Integrated computer simulation on FIR FEL dynamics

Integrated computer simulation on FIR FEL dynamics

a Nuclear Instruments and Methods in Physics Research A 375 ( 1996) 194-197 NUCLEAR INSTRUMENTS & METHODS IN PHVSICS RESEARCH Sectlor A d __ __ li...

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a

Nuclear Instruments and Methods in Physics Research A 375 ( 1996) 194-197

NUCLEAR INSTRUMENTS & METHODS IN PHVSICS RESEARCH Sectlor A

d __ __

liiz ELSEVIER

Integrated computer simulation on FIR FEL dynamics H. Furukawaa, “Institute

K. Mimab, Y. Sentoku”, for

hInstitute ‘Mitsubishi

Research

Laser

S. Kuruma”, K. Imasaki”, C. Yamanakaa

Technology,

Osaka Universiry,

Yarnada-oka

of Laser Engineering.

Osaka Universizy.

Yamada-oka

Institute,

INC..

Time & Life Building

3-6. Otemachi

2-6, Suita Osaka 565. Japan -7-6, Suita Osaka 565, Japan Z-chorne Chivoda-ku,

Tokyo

100. Japan

Abstract By the simulations with the parameters of an ILT/ILE experiment, the pulse shape and the energy spectra of the electron beam accelerated by the linac are obtained. In the RF-linac FEL total simulations with the parameters of an ILT/ILE experiments, the start up of the FEL oscillations is found to depend on the pulse shape of the electron beam from the linac. As a conclusion, the coherent spontaneous emission effects and the quick start up of FEL oscillations are observed by the integrated RF-linac FEL total simulations.

1. Introduction An integrated computer simulation code has been developed to analyze the RF-linac FEL dynamics. First, the simulation code on the electron beam acceleration and transport processes in the RF-linac (LUNA) has been developed to analyze the characteristics of the electron beam and to optimize the parameters of RF-linac. Second, a space-time dependent 3-dimensional FEL simulation code (Shipout) has been developed [l]. The integrated RF-linac FEL simulations have been performed by using the electron beam data from LUNA in Shipout. At ILTIILE, Osaka, an 8.5 MeV RF-linac with a photocathode RF-gun is used for FEL oscillator experiments. By using a 2 cm wiggler, the FEL oscillator experiments at a wavelength approximately of 46 pm have been carried out. In this paper, the theoretical analysis of the experiment by the integrated computer simulation code is described. In Section 2, the simulation code of the electron beam acceleration and transport in RF-linac (LUNA) is described. In Section 3, the RF-linac FEL total simulation is described. Section 4 is the summary.

2. The simulation RF-linac (LUNA)

code, the space charge effect is included, which greatly degrades the emittance of electron beam. In Fig. I, the energy spectrum of the optimized electron beam from the linac is shown. The solid line represents the simulation result and the dashed line represents the Gaussian fitted curve. The peak energy is 8SOMeV and the energy spread is 0.064 MeV. Note that we adjust the parameters of the elements of the RF-linac as the peak energy and energy spread agree with those of experiments. In this calculation, the current from the cathode is 13 A and the differences of the phases between the RF-gun and the main accelerator is 9.5 ps. Note that the radio frequency of this linac is 2856 MHz. One ps corresponds to one degree. Fig. 2, the pulse shape of electron beam from the is shown. The pulse shape of the electron beam has sharp rise-up, 2 ps sharp fall-down and it slowly

40-

code of the electron beam in the

A 3-dimensional simulation code of the electron beam in RF-linac (LUNA) has been developed to analyze the characteristics of the electron beam and to optimize the parameters of the RF-linac which consists of the RF-gun, quadrupole magnet, a-magnet, main-accelerator, etc. The behavior of the electron beam is analyzed by integrating the equation of motion for all particles numerically. In this 0168-9002/96/$15.00 Copyright SSDZ 0168-9002(95)01430-6

8.2

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Energy

8.5

8.6

8.7

8.8

(MeV)

Fig. 1. The energy spectrum of optimized electron beam from the RF-linac.

0 1996 Elsevier Science B.V. All rights reserved

195

H. Furukawa et al. / Nucl. Instr. and Meth. in Phys. Res. A 375 (1996) 194-197

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3. Integrated

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Fig. 3. The dependences of the energy spectrum of the electron beam on the differences of the phases between RF-gun and main accelerator.

RF-linac FEL simulation

We performed the integrated RF-linac FEL simulation by using the data for the actual electron beam from LUNA in Shipout. The details of Shipout are described in Ref. [ 11. The parameters are summarized in Table 1. First, we describe the connection of LUNA with Shipout. The super particle used in Shipout can have an arbitrary shape. In order to estimate the dependences of the startup of FEL oscillations on the pulse shape of the electron beam, we determine the initial shape of super particle in Shipout as follows:

Table 1 The parameters

.

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Time2 (psf

of the pulse shape of the electron beam on the initial current from the cathode.

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1

Fig. 4. The dependences

decays with the width of 1.5ps as a function of time. The peak current is 50 A. In Fig. 3, the dependences of the energy spectrum of the electron beam on the differences of the phases between RF-gun and main-accelerator are shown. The solid line stands for the energy spectrum, where the difference of the phases is 9.5 ps. The dashed line represents the case when the difference of the phases is IO ps. The dotted line represents the case when the difference of the phases is 9~s. The dashed line has two peaks and the shape of the current profile is noisy. In conclusion, the phases between RF-gun and main-accelerator has to be controlled with the accuracy of 0.5 ps. In Fig. 4, the dependences of the pulse shape of the electron beam on the initial current from the cathode are represented. The solid line denotes the pulse shape where the initial current is 13 A. The dashed line represents the case when the initial current is 12 A. The dotted line stands for that when the initial current is I4 A. As shown in Fig. 4, the difference of 1 A of the initial current causes a difference of 8 A at the end of RF-linac. But the differ-

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Fig. 2. The pulse shape of electron beam from the RF-linac.

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used in this simulation

Electron energy Energy spread Emittance Bunch length Peak current Wiggler period Wiggler length Wavelength of laser Detuning parameter Round-trip loss Rayleigh length Wiggler magnetic field K parameter Number of uarticles

8.5 MeV 0.064 MeV n mm mrad 3 ps (0.9 mm) 50A 2cm 1OOcm 44.1 pm - 22.05 pm 1% 50 cm 0.5 T 0.93 892

IV LONG WAVELENGTH

FELs

H. Furukmva

196

et al. I Nucl. lnstr. and Meth. in Phys. Res. A 375 (1996) 194-197

where f is the shape function of electron beam obtained from LUNA. f, is the shape of the jth particle, A is the wavelength of an electromagnetic wave, @, is the phase between the wave and the jth particle, uZ, is the z component of the speed of the jth particle and c the speed of light. The function f is determined as follows. In the calculation using LUNA. the arriving time from the cathode to the end of the main accelerator of each particle is obtained. For the arriving time mentioned above, we determine the distribution function5 And we determine the initial distribution functions of energy, velocity and position of super particles to satisfy the output results from LUNA. In Fig. 5, the dependences of the startup of FEL oscillations on the pulse shape are shown. In Fig. 5a, the actual pulse shape from LUNA and the Gaussian pulses with a half-width of 1. 2. 3 and 5 ps are shown. Note the total charges are fixed for each pulse in Fig. 5a. The Gaussian function is determined as

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Time (ps) Fig. 6. The optical pulse shapes at 20 round trips.

Fig. 5b shows the start up of FEL oscillations as a function of round-trip number using the pulse shapes in Fig. 5a. As shown in Fig. 5a. the start-up for the actual RF-linac pulse is almost same as for a 1 ps Gaussian pulse. The emission energy after 20 round trips for the actual RF-linac pulse is about 0.25 times that for a 1 ps Gaussian pulse and roughly 80 times that for a 2 ps Gaussian pulse. When the RF-linac pulse is used, the interaction length is longer than that for a 1 ps Gaussian pulse because of the slow decay of the optimized pulse shape. Therefore, if the round-trip number is larger than 20. the emission energy for the RF-linac pulse might be higher than that for a I ps Gaussian pulse. Fig. 6 shows the optical pulse shapes after 20 round trips. The solid line represents that for the RF-linac pulse and the dotted line for a 1 ps Gaussian pulse. Note that the slippage length is about 8 ps. For the case of the RF-linac pulse, the peak position of optical pulse shape is nearly equal to that of electron beam. But for the case of a I ps Gaussian pulse. the peak position of the optical pulse shape is in front of that of electron beam. It seems that for the case of the RF-linac pulse, the light is emitted from both of rising-up and slow decay part. Fig. 7 shows the energy spectrum of FEL at the end of

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Fig. 5. (a) The actual pulse shape from LUNA and the Gaussian pulses with a half width of 1, 2. 3 and 5 ps. (b) The start up of FEL oscillations as a function of round-trip number using the pulse shapes in Fig. 6a.

-6

-5

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Ao ( 1012 rad/s

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)

Fig. 7. The energy spectrum of FEL at the end of wiggler after 20 round trips.

H. Furukawa

et al. I Nucl. Instr. and Meth. in Phys. Res. A 3Z

wiggler after 20 round trips. The horizontal axis is the displacement from the central angular frequency (4.27 X 1O’j rad/s). The solid line represents that for the RF-linac pulse and the dotted line for a I ps Gaussian pulse. For the case of the RF-linac pulse, the energy spectrum is slightly different from the Gaussian case.

4. Summary An integrated computer simulation code has been developed to analyze the RF-linac FEL dynamics. First, the simulation code on the electron beam acceleration and transport processes in the RF-linac (LUNA) has been developed to analyze the characteristics of the electron beam in a RF-linac and to optimize the parameters of the RF-linac. Second. a space-time dependent 3-dimensional FEL simulation code (Shipout) has been developed [ 11. By simulations using LUNA with the parameters of an ILT/ ILE experiment, the pulse shape and the energy spectra of the electron beam at the end of the linac are estimated. The

(1996) 193-197

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peak energy is 8.50 MeV and the energy spread is 0.064 MeV. The pulse shape of the electron beam has 1 ps sharp rise-up, 2 ps sharp fall-down and it decays slowly with a width of 15 ps as a function of time. The peak current is 50 A. By the integrated RF-linac FEL simulations with the parameters of an ILTlILE experiment, the dependences of the start up of the FEL oscillations on the pulse shape of the electron beam from the linac are found. The coherent spontaneous emission effects and the quick startup of FEL oscillations have been observed in the integrated RF-linac FEL simulations. It seems that the pulse shape of the actual RF-linac electron beam is better for the quick startup than the Gaussian pulse shape, when the HWHM is given.

Reference [ 11 Y. Sentoku. H. Furukawa. K. Mima et al., Nucl. Instr. and Meth. A 358 (1995) 463.

Iv. LONG WAVELENGTH FELs