- Email: [email protected]
FELICITA II, a design study for a VUV-high-gain FEL at the storage ring DELTA
N INSTR & METHODS IN PHYSICS RESEARCH SecteA
Nuclear Instruments and Methods in Physics Research A318 (1992) 593-599 North-Holland
FÉLICITA II, a design study for a VUV-high-gain FEL at the storage ring DELTA D. Hölle
University ofDortmund, Acceleratorphysics, P.O. Box 500, 4600 Dortmund 50, Germany FELICITA II (free electron laser in a circular test accelerator) is the second FEL experiment planned et DELTA, the storage ring facility at the University of Dortmund, following a more conventional experiment in the visible and near UV [1]. It is designed to operate in the wavelength regime of 100 nm and considerably below . Due to the high losses of the optical cavity FELICITA II has to provide extremely high gain. This paper presents a design study of this FEL, giving preliminary parameters for the undulator, the ring resonator and the installation into the storage ring. Furthermore, simulation results concerning gain, susceptibility to energy spread and emittance, and the operation of FELICITA II in DELTA will be presented . 1. Introduction DELTA is a 1.5 GeV storage ring, under construction at the University of Dortmund [2] . Due to its low emittance and two long straight sections, it is an excellent driver for short wavelength FELs. FELICITA II will be the second FEL project at DELTA, following a more conventional experiment in the visible and UV regime [1] . It will be a high gain FEL capable of operating at wavelengths as short as 20 nm. In the following, preliminary design parameters of FELICITA II concerning the undulator, the optical cavity and the installation into DELTA will be discussed . Furthermore, simulation results, obtained from the 3D simulation code "FELS" will be presented [4,5]. 2. FEL requirements on the storage ring DELTA There are three main requirements a storage ring has to satisfy for FEL operation [6] : (1) Long dispersion-free straight sections for undulator magnets. DELTA has a racetrack shape, providing straight sections about 20 m long. Except for quadrupoles needed to match the betafunctions and the dispersion in the undulator, which reduce the available length to about 14 m, these sections are free from installations . (2) High peak currents in order to overcome the mirror losses in the short wavelength regime. In order to minimize the Touschek effect [7] to store high particle densities in DELTA, the optical
system was optimized for high energy acceptance [6]. Furthermore, the vacuum chamber was designed without steps to obtain an extremely small overall impedance. This reduces the feedback of wakefields back to the electron bunch and therefore minimizes bunch lengthening [8]. The extremely low pressure will minimize particle loss due to scattering with the rest gas . For further improvement of the bunch length, special mode damped cavities will be developed [2]. Moreover, the installation of additional rf power is foreseen to achieve a further reduction of the bunch length, yielding higher peak current . (3) Extremely small electron beam and divergence in the undulator, requiring extremely low emittance. In order to get a small natural emittance for DELTA, the optical system is based on triplet cells [2,9]. Due to the minimum of the dispersion in the dipole magnet, quantum excitation by the synchrotron radiation is rather small for this lattice [10]. Many cells with a rather small bending radius per cell yield a further reduction of the emittance [11]. As the dispersion is matched to zero in the undulâïor, no emittance blowup is expected due to the FEL interaction . These design goals meet the requirement of short damping times because high synchrotron radiation power can be emitted without serious quantum excitation. 3. The FÉLICITA II undulator To obtain the highest possible gain, the dimensionless current has to be maximized under the constraints
0168-9002/92/$05.00 © 1992 -- Elsevier Science Publishers B.V. All rights reserved
Vlll. NUMERICAL SIMULATIONS
594
D. Nölle / FELICITA II
determined by undulator technology and accelerator performance, that read for FELICITA II [4]: (1) FEL wavelength of about 100 nm at the minimum energy. (2) The electron beam energy higher than 500 MeV. DELTA is designed for a maximum energy of 1 .5 GeV, so that operation below 500 MeV might result in poor performance. (3) The maximum length of the straight section is 14 m. (4) 1 T peak undulator field is estimated to be the upper limit, obtainable with advanced undulator technology. Of course the highest gain will be reached at lowest energy. At 500 MeV these requirements yield the design values for the FELICITA II undulator given in table 1.
Table 2 Parameters of the ring resonator optical cavity for FELICITA II. The Rayleigh length and beam waist are given for operation at 500 MeV, corresponding to a wavelength of 115 nm
4. Design of a ring resonator for FELICITA II
Resulting optical properties Rayleigh length (undulator section) Beam waist (undulator section) Circumference Reflectivity per mirror Total reflectivity
Below 100 nm there is a strong decrease of the mirror reflectivity at normal incidence [12,13]. Therefore, only a ring resonator using mirrors at grazing incidence is possible for FELICITA II. Since the highest peak current is reached in single bunch operation of DELTA, the circumference of optical cavity and storage ring have to be equal. The ring resonator of FELICITA II will operate with a horizontal incident angle of 10° measured from the mirror surface to the laser beam. This corresponds to 18 mirrors for one roundtrip, arranged into 4 optical systems, two defocusing hyperbolical mirrors near the electron beam orbit and two focusing multifacet mirrors, as proposed by Newnam [14]. The optical beam waist in the recirculation section is designed to be 10 times larger than in the center of the undulator, yielding a considerable reduction of the power load on the multifacet mirrors compared to the front hyperboloid. Furthermore, only the front hyperboloid is irradiated by the extremely short-wavelength contributions of the spontaneous radiation. Each of the two multifacet mirrors consists of eight mirrors. To avoid diffraction losses, the size of each facet is chosen to be equal to five times the beam waist in the long recirculation section. Table 1 Parameters of the FELICITA II undulator Overall length Period length Number of periods Peak magnetic field K-value
13 .94 m 3.4 cm 411 1.07 T 3.4
Lengths of the drift spaces Undulator straight section Recirculation section Distance between hyperboloids and multifacet arcs Parameters of the multifacet mirrors Number of facets Incident angle (to the mirror surface) Width of a facet Horizontal curvature radius Vertical curvature radius Parameters of the hyperbolical mirrors Horizontal curvature radius Vertical curvature radius
25 .7 m 54 .89 m 15 .76 m 8 10° 22.5 cm 2215.5 m 384.72 m - 216.0 m - 37 .5 m 4.16 m 3.9 x 10 -4 m 115.2 m 0.95 0.4
The resulting parameters of the ring resonator optical cavity for FELICITA II are given in table 2. 5. Installation of FELICITA II in DELTA The undulator of FELICITA II, designed with plane pole faces, will be installed in one long straight section of DELTA [4]. Since the vertical tune shift due to this magnet is of the same order of magnitude as the natural tune of DELTA, a special beam optics has to be designed. With the present undulator design two different operation modes for FELICITA II are possible [16]. As shown in fig. 1, version 1 has a rather big horizontal but nearly constant betafunction in the undulator. In contrast, as shown in fig. 2, the second design (version 2) has a much smaller horizontal betafunction there, yielding a stronger divergence of the electron beam. Both beam optics show two betatron oscillations in the undulator in the vertical direction. As the difference between these two results only from different quadrupole strengths without any changes of the lattice, it is easy to operate with both versions . For single electron bunch operation the peak current of DELTA at 500 MeV will be about 150 A, corresponding to a moderate average current of 50 mA. The horizontal emittance of the electron beam obtained at 500 MeV is estimated to be 1.5 x 10 -s mrad and a factor of 10 smaller in vertical direction.
D. Nölte / FELICITA Il
595
b
1 o- g .
pc,s , t
~ on
[m]
Fig. 1 . Evolution of the betafunctions for version 1 of the DELTA optics. The curves labeled by (a) represent the result from a common storage ring optics code, whereas curve (b) is a result of the simulation code.
Fig . 2. Betafunctions for version 2 ofthe DELTA optics. As in case of fig. 1 there is a good agreement between the results of the beam optics program (a) and the simulation code (b).
This is about one order of magnitude bigger than the natural emittance of DELTA, and takes intra-beam scattering into account [2,15] . The parameters of DELTA essential for the FELICITA II experiment are listed in table 3.
especially as DELTA will be oprated with a flat electron beam. Moreover, the betatron oscillatiûn results in strong changes of the electron beam size and of the electron density within the laser beam. Even for a circular beam neglecting the betatron motion results in differences of the gain of about 100% K51. Figs. 3 and 4 show the gain of FELICITA II for both versions of the DELTA optics. At a wavelength of 115 nm the maximum gain is about one order of magnitude higher for version 2, as the smaller average beam size yields a higher average electron density in the interaction region . The disadvantage of this optics
6. Gain calculation for the FELICITA II experiment
It has to be emphasized that only 3D-calculations, including energy spread transverse momentum, are capable of getting realistic gain values for FELICITA II, Table 3 Estimated operation parameters at 500 MeV for both FEL optics Opticalfunctions
Horizontal betafunction (undulator entrance) Vertical betafunction (undulator entrance) Horizontal alphafunction (undulator entrance) Vertical alphafunction (undulator entrance) Horizontal tune Vertical tune Vertical tune-shift in the undulator Dispersion in the undulator
'eyin a xin a Ym Qx
QY
AQX
D
Electron beam parameters
Horizontal emittance Vertical emittance Beam energy Energy spread Peak current Average current (QZ =1 .5 cm) a
x
E
EY
Y
oy/y A
I
High /3x version 32 .41 m 17.29 m 0.23 rad 0.16 rad 8.6848 4.2709 1 .002 0.0 m
Low ß,r version a 22.88 m 0.27 m 2 .94 rad 0.17 rad 9.5618 5.0905 1 .054 0.0 m
1 .5 X 10 -s mrad 1.5 X 10-y mrad 1000 [mc2]
0.7 X 10-3 150 A 50 mA
Optics assuming fourfold symmetry of the DELTA lattice . Vlll. NUMERICAL SIMULATIONS
D. Nöße / FELICITA 11
596 a
2 c,
J
ci- L u" , " D
"-
Fig. 3. Gain calculation for FELICITA 11 at 115 nm for version I of the FEL optics. The curve with highest gain (a) corresponds to a '"cold" electron beam, whereas the lowest curve (d) includes energy spread and transverse momentum. The two other curves are calculated with only one degrading effect, either energy spread (c) or transverse momentum (b) included. Rhombi correspond to runs with harmonics included.
is that the electron beam will be more affected by the Touschek effect [7] or intra-beam-scattering [151. This may lead to a serious %itation of current and lifetime. Furthermore, this operation mode is more sensitive to emittance growth (fig. 4). The main effect of gain degradation is due to energy spread, as shown in figs. 5 and 6. Fig . 5 shows the dependence of the gain on the energy spread . For typical values of the energy spread (10 -4 < Qy/y < 10-;) the gain of FELICITA II decreases exponentially . The results with the "cold" electron beam and the calculation with energy spread and transverse momentum included differ by about one order of magnitude . Therefore, these effects have to be included in the calculations in a self-consistent manner. Analytically calculated degradation factors, usual in the small gain regime [18], cannot be used in the high-gain regime . Half of all the data points in figs. 5 and 6 have been calculated with the harmonics included [4], showing no influence of the harmonics on the gain of the fundamental . Up to now only the operation at the "long" wavelength of 115 nm has been considered. At shorter wavelengths the source function decreases drastically with increasing energy . On the other hand, the performance of DELTA will increase with energy, reaching
cl e t
-g
r, u
Fig. 4. This figure shows the same curves as in fig. 3 but for version 2 of the DELTA optics. The effect of energy spread and transverse momentum yield similar gain degradation as in case of fig. 3d.
its optimum at 1 GeV. Therefore, much higher peak currents and smaller z:mittances counteract this decrease . Fig . 7 shows the evolution of the gain versus wavelength for both versions of the DELTA optics. Assuming constant losses of the optical cavity of about 60%, the shortest wavelength obtainable with FE-
enBrg~. Spread Cr,u Fig. 5. Dependence of the FEL gain on the energy spread of the electron beam for both optics . Curves (a) and (b) belong to version 1 of the DELTA optics and correspond to calculation without and with transverse momentum included. The curves (c) and (d) show the results for version 2 of the DELTA optics.
D. Nölle / FELICITA 11
597
0 3
......... .....\
Fig . 6. Influence bf the electron beam emittance on the FEL gain. The curve (a) and (c) correspond to the calculation for version I and 2, respectively, without energy spread, whereas energy spread is included in curves (b) and (d). These plots show that the gain of FÉLICITA II with version 2 of the DELTA optics is more seriously affected by emittance effects .
LICITA II will be about 20 nm. The corresponding evolution of emittance and peak current in DELTA is shown in figs. 8 and 9 . Energy spread and bunch length are estimated to remain constant over the whole energy interval.
7. Simulation of a single laser pulse in FÉLICITA II In storage ring FELs the recirculation of the electron beam results in a steady increase of the energy spread during the interaction . The damping mecha-
a 3
EEL wavelength
Cnm3
Fig . 7. Evolution of the peak gain versus the FEL wavelength, for both "cold" (c) and "hot" (h) electron beam, and for version I (a) and 2 (b) of the DELTA optics . The data points are all calculated with the electron beam parameters adjusted according to the energy as shown in figs. 8 and 9. The gain values using version 2 of the DELTA optics decrease faster with increasing energy and decreasing wavelength (b), respectively. Calculations including gain degradation promise operation down to 20 nm. The bar represents the oscillator threshold for 60% !esses of the optical cavity. VIII. NUMERICAL SIMULATIONS
D. Nölle / FÉLICITA II
598
12 . 5 rn
20 nm
5 Q Y
29 nm
n e . 3
45 NO
a Q
u
4 . 4®®
e®®
Ere~rgy
fl Emev3
Fig. 8. Evolution of peak current versus energy . The stability adn performance of the accelerator increases with increasing beam energy. At low energies the beam is affected by several degrading effects and becomes more stable at higher energy, yielding a linear increase ofthe peak current. nism of the storage ring acts on a much larger time scale, and can thus be neglected for the purpose of this analysis [4]. Furthermore, only the operation of a device with extremely high gain will be considered. Hence, also the synchrotron oscillation of the ring can be neglected. The simulation run starts from a power level of the order of the spontaneous radiation of the undulator magnet [19]. The rather high effective gain yields a fast rise of the laser intensity (fig. 10). Simultaneously, the
Fig. 9. Evolution of the emittance versus energy. At low energy there is emittance blow-up due to intra-beam scatter ing which diminishes with increasing energy. For high energies the emittance grows quadratically with the energy. heating of the energy spread increases (fig. 11), yielding serious gain degradation (fig. 12). Although the growth of the FEL power has already stopped, the heating of the energy spread continues on, and decays with the field power in the optical cavity. In this case this is rather fast due to the poor overall reflectivity . The recovery time between two macropulses is determined by the damping time of the storage ring, corresponding to about 100 ms for DELTA at 500 MeV. The simulation results provide an estimate of 25 MW for the intracavity peak power of FELICITA II.
number of passes Fig. 10. intracavity peak power versus the number of passes . The drastical decrease of the gain at peak power, shown in fig. 12, is due to the rapid increase of energy spread during the pulse, as shown in fig. 11 . Therefore, the rise of the pulse is stopped and it decays according to the losses of the optical cavity.
D. Nölte / FELICITA II
599
will be about 3 p,s. Assuming a Gaussian distribution of the current and the laser field in longitudinal direction, one can estimate the width of the micropulse [4]. For FELICITA II this is 18 ps. 8. Conclusion
n u mb e r
O -F
p 355e s
Fig. 11 . Evolution of the energy spread versus the number of passes . The rise of the energy spread is correlated to the intracavity power during the interaction . Therefore, it increases more strongly as the pulse intensity grows.
The macropulse duration is expected to be about 2.5 Ws, corresponding to 7 roundtrips of the electron beam in DELTA. The time the pulse needs for building up
number
of passes
Fig. 12 . FEL gain versus number of passes . The gain remains on a high level during start-up. After high intracavity power is established, the gain breaks down due to the growth of energy spread .
In this paper the preliminary design of FELICITA II, a high-gain FEL for the storage ring DELTA, was presented. Since the accelerator is still under construction, measured quantities for the performance of DELTA are not available now. Therefore, a final design of this FEL device is not possible at the moment. But the numbers given for the accelerator performance represent rather conservative estimates, so that FELICITA II will surely be capable of operating in the wavelength regime from 100 nm to 20 nm. Peak powers of about 25 MW are expected for operation near 100 nm. References [1] D. Nölte et al., Nucl . Instr. and Meth. A296 (1990) 263.
[2] DELTA Group, DELTA, a status report, University of Dortmund, August 1990. [3] S. Benson, private communication. [4] D. N61te, Ph .D. Thesis, University of Dortmund, 1991 . [51 D. N61te, these Proceedings (13th Int. Free Electron Laser Conf., Santa Fe, USA, 1991) Nucl . Instr. and Meth . A318 (1992) 600. [6] D. Nölte and K. Wille, Research Trends in Physics: Coherent Radiation Generation and Particle Accelerators, ed. A. Prolharov et al . (AIP, 1992). [7] C. Bernadini et al., Nuovo Cimento 34 (1964) 1473. [8] T. Weiland, DESY 81/88,1988. [9] D. Ndlte et al ., Nucl. Instr. and Meth . A296 (1990) 263. [10] G. Mülhaupt, CERN 90-03 (1990) 98. [11] A. Ropert, CERN 90-03 (1990) 158. [121 D.T . Attwood, AIP Conf. Proc. 118 (1984) 263. [13] M.L. Scott, Appl . Opt. 27 (1988) 1503 . [14] B.E. Newnam, Proc. SPIE 738 (1987) 165. [15] J. Bjorken and S. Mtingawa, Part . Accel. 13 (1983) 115. [16] D. Schirmer, DELTA internal report 91-04, 1991 . [17] E.T. Scharlemann, J. Appl. Phys. 58 (1985) 2154. [18] U. Bizzarri et al ., Riv. Nuovo Cimento 10 (1987) 1. [19] K.J . Kim, X-Ray Data Booklet, ed. D. Vaughan (LBL PUB-490, 1986).
VIII . NUMERICAL SIMULATIONS
Nuclear Instruments and Methods in Physics Research A318 (1992) 593-599 North-Holland
FÉLICITA II, a design study for a VUV-high-gain FEL at the storage ring DELTA D. Hölle
University ofDortmund, Acceleratorphysics, P.O. Box 500, 4600 Dortmund 50, Germany FELICITA II (free electron laser in a circular test accelerator) is the second FEL experiment planned et DELTA, the storage ring facility at the University of Dortmund, following a more conventional experiment in the visible and near UV [1]. It is designed to operate in the wavelength regime of 100 nm and considerably below . Due to the high losses of the optical cavity FELICITA II has to provide extremely high gain. This paper presents a design study of this FEL, giving preliminary parameters for the undulator, the ring resonator and the installation into the storage ring. Furthermore, simulation results concerning gain, susceptibility to energy spread and emittance, and the operation of FELICITA II in DELTA will be presented . 1. Introduction DELTA is a 1.5 GeV storage ring, under construction at the University of Dortmund [2] . Due to its low emittance and two long straight sections, it is an excellent driver for short wavelength FELs. FELICITA II will be the second FEL project at DELTA, following a more conventional experiment in the visible and UV regime [1] . It will be a high gain FEL capable of operating at wavelengths as short as 20 nm. In the following, preliminary design parameters of FELICITA II concerning the undulator, the optical cavity and the installation into DELTA will be discussed . Furthermore, simulation results, obtained from the 3D simulation code "FELS" will be presented [4,5]. 2. FEL requirements on the storage ring DELTA There are three main requirements a storage ring has to satisfy for FEL operation [6] : (1) Long dispersion-free straight sections for undulator magnets. DELTA has a racetrack shape, providing straight sections about 20 m long. Except for quadrupoles needed to match the betafunctions and the dispersion in the undulator, which reduce the available length to about 14 m, these sections are free from installations . (2) High peak currents in order to overcome the mirror losses in the short wavelength regime. In order to minimize the Touschek effect [7] to store high particle densities in DELTA, the optical
system was optimized for high energy acceptance [6]. Furthermore, the vacuum chamber was designed without steps to obtain an extremely small overall impedance. This reduces the feedback of wakefields back to the electron bunch and therefore minimizes bunch lengthening [8]. The extremely low pressure will minimize particle loss due to scattering with the rest gas . For further improvement of the bunch length, special mode damped cavities will be developed [2]. Moreover, the installation of additional rf power is foreseen to achieve a further reduction of the bunch length, yielding higher peak current . (3) Extremely small electron beam and divergence in the undulator, requiring extremely low emittance. In order to get a small natural emittance for DELTA, the optical system is based on triplet cells [2,9]. Due to the minimum of the dispersion in the dipole magnet, quantum excitation by the synchrotron radiation is rather small for this lattice [10]. Many cells with a rather small bending radius per cell yield a further reduction of the emittance [11]. As the dispersion is matched to zero in the undulâïor, no emittance blowup is expected due to the FEL interaction . These design goals meet the requirement of short damping times because high synchrotron radiation power can be emitted without serious quantum excitation. 3. The FÉLICITA II undulator To obtain the highest possible gain, the dimensionless current has to be maximized under the constraints
0168-9002/92/$05.00 © 1992 -- Elsevier Science Publishers B.V. All rights reserved
Vlll. NUMERICAL SIMULATIONS
594
D. Nölle / FELICITA II
determined by undulator technology and accelerator performance, that read for FELICITA II [4]: (1) FEL wavelength of about 100 nm at the minimum energy. (2) The electron beam energy higher than 500 MeV. DELTA is designed for a maximum energy of 1 .5 GeV, so that operation below 500 MeV might result in poor performance. (3) The maximum length of the straight section is 14 m. (4) 1 T peak undulator field is estimated to be the upper limit, obtainable with advanced undulator technology. Of course the highest gain will be reached at lowest energy. At 500 MeV these requirements yield the design values for the FELICITA II undulator given in table 1.
Table 2 Parameters of the ring resonator optical cavity for FELICITA II. The Rayleigh length and beam waist are given for operation at 500 MeV, corresponding to a wavelength of 115 nm
4. Design of a ring resonator for FELICITA II
Resulting optical properties Rayleigh length (undulator section) Beam waist (undulator section) Circumference Reflectivity per mirror Total reflectivity
Below 100 nm there is a strong decrease of the mirror reflectivity at normal incidence [12,13]. Therefore, only a ring resonator using mirrors at grazing incidence is possible for FELICITA II. Since the highest peak current is reached in single bunch operation of DELTA, the circumference of optical cavity and storage ring have to be equal. The ring resonator of FELICITA II will operate with a horizontal incident angle of 10° measured from the mirror surface to the laser beam. This corresponds to 18 mirrors for one roundtrip, arranged into 4 optical systems, two defocusing hyperbolical mirrors near the electron beam orbit and two focusing multifacet mirrors, as proposed by Newnam [14]. The optical beam waist in the recirculation section is designed to be 10 times larger than in the center of the undulator, yielding a considerable reduction of the power load on the multifacet mirrors compared to the front hyperboloid. Furthermore, only the front hyperboloid is irradiated by the extremely short-wavelength contributions of the spontaneous radiation. Each of the two multifacet mirrors consists of eight mirrors. To avoid diffraction losses, the size of each facet is chosen to be equal to five times the beam waist in the long recirculation section. Table 1 Parameters of the FELICITA II undulator Overall length Period length Number of periods Peak magnetic field K-value
13 .94 m 3.4 cm 411 1.07 T 3.4
Lengths of the drift spaces Undulator straight section Recirculation section Distance between hyperboloids and multifacet arcs Parameters of the multifacet mirrors Number of facets Incident angle (to the mirror surface) Width of a facet Horizontal curvature radius Vertical curvature radius Parameters of the hyperbolical mirrors Horizontal curvature radius Vertical curvature radius
25 .7 m 54 .89 m 15 .76 m 8 10° 22.5 cm 2215.5 m 384.72 m - 216.0 m - 37 .5 m 4.16 m 3.9 x 10 -4 m 115.2 m 0.95 0.4
The resulting parameters of the ring resonator optical cavity for FELICITA II are given in table 2. 5. Installation of FELICITA II in DELTA The undulator of FELICITA II, designed with plane pole faces, will be installed in one long straight section of DELTA [4]. Since the vertical tune shift due to this magnet is of the same order of magnitude as the natural tune of DELTA, a special beam optics has to be designed. With the present undulator design two different operation modes for FELICITA II are possible [16]. As shown in fig. 1, version 1 has a rather big horizontal but nearly constant betafunction in the undulator. In contrast, as shown in fig. 2, the second design (version 2) has a much smaller horizontal betafunction there, yielding a stronger divergence of the electron beam. Both beam optics show two betatron oscillations in the undulator in the vertical direction. As the difference between these two results only from different quadrupole strengths without any changes of the lattice, it is easy to operate with both versions . For single electron bunch operation the peak current of DELTA at 500 MeV will be about 150 A, corresponding to a moderate average current of 50 mA. The horizontal emittance of the electron beam obtained at 500 MeV is estimated to be 1.5 x 10 -s mrad and a factor of 10 smaller in vertical direction.
D. Nölte / FELICITA Il
595
b
1 o- g .
pc,s , t
~ on
[m]
Fig. 1 . Evolution of the betafunctions for version 1 of the DELTA optics. The curves labeled by (a) represent the result from a common storage ring optics code, whereas curve (b) is a result of the simulation code.
Fig . 2. Betafunctions for version 2 ofthe DELTA optics. As in case of fig. 1 there is a good agreement between the results of the beam optics program (a) and the simulation code (b).
This is about one order of magnitude bigger than the natural emittance of DELTA, and takes intra-beam scattering into account [2,15] . The parameters of DELTA essential for the FELICITA II experiment are listed in table 3.
especially as DELTA will be oprated with a flat electron beam. Moreover, the betatron oscillatiûn results in strong changes of the electron beam size and of the electron density within the laser beam. Even for a circular beam neglecting the betatron motion results in differences of the gain of about 100% K51. Figs. 3 and 4 show the gain of FELICITA II for both versions of the DELTA optics. At a wavelength of 115 nm the maximum gain is about one order of magnitude higher for version 2, as the smaller average beam size yields a higher average electron density in the interaction region . The disadvantage of this optics
6. Gain calculation for the FELICITA II experiment
It has to be emphasized that only 3D-calculations, including energy spread transverse momentum, are capable of getting realistic gain values for FELICITA II, Table 3 Estimated operation parameters at 500 MeV for both FEL optics Opticalfunctions
Horizontal betafunction (undulator entrance) Vertical betafunction (undulator entrance) Horizontal alphafunction (undulator entrance) Vertical alphafunction (undulator entrance) Horizontal tune Vertical tune Vertical tune-shift in the undulator Dispersion in the undulator
'eyin a xin a Ym Qx
QY
AQX
D
Electron beam parameters
Horizontal emittance Vertical emittance Beam energy Energy spread Peak current Average current (QZ =1 .5 cm) a
x
E
EY
Y
oy/y A
I
High /3x version 32 .41 m 17.29 m 0.23 rad 0.16 rad 8.6848 4.2709 1 .002 0.0 m
Low ß,r version a 22.88 m 0.27 m 2 .94 rad 0.17 rad 9.5618 5.0905 1 .054 0.0 m
1 .5 X 10 -s mrad 1.5 X 10-y mrad 1000 [mc2]
0.7 X 10-3 150 A 50 mA
Optics assuming fourfold symmetry of the DELTA lattice . Vlll. NUMERICAL SIMULATIONS
D. Nöße / FELICITA 11
596 a
2 c,
J
ci- L u" , " D
"-
Fig. 3. Gain calculation for FELICITA 11 at 115 nm for version I of the FEL optics. The curve with highest gain (a) corresponds to a '"cold" electron beam, whereas the lowest curve (d) includes energy spread and transverse momentum. The two other curves are calculated with only one degrading effect, either energy spread (c) or transverse momentum (b) included. Rhombi correspond to runs with harmonics included.
is that the electron beam will be more affected by the Touschek effect [7] or intra-beam-scattering [151. This may lead to a serious %itation of current and lifetime. Furthermore, this operation mode is more sensitive to emittance growth (fig. 4). The main effect of gain degradation is due to energy spread, as shown in figs. 5 and 6. Fig . 5 shows the dependence of the gain on the energy spread . For typical values of the energy spread (10 -4 < Qy/y < 10-;) the gain of FELICITA II decreases exponentially . The results with the "cold" electron beam and the calculation with energy spread and transverse momentum included differ by about one order of magnitude . Therefore, these effects have to be included in the calculations in a self-consistent manner. Analytically calculated degradation factors, usual in the small gain regime [18], cannot be used in the high-gain regime . Half of all the data points in figs. 5 and 6 have been calculated with the harmonics included [4], showing no influence of the harmonics on the gain of the fundamental . Up to now only the operation at the "long" wavelength of 115 nm has been considered. At shorter wavelengths the source function decreases drastically with increasing energy . On the other hand, the performance of DELTA will increase with energy, reaching
cl e t
-g
r, u
Fig. 4. This figure shows the same curves as in fig. 3 but for version 2 of the DELTA optics. The effect of energy spread and transverse momentum yield similar gain degradation as in case of fig. 3d.
its optimum at 1 GeV. Therefore, much higher peak currents and smaller z:mittances counteract this decrease . Fig . 7 shows the evolution of the gain versus wavelength for both versions of the DELTA optics. Assuming constant losses of the optical cavity of about 60%, the shortest wavelength obtainable with FE-
enBrg~. Spread Cr,u Fig. 5. Dependence of the FEL gain on the energy spread of the electron beam for both optics . Curves (a) and (b) belong to version 1 of the DELTA optics and correspond to calculation without and with transverse momentum included. The curves (c) and (d) show the results for version 2 of the DELTA optics.
D. Nölle / FELICITA 11
597
0 3
......... .....\
Fig . 6. Influence bf the electron beam emittance on the FEL gain. The curve (a) and (c) correspond to the calculation for version I and 2, respectively, without energy spread, whereas energy spread is included in curves (b) and (d). These plots show that the gain of FÉLICITA II with version 2 of the DELTA optics is more seriously affected by emittance effects .
LICITA II will be about 20 nm. The corresponding evolution of emittance and peak current in DELTA is shown in figs. 8 and 9 . Energy spread and bunch length are estimated to remain constant over the whole energy interval.
7. Simulation of a single laser pulse in FÉLICITA II In storage ring FELs the recirculation of the electron beam results in a steady increase of the energy spread during the interaction . The damping mecha-
a 3
EEL wavelength
Cnm3
Fig . 7. Evolution of the peak gain versus the FEL wavelength, for both "cold" (c) and "hot" (h) electron beam, and for version I (a) and 2 (b) of the DELTA optics . The data points are all calculated with the electron beam parameters adjusted according to the energy as shown in figs. 8 and 9. The gain values using version 2 of the DELTA optics decrease faster with increasing energy and decreasing wavelength (b), respectively. Calculations including gain degradation promise operation down to 20 nm. The bar represents the oscillator threshold for 60% !esses of the optical cavity. VIII. NUMERICAL SIMULATIONS
D. Nölle / FÉLICITA II
598
12 . 5 rn
20 nm
5 Q Y
29 nm
n e . 3
45 NO
a Q
u
4 . 4®®
e®®
Ere~rgy
fl Emev3
Fig. 8. Evolution of peak current versus energy . The stability adn performance of the accelerator increases with increasing beam energy. At low energies the beam is affected by several degrading effects and becomes more stable at higher energy, yielding a linear increase ofthe peak current. nism of the storage ring acts on a much larger time scale, and can thus be neglected for the purpose of this analysis [4]. Furthermore, only the operation of a device with extremely high gain will be considered. Hence, also the synchrotron oscillation of the ring can be neglected. The simulation run starts from a power level of the order of the spontaneous radiation of the undulator magnet [19]. The rather high effective gain yields a fast rise of the laser intensity (fig. 10). Simultaneously, the
Fig. 9. Evolution of the emittance versus energy. At low energy there is emittance blow-up due to intra-beam scatter ing which diminishes with increasing energy. For high energies the emittance grows quadratically with the energy. heating of the energy spread increases (fig. 11), yielding serious gain degradation (fig. 12). Although the growth of the FEL power has already stopped, the heating of the energy spread continues on, and decays with the field power in the optical cavity. In this case this is rather fast due to the poor overall reflectivity . The recovery time between two macropulses is determined by the damping time of the storage ring, corresponding to about 100 ms for DELTA at 500 MeV. The simulation results provide an estimate of 25 MW for the intracavity peak power of FELICITA II.
number of passes Fig. 10. intracavity peak power versus the number of passes . The drastical decrease of the gain at peak power, shown in fig. 12, is due to the rapid increase of energy spread during the pulse, as shown in fig. 11 . Therefore, the rise of the pulse is stopped and it decays according to the losses of the optical cavity.
D. Nölte / FELICITA II
599
will be about 3 p,s. Assuming a Gaussian distribution of the current and the laser field in longitudinal direction, one can estimate the width of the micropulse [4]. For FELICITA II this is 18 ps. 8. Conclusion
n u mb e r
O -F
p 355e s
Fig. 11 . Evolution of the energy spread versus the number of passes . The rise of the energy spread is correlated to the intracavity power during the interaction . Therefore, it increases more strongly as the pulse intensity grows.
The macropulse duration is expected to be about 2.5 Ws, corresponding to 7 roundtrips of the electron beam in DELTA. The time the pulse needs for building up
number
of passes
Fig. 12 . FEL gain versus number of passes . The gain remains on a high level during start-up. After high intracavity power is established, the gain breaks down due to the growth of energy spread .
In this paper the preliminary design of FELICITA II, a high-gain FEL for the storage ring DELTA, was presented. Since the accelerator is still under construction, measured quantities for the performance of DELTA are not available now. Therefore, a final design of this FEL device is not possible at the moment. But the numbers given for the accelerator performance represent rather conservative estimates, so that FELICITA II will surely be capable of operating in the wavelength regime from 100 nm to 20 nm. Peak powers of about 25 MW are expected for operation near 100 nm. References [1] D. Nölte et al., Nucl . Instr. and Meth. A296 (1990) 263.
[2] DELTA Group, DELTA, a status report, University of Dortmund, August 1990. [3] S. Benson, private communication. [4] D. N61te, Ph .D. Thesis, University of Dortmund, 1991 . [51 D. N61te, these Proceedings (13th Int. Free Electron Laser Conf., Santa Fe, USA, 1991) Nucl . Instr. and Meth . A318 (1992) 600. [6] D. Nölte and K. Wille, Research Trends in Physics: Coherent Radiation Generation and Particle Accelerators, ed. A. Prolharov et al . (AIP, 1992). [7] C. Bernadini et al., Nuovo Cimento 34 (1964) 1473. [8] T. Weiland, DESY 81/88,1988. [9] D. Ndlte et al ., Nucl. Instr. and Meth . A296 (1990) 263. [10] G. Mülhaupt, CERN 90-03 (1990) 98. [11] A. Ropert, CERN 90-03 (1990) 158. [121 D.T . Attwood, AIP Conf. Proc. 118 (1984) 263. [13] M.L. Scott, Appl . Opt. 27 (1988) 1503 . [14] B.E. Newnam, Proc. SPIE 738 (1987) 165. [15] J. Bjorken and S. Mtingawa, Part . Accel. 13 (1983) 115. [16] D. Schirmer, DELTA internal report 91-04, 1991 . [17] E.T. Scharlemann, J. Appl. Phys. 58 (1985) 2154. [18] U. Bizzarri et al ., Riv. Nuovo Cimento 10 (1987) 1. [19] K.J . Kim, X-Ray Data Booklet, ed. D. Vaughan (LBL PUB-490, 1986).
VIII . NUMERICAL SIMULATIONS