174. [6] T. Tomimasu et al., Nucl. lnstr. and Meth. A 383 (1996) 337. [7] T. Tomimasu et al., Nucl. Instr. and Meth. A 375 (1996) 626. [S] U. Bizzarri et al., The free electron laser: status and perspectives, ENEA Report RT/TIB/85/49. [9] G. Dattoli et al., IEFE 3. Quantum Electron. QE-20 (1984) 631. [lo] Y. Miyauchi et al., Nucl. Instr. and Meth. A 375 (1996) ABS42. [l l] S. Okuma et al., Presented at 18th FEL Cont. Rome, Italy. 1996. [12] D.W. Small et al., Nucl. Instr. and Meth. A 375 (1996~ ABS61. [13] W.B. Colson, Ref. [3], p. 180. [14] T. Tomimasu et al., Nucl. Instr. Meth. A 341 (1994) ABS33. [I51 E. Oshita et al.. IEEE PAC ‘95. Dallas, May l-5. 1995. pp. 1608. [16] A. Zako et al., Proc. 20th Linear Accelerator Meeting in Japan, FELI. 6-8 September 1995, Osaka, Japan, p. 260.
IV. LONG-WAVELENGTH
FELs