JAERIPULSE — a versatile FEL simulation code on a supercomputer

Nuclear Instruments and Methods in Physics Research A 331 (1993) 450-458 North-Holland

NUCLEAR iNSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA

JAERIPULSE

- a versatile FEL simulation code on a supercomputer

Ken Sasaki b Ryoji Nagai a Nobuhiro Kikuzawa c, Masaru Sawamura a, Masaru Takao Masayoshi Sugimoto a, Eisuke Minehara a, Makio Ohkubo a, Yasuo Suzuki a and Yuuki Kawarasaki a

a

a Free-Electron Laser Laboratory, Department of Physics, Japan Atomic Energy Research Institute (JAERI), Tokai-mura, Ibaraki-ken, 319-11, Japan b Division of Computer Code Development, Nuclear Energy Data Center, Tokai-mura, Ibaraki-ken, 319-11, Japan c Department of Nuclear Engineering, Kyushu University, Higashi-ku, Fukuoka-shi, Fukuoka-ken, 812, Japan

We have developed a versatile one-dimensional simulation code for short-pulse and multi-pass operation of the free-electron laser. This code runs on the main frame computer FACOM 780/20, while its vectorized version runs on the supercomputer FACOM VP2600/10. By making use of the code we have performed several preliminary simulations with a large number of passages of optical pulses through the undulator and obtained very useful information on the nonlinear response of the optical pulse to the beam current in the typical model of the free electron laser.

1. Introduction In parallel with the development of the J A E R I FEL, we have been developing a reliable one-dimensional simulation code for the F E L since 1990, and quite recently we have reached the final stage of the development. So we present here some preliminary results of application of our simulation code, J A E R I P U L S E . This paper may be the first report of our studies of that kind; the applications of the code to the various FELs, not to speak of the code itself, that are to be inserted in the future.

2. Characteristics of the code and computation We p r o g r a m m e d the code in F O R T R A N 7 7 based on Brau's dimensionless F E L equations [1]. The simultaneous differential equations were integrated by the simplest E u l e r method. In this framework the time of passage through the undulator was divided into 100 in most cases, thus giving the reduced time interval A~- = 0.01, while the length of the electron microbunch was divided into 2048 and divided further so that a wavelength may include 2 N field points, where the best N is chosen automatically in order to represent the fine detail of the optical field over a wavelength. The algorithm of the fast Fourier transform (FFT) with the extended range of optical field was implemented into the code to calculate the optical spectra most aceu-

rately and special attention was paid to suppress the spurious sidelobe effects completely [2]. We are going to study the growth of an optical pulse during the time for a large number of passages through the U M in synchronism with electron microbunches passing in succession, since a single electron macrobunch consists of several tens of thousands of microbunches in the J A E R I F E L as in the typical other superconducting F E L s [3]. So it is indispensable for us to reduce the computation error per passage as small as possible so as to minimize the errors which may accumulate after a large number of passages. In the older version of the algorithm the largest error was found to occur in the process of averaging the sines and cosines of the phases o f the test electrons over each of the space intervals A~i; therefore we improved the algorithm of this process in the Version 5 so that the principle of energy conservation may hold as well as possible at each step of integration. W e attained an accuracy of less than 1% for the law of energy conservation except for several percent at the startup of the F E L when the optical field is due to the spontaneous emission and is vanishingly weak. W e also circumvented the difficulty of memory overflow by adopting cartridge tapes as an additional memory resource and by storing the data like the instantaneous optical fields, which are necessary in the successive computations, exclusively at intervals of several tens of passages. O t h e r data, the enormous electronic data among others, are dumped at every end of

0168-9002/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

451

K. Sasaki et al. / JAERIPULSE

passage except the graphical output of them at intervals of several tens of passages. The code runs on the main frame computer FAC O M M - 7 8 0 / 2 0 and can be easily accessed on the terminal display if any change in the input data is necessary. The speed of computation is not so fast at present: a C P U time of 7 s per passage in the simulations (given in section 3). W e also tried preliminary computations with the vectorized version of this code on the supercomputer F A C O M VP-2600/10. Reduction of C P U time by a factor of 1.7 was obtained in that trial.

3. Results of the simulations

W e made several simulations by making use of the J A E R I P U L S E - V e r s i o n 5. The parameters used in the simulations are listed in table 1. The results of the simulation are summarized in the twelve figures as given in the present section. Figs. l a and l b illustrate the profile of the optical pulse after thousand passages through the undulator and the extraction efficiency versus pass number, respectively, in the F E L where the cavity length is just in

synchronism (with zero cavity detuning) and the b e a m current is not high enough for lasing. Fig. l a shows that synchrotron instability does not take place when the b e a m current is low enough and that the optical pulse is getting higher and thinner since the amplification exceeds the cavity losses at the posterior part of each electron micropulse, while the losses exceed the amplification due to the lethargy effect at the anterior part of each micropulse as well as the forward shift of the leading edge on the optical pulse out of overlap with each electron micropulse. We observe in fig. lb the characteristic gentle hump of extraction efficiency. W e infer that this hump is originated from the temporal change in balance, or competition, between the amplification and thinning mentioned al0ove. We should pay attention to the fact that the hump occurs after several hundreds of passages. We should also notice that the values of the extraction efficiency in fig. l b are smaller by several orders of magnitude than those in figs. 2b, 3b, and 4b where the lasing is taking place. Figs. 2a, 2b, 2c and 2d depict the profile of the optical pulse after 1000 passages through the undulator, the extraction efficiency versus pass number, the optical gain versus pass number, and the optical spec-

Table 1 Parameters used in the simulations Device parameters Wiggler period, Aw [m] Wiggler length, L w [m] Wiggler period, N w Maximum magnetic induction on the axis, B w [T] Wiggler constant, a w

0.029 1.74 60 0.47 0.9

Optical parameters Harmonic number, N H Goal of pass number, Np Cavity reflectance, R1R1 Detuning of cavity length, AL c [txm] Wavelength of resonant light, AR [l~m] Initial electric field of spontaneous emission, E s [V/m]

1 1000 0.90 -50.0, 0.0, and 50.0 40.0 10 4

Electronic parameters Charge of electron microbunch, e B [C] Radius of electron beam, r n [m] Length of electron microbunch in slippage, L n Number of test electrons, Ne Noise factor, Length of electron macrobunch, 'r M [ms] Energy spread of electrons, A E [%]

0.36×10 9,0.18x10 8 1.5×10 3 10.0 10000 10 -3 1.0 0.5

Computation parameters Number of time steps per pass, N s Initial number of field points in a microbunch, Mf Number of field points in a resonant wavelength, M d

100 2048 automatically chosen by modifying Mf VIII. COMPTON FEL THEORY

452

K~ Sasaki et al. / JAERIPULSE

trum after 1000 passages through the undulator, respectively, in the F E L where the cavity length is just in synchronism as in figs. la and 2b, but the beam current is five times as high as in figs. l a and lb thus high enough for lasing.

(a)

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The profile of the optical pulse in fig. 2a is quite different from that in fig. la and is strongly modulated due to the growth of synchrotron instabilities. We find in fig. 2b that the extraction efficiency reaches a rather high saturated value, around 1.3%, which is greater

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Fig. 1. (a) Profile of the optical pulse after 1000 passages through the undulator in the FEL where the cavity length is just in synchronism and the beam current is not high enough for lasing. (b) Extraction efficiency vs pass number in the same FEL as given in (a).

4.53

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t h a n 1 / ( 2 N w) (in p e r c e n t a g e : 0.83%) after a b o u t 200 passages a n d it u n d u l a t e s r a t h e r ruggedly a r o u n d t h e s a t u r a t e d value. It recently came to o u r k n o w l e d g e t h a t

W a r r e n et al. h a d o b s e r v e d a similar ruggedness of optical p o w e r in t h e i r F E L e x p e r i m e n t s with zero d e t u n i n g at L A N L [4]. A t first sight this r u g g e d n e s s of

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Fig, 2. (a) Profile of the optical pulse after 1000 passages through the undulator in tile FEL where the cavity length is just in synchronism and the beam current is five times as high as that in figs. la and lb and induces lasing. (b) Extraction efficiency vs pass number in the same FEL as given in (a), (c) Optical gain vs pass number in the same FEL as given in (a). (d) Optical spectrum after 1000 passages through the undulator in the same FEL as given in (a). VIII. COMPTON FEL THEORY

454

1(2 Sasaki et al. / JAERIPULSE 3.5

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optical power seems to be like the stable limit cycle oscillations of the optical energy demonstrated in FELIX by Jaroszynski et al. [5]. However the limit cycle behavior was observed in FELIX only with negative detuning and with the electron micropulses which were

much shorter than the slippage NwA. So our rugged undulation of saturated optical power, which occurred even with zero detuning and with electron micropulses with a length ten times as long as the slippage, has nothing to do with such a limit cycle behavior, but is

455

K. Sasaki et al. / JAERIPULSE

likely to be connected with the irregularities of temporal ups and downs of separate optical spikes under the combined action of coherent spontaneous emission from electrons at the slipped end of each spike and

(a)

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lethargy of electrons at the slipped front of each spike in the optical cavity with losses as large as 0.1. In fig. 2c the optical gains on pass number 1 and 2 are very large. We calculated these values within sev-

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Fig. 3. (a) Profile of the optical pulse after 1000 passages through the undulator in the FEL where the cavity length is detuned from synchronism by - 5 0 I~m and the beam current is the same as given in fig. 2a, thus high enough to induce lasing. (b) Extraction efficiency vs pass number in the same FEL as given in (a). (c) Optical spectrum after 1000 passages through the undulator in the same FEL as given in (a). VIII. COMPTON FEL THEORY

456

K. Sasaki et a L / JAERIPULSE ,18 9.0-

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eral percent of relative error for the law of energy conservation. Whether these values are realistic or not may depend on the model of the spontaneous emission and the noise we adopted. After passing the small hump between pass number 2 and about 25 the optical gain rapidly reaches the saturated value 0.111 . . . appropriate for the assumed value of the cavity reflectance: RIR2 = 0.9. The optical spectrum of the laser light in fig. 2d is complex in structure, reflecting the synchrotron instability. However, the central peak around 40.7 ~m is strong and has a fairly narrow width due to the broad envelope function of the optical pulse as shown in fig. 2a. The wavelength of the central peak is shifted to the longer side from the expected wavelength 40.0 ~m. This suggests that the mean energy of the electrons should be raised above the resonant electron energy if the resonant wavelength 40.0 ~m is to be fixed. Figs. 3a, 3b and 3c represent the profile of the optical pulse after 1000 passages through the undulator, the extraction efficiency versus pass number, and the optical spectrum after 1000 passages through the undulator, respectively, in the FEL where the cavity length is detuned from synchronism by - 5 0 . 0 p.m and the beam current is the same as given in figs. 2a, 2b, 2c and 2d, thus high enough for lasing. The profile of the optical pulse in fig. 3a is similar

to that in fig. 2a and highly modulated due to the growth of synchrotron instabilities, but is reduced somewhat in integrated intensity. The extraction efficiency in fig. 3b has a behavior similar to that in fig. 2b but it is reduced in magnitude in accordance with the detuning curve. We find it most interesting that the optical spectrmn in fig. 3c is much more clean than that in fig. 2d and the central peak in fig. 3c is twice as high as that in fig. 2d due to the more symmetric envelope of the optical profile in fig. 3a than that in fig. 2a. The width of the central peak in fig. 3c is also thinner than that in fig. 2d. This suggests that a negative detuning is very useful for extracting laser light of good quality from the FEL. Figs. 4a, 4b and 4c are the profile of the optical pulse after 500 passages through the undulator, the extraction efficiency versus pass number and the optical spectrum after 500 passages through the undulator, respectively, in the FEL where the cavity length is detuned from synchronism by + 50.0 ~m and the beam current is the same as given in figs. 2a, 2b, 2c and 2d, thus high enough for lasing. The optical profile in fig. 4a is rather different from those in figs. 2a and 3a and modulated differently since the frequency-creep mechanism is absent when the detuning is positive enough as pointed out by Warren

K. Sasaki et al. / JAERIPULSE

et al. [4]. T h e d e t a i l e d m e c h a n i s m of this m o d u l a t i o n is, however, n o t yet clear to us. T h e intensity is also r a t h e r w e a k in c o m p a r i s o n with those in figs. 2a a n d 3a in a c c o r d a n c e with t h e typical of d e t u n i n g curve.

(a)

457

T h e extraction efficiency in fig. 4b is also different from t h e b e h a v i o r s of all o t h e r extraction efficiencies as given in figs. lb, 2b a n d 3b: the r u g g e d h u m p is followed by t h e t r u e leveling-off of the extraction effi-

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Fig. 4. (a) Profile of the optical pulse after 500 passages through the undulator in the FEL where the cavity length is detuned from synchronism by +50 Ixm and the beam current is the same as given in fig. 2a, thus high enough to induce lasing, (b) Extraction efficiency vs pass number in the same FEL as given in (a). (c) Optical spectrum after 500 passages through the undulator in the same FEL as given in (a). VIII. COMPTON FEL THEORY

458

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ciency. Its values are much smaller in magnitude than those in figs. 2b and 3b. The origin of such rigid stationary state of the extraction efficiency is also unclear to us. The optical spectrum in fig. 4c is clean but the width of the central peak is rather broad in comparison with those in figs. 2d and 3c due to the thinner width and asymmetry of the envelope of the optical profile as given in fig. 4a.

4. Conclusion We have developed a reliable one dimensional F E L simulation code which is versatile in its potentiality. By making use of the code we made several preliminary simulations by varying the beam-current density and the detuning condition for the F E L which is supposed to generate laser light with a wavelength around 40.0 p~m. In these simulations we have found many interesting nonlinear responses of the optical pulse to the b e a m current. In particular we have realized that detuning with a shortened cavity length is important for the F E L to improve the quality of the laser light, while some of their origins are yet unknown to us. We think that our code would also be useful to clarify these points in the future. We also stress that many Of the interesting phenomena were not found until the simulations were conducted over a large number of passages.

Acknowledgements W e are much obliged to Prof. Charles A. Brau for valuable discussions and helpful private communications from which we could confirm the details of his algorithm. W e would like to acknowledge Dr. M. Ishii for continual encouragement. O n e of the authors (K.S.) is most grateful to Drs. M. Nozawa, T. Iijima, T. Suzuki, S. Igarasi and Mr. Izumi for heartful encouragements and to Mr. M. Machida for support on coding the vectorized version of the J A E R I P U L S E , to Mr. K. Nakagawa for support on c o d i n g t h e J C L and P R O C L I B for the J A E R I P U L S E and to Mr. T. Tsuruoka for consulting on the computation errors.

References [1] C.A. Brau, Free-Electron Lasers, 2nd ed. (Academic Press, Boston, 1991). [2] E.O. Brigham, The Fast Fourier Transform (Prentice Hall, 1974). [3] R. Rohatagi, H.A. Schwettman, T.I. Smith and R.L. Swent, NucL Instr. and Meth. A272 (1988) 32. [4] R.W. Warren, J.E. Sollid, D.W. Feldman, W.E. Stein, W.J. Johnson, A.H. Lumpkin and J.C. Goldstein, Nucl. Instr. and Meth. A285 (1989) 1. [5] D.A. Jaroszyski; R.J. Bakker, D. Oepts, A.F.G. van der Meer and P.W. van Amersfoort, these Proceedings (14th Int. Free Electron Laser Conf., Kobe, Japan, 1992) Nucl. Instr. and Meth. A 331 (1993) 52.