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Super-ACO FEL oscillation with longitudinal to transverse coupled beam dynamics
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
Super-ACO FEL oscillation with longitudinal to transverse coupled beam dynamics C. Brunia,b,*, G.L. Orlandia,b, D. Garzellaa,b, G. De Ninnoc, M.E. Coupriea,b, R. Bartolinid, C. Rippond, G. Dattolid a # 522, 91 191 Gif-sur-Yvette, France CEA/DRECAM/SPAM, bat # 209D, Orsay 91 898 BP 34, France Lure CEA, Universit!e Paris Sud, bat c Sincrotrone Trieste, Trieste 34012, Italy d ENEA, Divisione Fisica Applicata, Centro Ricerche Frascati, Roma, Italy b
Abstract The Super-ACO storage ring Free Electron Laser (FEL) has been operated using an alternative operating point characterized by a non-zero dispersion function in the undulator straight section, linking the transverse motion of the electrons to the energy spread, and by a low momentum compaction factor. The longitudinal to transverse coupled electron beam motion induces a modified dynamics of the Super-ACO FEL. The FEL characteristics, such as the FEL power, pulse duration and spectral width are presented and analyzed in terms of storage ring FEL dynamics. r 2003 Elsevier Science B.V. All rights reserved. PACS: 41.60.Cr; 29.20.Dh Keywords: Storage ring; Free electron laser; Momentum compaction factor; FEL saturation
1. Low momentum compaction factor optics A new working point was recently analyzed at Super-ACO [1]. The usual optics for Super-ACO Free Electron Laser (FEL) operation is presented in Fig. 1a. Another optics with a reduced momentum compaction factor, a, can also be set up on Super-ACO for FEL operations. The initial goal of such optics is to reach the theoretical minimum emittance [2]. This optics leads to a distributed dispersion function ZX ; a lower emit*Corresponding author. Lure CEA, Universit!e Paris Sud, b#at 209D, Orsay 91 898 BP 34, France. Tel.: +31-1-6446-8116; fax: +33-1-6449-4148. E-mail address: [email protected] (C. Bruni).
tance e and a lower momentum compaction factor a (see Table 1). These three features have implications on the FEL characteristics and dynamics. First, the presence of dispersion function in the FEL straight section induces a longitudinal to transverse beam dynamics coupling, which modifies the FEL saturation process. Second, the reduction of the emittance leads to an increase of the electron bunch density, and gets the small signal gain of the amplification process higher [3]. Fig. 2 shows that the initial gain is almost two times higher for the low a operation with respect to the nominal one. Third, the low a optics leads to a reduced synchrotron frequency fS (a and fS2 being proportional), which slows the longitudinal motion of the electrons around the synchronous
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)00930-6
ARTICLE IN PRESS 286
C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
4
G0 (%)
3
2
1
0
20
0
60
40
I (mA)
Fig. 1. Half-cell optics of the Super-ACO storage ring for different momentum compaction factors: (a) a ¼ 0:0148; (b) a ¼ 0:008: Table 1 Super-ACO storage ring optics parameters for different momentum compaction factor a: ex and ez being the horizontal and vertical emittance, fs the synchrotron frequency, and se the longitudinal dimension of the electron bunch. In the FEL straight section: ZX being the dispersion function, bX and bZ the horizontal and vertical betatron function, sx and sz the horizontal and vertical bunch dimensions a ex ; ez (nmrad) fs (kHz) se (ps) Zx (m) bx ; bz (m) sx ;sz (mm)
0.0148 13.5;13.5 14.3 85 0 5.4; 5.4 389; 387
0.008 6.3; 6.3 10.5 62 0.26 1.2; 5.8 165;191
particle. The FEL micropulse temporal distribution can present some substructures [4–7], which are, according to theoretical results [5], amplified in low a operation. The experimental results obtained on the substructures should be more deeply investigated. The bunch lengthening due to the microwave instability does not change, while the energy spread is larger. In the following are presented the experimental results obtained during the low a operation.
wavelength (nm)
Fig. 2. FEL small signal gain deduced from the electron bunch measured parameters [3] for different momentum compaction factors versus the total current stored in two bunches: (J) a ¼ 0:0148; (K) a ¼ 0:008: The horizontal line indicates the threshold current for total losses of 0.95%.
355.0
355.2
355.4
0
1
2 3 4 Intensity (arb. units.)
5
6
Fig. 3. FEL spectral distribution.
2. FEL transverse and longitudinal distributions 2.1. FEL transverse characteristics The FEL transverse characteristics depend mostly on the set-up of the optical cavity. Mirrors, whose maximum reflectivity and transmission (0.07%) are given for a wavelength around 350 nm, have been used for the low a operation. Adjusting the optical klystron parameters, the wavelength of the laser was 355 nm with a FWHM spectral width of 0.06 nm (see Fig. 3). The laser waist of the TEM00 optical mode depends on the curvature radius of the mirrors (10.2 and 9.4 m), the cavity length (18 m) and the laser wavelength [8]. The waist was around 500 mm and the Rayleigh length of 2.3 m. The mirrors’ losses measured in situ [9] were 0.95%. Consequently, the laser threshold should have been at 4 mA (see Fig. 2), while it was at 8 mA (see Fig. 5) undoubtedly, because of the mirrors degradation [10].
ARTICLE IN PRESS C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
2.2. FEL micro-pulse duration The FEL reproduces the pulsed temporal structure of the electron beam. In the SuperACO case, two electron bunches are stored in the ring, spaced out at 120 ns. The laser longitudinal dynamics depends on the synchronization condition between the repetition rate of the optical wave in the optical cavity and of the electron bunch in the undulator. This tuning condition can be experimentally obtained by changing the frequency of the radio frequency (rf) cavity, thus the electron revolution period. Experimentally, as shown in Fig. 4a, the laser pulse duration increases globally with the current I stored in the ring. Its rms minimum value is 10 ps at 10 mA of total current, and its maximum value is 25 ps at 44 mA. The data spread is due to different transverse mirrors’ alignment, which modifies the longitudinal overlap between the laser pulse and the electron bunch along the undulator. Fig. 4b represents the laser pulse duration versus the detuning of the rf cavity. For a perfect tuning, the laser pulse is smaller, and increases with the absolute value of the detuning, first, very rapidly and then it seems to saturate for larger detuning. This feature is reproduced by numerical codes
287
[11,12]. Similar dependence of the laser pulse width versus the detuning has also been observed on the OK-4/Duke storage ring FEL [13], on the UVSOR FEL [14], and on ELETTRA [15].
3. FEL saturation The laser interacts with the electron bunch, increasing the energy spread, and consequently the longitudinal electron bunch dimensions, thus the laser gain decreases. The laser reaches the saturation when the laser gain achieves the level of the mirrors losses. 3.1. FEL power Fig. 5 represents the average extracted power versus the total current stored in the ring. The maximum extracted average power was 25 mW at 46 mA. The power increases with the current as expected by the theory [16,17]. The FEL power obtained with the low a seems to be slightly higher than the FEL power obtained with the nominal a; probably because of the higher small signal gain in the low a case. 3.2. Electron bunch behaviour
σlaser (ps)
30 20 10 0
0
10
20
30
40
50
I (mA)
(a)
Because the FEL saturation results from an increase of the energy spread, one can also observe the FEL longitudinal bunch lengthening to characterize the FEL saturation. Fig. 6a shows the longitudinal bunch length versus the detuning for the nominal a: For a perfect tuning, the bunch length enhancement is around 11% with respect to 30
20 P (mW)
σlaser (ps)
30
10 0 -40
(b)
-20
0
∆fRF (Hz)
20
20
10
40
Fig. 4. FEL RMS temporal width (a) versus I; (b) versus the detuning.
0 0
10
20
30
40
50
I (mA)
Fig. 5. FEL average power extracted versus I:
ARTICLE IN PRESS C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
288
dispersion function in the FEL section shows a new mode of saturation, including the longitudinal to transverse electron beam coupling. More investigations should be done for the FEL during the low a operation such as the substructures, the detuning curves, the Touschek lifetime, to fully characterize the FEL.
σe (ps)
200 180 160 140 (a)
0
-100
100
σe (ps)
140 135
Acknowledgements
130
We would like to express our thanks to all the operators group for their help during this experiment.
125 120 -40 (b)
-20
0
20
40
∆fRF (Hz)
Fig. 6. Bunch longitudinal dimensions versus the detuning for different experimental conditions: (a) a ¼ 0:0148; I ¼ 60 mA, (b) a ¼ 0:008; I ¼ 40 mA.
the ‘‘FEL off’’ case. The FEL action on the bunch length is reduced when the detuning increases till reaching the bunch length for the ‘‘FEL off’’ case. With the low a; the behaviour is less evident (see Fig. 6b). The bunch length seems to remain more or less constant with the detuning, at 13372 ps around the ‘‘FEL off’’ value. This behaviour has already been observed in the nominal a case. In fact, the FEL damps the beam longitudinal instabilities [18]. Thus the longitudinal bunch lengthening due to the FEL should be compared with the one measured at zero current. In the low a case, the energy spread increase, due to the FEL, induces a growth of the transverse dimensions, leading to a considerable increase of the beam lifetime due to the FEL: at 40 mA, for a=0.0148, 6.5 h ‘‘FEL off’’, 7.7 h ‘‘FEL on’’; for a=0.008, 1.6 h ‘‘FEL off’’, 4.8 h ‘‘FEL on’’.
4. Conclusion The low a FEL operation presents a higher small signal gain. In addition, the non-zero
References [1] C. Bruni, et al., Nucl. Instr. and Meth. A 483 (2001) 167. [2] A. Nadji, Proceedings of the EPAC, 2000, pp. 1057. [3] P. Elleaume, J. Phys. (Paris) 44 (1983) C1. [4] V.N. Litvinenko, et al., Nucl. Instr. and Meth. A 358 (1995) 369. [5] G. De Ninno, et al., Phys. Rev. E 64 (2) (2001) 6052. [6] H. Hama, et al., Nucl. Instr. and Meth. A 358 (1995) 365. [7] M.E. Couprie et al., Proceeding of the EPAC, 2000, pp. 735. [8] H. Kogelnik, T. Li, Appl. Opt. 5 (10) (1966) 1550. [9] D. Garzella, Thesis, Universit!e Paris Sud, 1996. [10] A. Gatto, et al., Nucl. Instr. and Meth. A 483 (2001) 172. [11] T. Hara, et al., Nucl. Instr. and Meth. A 358 (1995) 341. [12] R. Bartolini, STOK 2D: a computer program for analysis of the longitudinal beam dynamics in a storage ring optical klystron FEL, TMR network report, Frascati, Italy. [13] V.N. Litvinienko, et al., Nucl. Instr. and Meth. A 475 (2001) 240. [14] H. Hama, et al., Nucl. Instr. and Meth. A 375 (1996) 32. [15] R.P. Walker, et al., Nucl. Instr. and Meth. A 475 (2001) 20. [16] A. Renieri, Il Nuovo Cimento 53B (1979) 160. [17] G.L. Orlandi et al., Proceeding of the International FEL Conference, Argone (2002), unrefered. [18] G. Dattoli, et al., Nucl. Instr. and Meth. A 393 (1997) 70.
Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
Super-ACO FEL oscillation with longitudinal to transverse coupled beam dynamics C. Brunia,b,*, G.L. Orlandia,b, D. Garzellaa,b, G. De Ninnoc, M.E. Coupriea,b, R. Bartolinid, C. Rippond, G. Dattolid a # 522, 91 191 Gif-sur-Yvette, France CEA/DRECAM/SPAM, bat # 209D, Orsay 91 898 BP 34, France Lure CEA, Universit!e Paris Sud, bat c Sincrotrone Trieste, Trieste 34012, Italy d ENEA, Divisione Fisica Applicata, Centro Ricerche Frascati, Roma, Italy b
Abstract The Super-ACO storage ring Free Electron Laser (FEL) has been operated using an alternative operating point characterized by a non-zero dispersion function in the undulator straight section, linking the transverse motion of the electrons to the energy spread, and by a low momentum compaction factor. The longitudinal to transverse coupled electron beam motion induces a modified dynamics of the Super-ACO FEL. The FEL characteristics, such as the FEL power, pulse duration and spectral width are presented and analyzed in terms of storage ring FEL dynamics. r 2003 Elsevier Science B.V. All rights reserved. PACS: 41.60.Cr; 29.20.Dh Keywords: Storage ring; Free electron laser; Momentum compaction factor; FEL saturation
1. Low momentum compaction factor optics A new working point was recently analyzed at Super-ACO [1]. The usual optics for Super-ACO Free Electron Laser (FEL) operation is presented in Fig. 1a. Another optics with a reduced momentum compaction factor, a, can also be set up on Super-ACO for FEL operations. The initial goal of such optics is to reach the theoretical minimum emittance [2]. This optics leads to a distributed dispersion function ZX ; a lower emit*Corresponding author. Lure CEA, Universit!e Paris Sud, b#at 209D, Orsay 91 898 BP 34, France. Tel.: +31-1-6446-8116; fax: +33-1-6449-4148. E-mail address: [email protected] (C. Bruni).
tance e and a lower momentum compaction factor a (see Table 1). These three features have implications on the FEL characteristics and dynamics. First, the presence of dispersion function in the FEL straight section induces a longitudinal to transverse beam dynamics coupling, which modifies the FEL saturation process. Second, the reduction of the emittance leads to an increase of the electron bunch density, and gets the small signal gain of the amplification process higher [3]. Fig. 2 shows that the initial gain is almost two times higher for the low a operation with respect to the nominal one. Third, the low a optics leads to a reduced synchrotron frequency fS (a and fS2 being proportional), which slows the longitudinal motion of the electrons around the synchronous
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)00930-6
ARTICLE IN PRESS 286
C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
4
G0 (%)
3
2
1
0
20
0
60
40
I (mA)
Fig. 1. Half-cell optics of the Super-ACO storage ring for different momentum compaction factors: (a) a ¼ 0:0148; (b) a ¼ 0:008: Table 1 Super-ACO storage ring optics parameters for different momentum compaction factor a: ex and ez being the horizontal and vertical emittance, fs the synchrotron frequency, and se the longitudinal dimension of the electron bunch. In the FEL straight section: ZX being the dispersion function, bX and bZ the horizontal and vertical betatron function, sx and sz the horizontal and vertical bunch dimensions a ex ; ez (nmrad) fs (kHz) se (ps) Zx (m) bx ; bz (m) sx ;sz (mm)
0.0148 13.5;13.5 14.3 85 0 5.4; 5.4 389; 387
0.008 6.3; 6.3 10.5 62 0.26 1.2; 5.8 165;191
particle. The FEL micropulse temporal distribution can present some substructures [4–7], which are, according to theoretical results [5], amplified in low a operation. The experimental results obtained on the substructures should be more deeply investigated. The bunch lengthening due to the microwave instability does not change, while the energy spread is larger. In the following are presented the experimental results obtained during the low a operation.
wavelength (nm)
Fig. 2. FEL small signal gain deduced from the electron bunch measured parameters [3] for different momentum compaction factors versus the total current stored in two bunches: (J) a ¼ 0:0148; (K) a ¼ 0:008: The horizontal line indicates the threshold current for total losses of 0.95%.
355.0
355.2
355.4
0
1
2 3 4 Intensity (arb. units.)
5
6
Fig. 3. FEL spectral distribution.
2. FEL transverse and longitudinal distributions 2.1. FEL transverse characteristics The FEL transverse characteristics depend mostly on the set-up of the optical cavity. Mirrors, whose maximum reflectivity and transmission (0.07%) are given for a wavelength around 350 nm, have been used for the low a operation. Adjusting the optical klystron parameters, the wavelength of the laser was 355 nm with a FWHM spectral width of 0.06 nm (see Fig. 3). The laser waist of the TEM00 optical mode depends on the curvature radius of the mirrors (10.2 and 9.4 m), the cavity length (18 m) and the laser wavelength [8]. The waist was around 500 mm and the Rayleigh length of 2.3 m. The mirrors’ losses measured in situ [9] were 0.95%. Consequently, the laser threshold should have been at 4 mA (see Fig. 2), while it was at 8 mA (see Fig. 5) undoubtedly, because of the mirrors degradation [10].
ARTICLE IN PRESS C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
2.2. FEL micro-pulse duration The FEL reproduces the pulsed temporal structure of the electron beam. In the SuperACO case, two electron bunches are stored in the ring, spaced out at 120 ns. The laser longitudinal dynamics depends on the synchronization condition between the repetition rate of the optical wave in the optical cavity and of the electron bunch in the undulator. This tuning condition can be experimentally obtained by changing the frequency of the radio frequency (rf) cavity, thus the electron revolution period. Experimentally, as shown in Fig. 4a, the laser pulse duration increases globally with the current I stored in the ring. Its rms minimum value is 10 ps at 10 mA of total current, and its maximum value is 25 ps at 44 mA. The data spread is due to different transverse mirrors’ alignment, which modifies the longitudinal overlap between the laser pulse and the electron bunch along the undulator. Fig. 4b represents the laser pulse duration versus the detuning of the rf cavity. For a perfect tuning, the laser pulse is smaller, and increases with the absolute value of the detuning, first, very rapidly and then it seems to saturate for larger detuning. This feature is reproduced by numerical codes
287
[11,12]. Similar dependence of the laser pulse width versus the detuning has also been observed on the OK-4/Duke storage ring FEL [13], on the UVSOR FEL [14], and on ELETTRA [15].
3. FEL saturation The laser interacts with the electron bunch, increasing the energy spread, and consequently the longitudinal electron bunch dimensions, thus the laser gain decreases. The laser reaches the saturation when the laser gain achieves the level of the mirrors losses. 3.1. FEL power Fig. 5 represents the average extracted power versus the total current stored in the ring. The maximum extracted average power was 25 mW at 46 mA. The power increases with the current as expected by the theory [16,17]. The FEL power obtained with the low a seems to be slightly higher than the FEL power obtained with the nominal a; probably because of the higher small signal gain in the low a case. 3.2. Electron bunch behaviour
σlaser (ps)
30 20 10 0
0
10
20
30
40
50
I (mA)
(a)
Because the FEL saturation results from an increase of the energy spread, one can also observe the FEL longitudinal bunch lengthening to characterize the FEL saturation. Fig. 6a shows the longitudinal bunch length versus the detuning for the nominal a: For a perfect tuning, the bunch length enhancement is around 11% with respect to 30
20 P (mW)
σlaser (ps)
30
10 0 -40
(b)
-20
0
∆fRF (Hz)
20
20
10
40
Fig. 4. FEL RMS temporal width (a) versus I; (b) versus the detuning.
0 0
10
20
30
40
50
I (mA)
Fig. 5. FEL average power extracted versus I:
ARTICLE IN PRESS C. Bruni et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 285–288
288
dispersion function in the FEL section shows a new mode of saturation, including the longitudinal to transverse electron beam coupling. More investigations should be done for the FEL during the low a operation such as the substructures, the detuning curves, the Touschek lifetime, to fully characterize the FEL.
σe (ps)
200 180 160 140 (a)
0
-100
100
σe (ps)
140 135
Acknowledgements
130
We would like to express our thanks to all the operators group for their help during this experiment.
125 120 -40 (b)
-20
0
20
40
∆fRF (Hz)
Fig. 6. Bunch longitudinal dimensions versus the detuning for different experimental conditions: (a) a ¼ 0:0148; I ¼ 60 mA, (b) a ¼ 0:008; I ¼ 40 mA.
the ‘‘FEL off’’ case. The FEL action on the bunch length is reduced when the detuning increases till reaching the bunch length for the ‘‘FEL off’’ case. With the low a; the behaviour is less evident (see Fig. 6b). The bunch length seems to remain more or less constant with the detuning, at 13372 ps around the ‘‘FEL off’’ value. This behaviour has already been observed in the nominal a case. In fact, the FEL damps the beam longitudinal instabilities [18]. Thus the longitudinal bunch lengthening due to the FEL should be compared with the one measured at zero current. In the low a case, the energy spread increase, due to the FEL, induces a growth of the transverse dimensions, leading to a considerable increase of the beam lifetime due to the FEL: at 40 mA, for a=0.0148, 6.5 h ‘‘FEL off’’, 7.7 h ‘‘FEL on’’; for a=0.008, 1.6 h ‘‘FEL off’’, 4.8 h ‘‘FEL on’’.
4. Conclusion The low a FEL operation presents a higher small signal gain. In addition, the non-zero
References [1] C. Bruni, et al., Nucl. Instr. and Meth. A 483 (2001) 167. [2] A. Nadji, Proceedings of the EPAC, 2000, pp. 1057. [3] P. Elleaume, J. Phys. (Paris) 44 (1983) C1. [4] V.N. Litvinenko, et al., Nucl. Instr. and Meth. A 358 (1995) 369. [5] G. De Ninno, et al., Phys. Rev. E 64 (2) (2001) 6052. [6] H. Hama, et al., Nucl. Instr. and Meth. A 358 (1995) 365. [7] M.E. Couprie et al., Proceeding of the EPAC, 2000, pp. 735. [8] H. Kogelnik, T. Li, Appl. Opt. 5 (10) (1966) 1550. [9] D. Garzella, Thesis, Universit!e Paris Sud, 1996. [10] A. Gatto, et al., Nucl. Instr. and Meth. A 483 (2001) 172. [11] T. Hara, et al., Nucl. Instr. and Meth. A 358 (1995) 341. [12] R. Bartolini, STOK 2D: a computer program for analysis of the longitudinal beam dynamics in a storage ring optical klystron FEL, TMR network report, Frascati, Italy. [13] V.N. Litvinienko, et al., Nucl. Instr. and Meth. A 475 (2001) 240. [14] H. Hama, et al., Nucl. Instr. and Meth. A 375 (1996) 32. [15] R.P. Walker, et al., Nucl. Instr. and Meth. A 475 (2001) 20. [16] A. Renieri, Il Nuovo Cimento 53B (1979) 160. [17] G.L. Orlandi et al., Proceeding of the International FEL Conference, Argone (2002), unrefered. [18] G. Dattoli, et al., Nucl. Instr. and Meth. A 393 (1997) 70.