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Beam-energy replacement in a compact fel
Nuclear Instruments and Methods in Physics Research A 418 (1998) 476— 481
Beam-energy replacement in a compact fel Godfrey Saxon* 32, Thorn Road, Bramhall SK7 1HQ, UK Received 27 May 1998
Abstract To achieve high energy extraction from a compact FEL requires a method to negate the energy loss from the electron beam. A number of proposals have been made to incorporate an accelerating system within the FEL to overcome this restriction. The present study has examined two RF structures that can be conveniently be interleaved with undulator magnets. A ‘muffin tin’ type of structure seems feasible for output wavelengths of the order of 100 lm, but a new type of structure using rectangular waveguide cavities, powered from a parallel coaxial line, looks promising for wavelengths in the range of 10—20 lm. Solutions for practical FELs are proposed and appropriate magnet designs considered. 1998 Elsevier Science B.V. All rights reserved. Keywords: RF structures; MAFIA investigations; FEL
1. Introduction It is well known that the output power of an FEL is limited because the electron beam-energy is reduced, so that it can no longer support the oscillation. At first, proposals were developed to taper the properties of the undulator to maintain the beam in approximate synchronism. Inevitably this was at the expense of gain. However, conversion ‘efficiencies’ of 4—5% were obtained at Los Alamos [1]. A number of proposals have been made to incorporate an accelerating structure, interleaved with the undulator magnets, within the FEL in order to overcome this restriction. The present paper illustrates two such ideas, one of which uses a planar
* Tel.: #44 161 439 4931.
aperture loaded linac geometry and is suitable for the longer infra-red wavelengths (100 lm##), whilst the second, suitable for shorter wavelengths (10—20 lm) uses a novel and relatively cheap structure, which is explained in this paper. Both proposals assume a relatively low electron energy. Magnet designs for both options are also given below. The author is aware of the various proposals by Ho, Pantell et al. [2—4] based on research at Stanford University, finally proposing a structure aimed to achieve a wavelength of the order of 10 lm. The author has no recent information about how far this idea has been pursued in practical terms. One interesting feature of total energy recovery, not widely recognized, is that the output beam from the FEL will have the same energy and current as the incident beam, though its quality may have deteriorated. It may be suitable for another FEL or
0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 8 9 4 - 8
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
477
some other use. All this for the expenditure on a few megawatts (peak) of RF power.
2. The far infra-red proposal The FEL arrangement, shown in Fig. 1, represents a series of coupled cells similar to a planar disc-loaded linear accelerator, but the structure is quite separate from the undulator magnet poles. Assuming S-band operation, the periodicity is defined by the operating mode, which has been assessed using MAFIA simulations in order to optimise important dimensions [6]. The n-mode has a good shunt impedance, since verified by perturbation measurements on a model. The magnet period is assumed to be 100 mm and the vertical aperture is 40 mm. It is clear from Fig. 1 that this FEL is tunable via variation of the magnetic field even though the structure is fixed. The range of tuning available as a function of electron energy and magnet gap is given in Fig. 2. Selection of a suitable magnet design has involved a comparison between permanent magnets and electromagnetic technology as illustrated in Fig. 3 [5]. The ideal small signal gain in an FEL based on this scheme, with a structure length of 1 m, has been calculated to be between 35% and 60% per pass over a wavelength range of 100—300 lm. But this does not allow for broadening effects. It assumes a peak current of 70 A as achieved at FELIX. Transverse effects, due to energy spread, will lower this estimate by 10—15%. However, pulse lethargy will have a greater effect, as much as a factor of five at the longer wavelengths. Nevertheless, adequate gain should be obtainable.
Fig. 1. Moving pole with fixed waveguide.
Fig. 2. Output tuning range with 100 mm period.
Fig. 3. Alternative PPM and EM schemes.
The overall layout of such an FEL is shown in Fig. 4. A separate source of RF power from that supplying the linac is needed, because of the requirement for fast phase and amplitude control, best done in the drive stages. The sources must, of course, have a common oscillator. The proposed structure presents an impedance to the electron beam and so gives beam loading over the whole macropulse. Therefore, RF power must be supplied to the structure in addition to the extra power needed to keep the energy constant during lasing. Clearly, there must be appropriate feedback systems. After extensive MAFIA investigations, previously reported [6], it was clear that the optimum structure for FELs in the indicated energy range was a n-mode structure with a 40 nm aperture (see Fig. 1). A smaller aperture could not be tolerated because of waveguide cut-off problems. The use of a n/2 mode structure to go to shorter wavelengths was also ruled out. MAFIA investigations showed that the structure investigated could give a shunt impedance, in real
478
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
Fig. 4. Overall layout of present proposal.
ohms, of about 26 M)/m at S-band frequencies. A model of the structure, investigated by perturbation techniques at Daresbury Laboratory confirmed a shunt impedance of 26 M)/m. Allowing for surface finish, etc., it seems that one can estimate performance on the basis of 20 M)/m. R. Miller [7], for instance, gives the energy gain in a resonant RF structure as (1#b) I R¸ 1 P " »# 15 4R ¸b (1#b) 1 where » is the voltage gain, R is the impedance in 1 real )/m, b is the coupling factor to the feeder, I is the average current during the pulse and ¸ is the structure length. If one chooses a beam current of 0.2 A and a b of 2 and assumes a linac length of 1 m, then one can find the RF power needed for an energy gain of 5 MeV in 1 m. For the parameters listed, this turns out to be 2.25 MW, assuming electrons to be riding at the peak of the wave. However, it may be desirable to offset the phase to obtain, for instance, a smaller energy spread. This would require a small increase in power, to say 2.7 MW. One must not overlook the power required to overcome beam loading even before lasing takes off; about 0.27 MW for a 0.2 A beam.
3. A new structure for short infra-red wavelengths It is clear that, in order to obtain FEL wavelengths in the 10—20 lm regime, then not only must the electron energy be increased but the undulator period must be reduced and the minimum
magnet gap must be small enough to obtain suitable K-values. For instance, with an electron energy in the range 25—30 MeV, then a tuning range with an undulator period of 50 mm can be as shown in Fig. 5 for K-values up to 1.5. A suitable magnet and interleaved RF structure is shown in Fig. 6. This allows the magnet gap to close down to about 30 mm. The question arises as to the nature of this RF structure and how power is to be coupled into it. The proposed solution uses half-wavelength resonant rectangular waveguide cavities in the TE 011 mode. Such a cavity could have the dimensions given in Fig. 7. The height of the cavities is determined by the space available between the magnet poles (12.5 mm) so that a cavity internal height of 10 mm seems feasible. Then one can choose the other two dimensions for the cavity, e.g. 60 mm width and 90 mm length. In order to feed this train of cavities, it is proposed to couple them to a parallel coaxial line via a slot in the wall of each cell (see Fig. 6). A similar system was used by Sundelin et al. [8] at Cornell, but at much longer wavelengths. It would seem beneficial to employ a variable short-circuit at the end of the coaxial line so that a standing-wave exists along its length. This has two advantages: the first is that it equalises the coupling to each cell (for equal voltages) and the second more important advantage is that by moving the short-circuit one can control the phase of bunches riding through the whole structure. This can be used, for instance, to minimise energy spread. There are, of course, small holes at the centre of each cavity allowing for the transmission of the electron and optical beams. They are too small to
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
479
Fig. 5. Output tuning range with 50 mm period.
affect the microwave coupling. From the text books, the Q-value and dimensions of the cavities are readily calculable, although MAFIA estimates have also been made [6]. These suggest an R/Q value of 118 ) at 3 GHz. If the Q-value is 5000, then R is 590 k) (in real ohms). In linac ohms (peak field squared with respect to power) this gives 1.18 M), but allowing for imperfections a more realistic estimate is 0.95 M). This is the shunt impedance of the unloaded cavity, but a coupling factor must be allowed to accomodate for the feeder impedance as well as the beam loading. Note that beam loading must be allowed for whether one is accelerating or not. A coupling factor of b"2 would allow for beam currents up 0.4 A, although one is only considering 0.2 A in the present proposal. With a b-value of 2, the effective shunt impedance is 0.315 M). One would like to achieve a peak field across each cavity of 100 kV. This represents a gradient across the 10 mm gap of 10 MV/m which seems acceptable. To produce this field in a non-beam loaded cavity would require a power of 21.5 kW. However, allowing for beam loading, the power demand per cell would be 38 kW at 0.2 A loading and 59 kW at 0.4 A.
Let us suppose that there are 60 cells, occupying 1.5 m, then for a 0.2 A beam, the total power demand would be 2.3 MW to give an energy gain of about 5.7 MeV. The assumption here is that electrons would not be riding at the crest of the wave but would have an energy gain of 95 keV per cell. One is looking at RF sources giving 3 MW over a long pulse length at S-band. Such sources are available. The RF regime which would be needed for this project would include a separate low power source from the injector linac, but, of course, at the same frequency. This would allow for phase and amplitude control appropriate to the project. During the formative period when optical compression of the beam is occurring, power must still be applied to the structure to overcome beaminduced loading. Once lasing takes off then increased power is needed. The way in which this is controlled needs further study, once a definitive scheme is proposed. With the parameters outlined, the ideal small signal gain with a structure of length 1.5 m can be calculated as 120% per pass at 10 lm. However, broadening effects must reduce this, by a factor of 0.675 for energy spread, 0.98 for emittance and
480
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
Fig. 6. Magnet/RF structure.
a larger figure for pulse slippage. One might end up with a gain of 64% per pass at 20 lm. Clearly this is adequate for lasing. The assumed peak injected current is 70 A as achieved at FELIX.
4. Conclusion
Fig. 7. Waveguide cavity dimensions.
An argument has been presented for a possible future for FEL facilities using beams from electron linacs with FEL outputs in the infra-red region. The advantages are not so much in higher ‘efficiency’ (FELs are never efficient in energy terms) as in enhancing the output power by at least an order of magnitude and this at not very high cost.
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
There is the further intriguing possibility that, since the electron energy is maintained constant, then the output beam could be used in some other way (possibly another FEL!). I hope that some FEL enthusiasts will try it. Clearly further work is needed e.g. with regard to the optical bunching of the beam before injection into the combined structure. This has not formed part of the present study, but, clearly, should be pursued. Acknowledgements The author is indebted to his collaborators at Daresbury Laboratory for their contribution to
481
these ideas, particularly, P.A. McIntosh for his analysis of the RF structures using both MAFIA and perturbation methods. M.W. Poole has been a constant source of encouragement for the project and has contributed in the area of magnet design.
References [1] [2] [3] [4] [5] [6] [7] [8]
R.W. Warren et al., J. IEEE QE 19 (1983) 391. Ho, Pantell et al., J. IEEE QE 23 (1987) 1545. Ho, Pantell et al., Nucl. Instr. and Meth. A 296 (1990) 631. Ho, Pantell et al., J. IEEE QE 27 (1991) 2650. M.W. Poole et al., EPAC (Sitges) (1996) 77. M.W. Poole, P.A. McIntosh, EPAC (Sitges) (1996) 1958. R.H. Miller, LA Conf. Proc., Stanford, 1986, p. 200. R. Sundelin et al., Nucl. Instr. and Meth. (1997) 558.
Beam-energy replacement in a compact fel Godfrey Saxon* 32, Thorn Road, Bramhall SK7 1HQ, UK Received 27 May 1998
Abstract To achieve high energy extraction from a compact FEL requires a method to negate the energy loss from the electron beam. A number of proposals have been made to incorporate an accelerating system within the FEL to overcome this restriction. The present study has examined two RF structures that can be conveniently be interleaved with undulator magnets. A ‘muffin tin’ type of structure seems feasible for output wavelengths of the order of 100 lm, but a new type of structure using rectangular waveguide cavities, powered from a parallel coaxial line, looks promising for wavelengths in the range of 10—20 lm. Solutions for practical FELs are proposed and appropriate magnet designs considered. 1998 Elsevier Science B.V. All rights reserved. Keywords: RF structures; MAFIA investigations; FEL
1. Introduction It is well known that the output power of an FEL is limited because the electron beam-energy is reduced, so that it can no longer support the oscillation. At first, proposals were developed to taper the properties of the undulator to maintain the beam in approximate synchronism. Inevitably this was at the expense of gain. However, conversion ‘efficiencies’ of 4—5% were obtained at Los Alamos [1]. A number of proposals have been made to incorporate an accelerating structure, interleaved with the undulator magnets, within the FEL in order to overcome this restriction. The present paper illustrates two such ideas, one of which uses a planar
* Tel.: #44 161 439 4931.
aperture loaded linac geometry and is suitable for the longer infra-red wavelengths (100 lm##), whilst the second, suitable for shorter wavelengths (10—20 lm) uses a novel and relatively cheap structure, which is explained in this paper. Both proposals assume a relatively low electron energy. Magnet designs for both options are also given below. The author is aware of the various proposals by Ho, Pantell et al. [2—4] based on research at Stanford University, finally proposing a structure aimed to achieve a wavelength of the order of 10 lm. The author has no recent information about how far this idea has been pursued in practical terms. One interesting feature of total energy recovery, not widely recognized, is that the output beam from the FEL will have the same energy and current as the incident beam, though its quality may have deteriorated. It may be suitable for another FEL or
0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 8 9 4 - 8
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
477
some other use. All this for the expenditure on a few megawatts (peak) of RF power.
2. The far infra-red proposal The FEL arrangement, shown in Fig. 1, represents a series of coupled cells similar to a planar disc-loaded linear accelerator, but the structure is quite separate from the undulator magnet poles. Assuming S-band operation, the periodicity is defined by the operating mode, which has been assessed using MAFIA simulations in order to optimise important dimensions [6]. The n-mode has a good shunt impedance, since verified by perturbation measurements on a model. The magnet period is assumed to be 100 mm and the vertical aperture is 40 mm. It is clear from Fig. 1 that this FEL is tunable via variation of the magnetic field even though the structure is fixed. The range of tuning available as a function of electron energy and magnet gap is given in Fig. 2. Selection of a suitable magnet design has involved a comparison between permanent magnets and electromagnetic technology as illustrated in Fig. 3 [5]. The ideal small signal gain in an FEL based on this scheme, with a structure length of 1 m, has been calculated to be between 35% and 60% per pass over a wavelength range of 100—300 lm. But this does not allow for broadening effects. It assumes a peak current of 70 A as achieved at FELIX. Transverse effects, due to energy spread, will lower this estimate by 10—15%. However, pulse lethargy will have a greater effect, as much as a factor of five at the longer wavelengths. Nevertheless, adequate gain should be obtainable.
Fig. 1. Moving pole with fixed waveguide.
Fig. 2. Output tuning range with 100 mm period.
Fig. 3. Alternative PPM and EM schemes.
The overall layout of such an FEL is shown in Fig. 4. A separate source of RF power from that supplying the linac is needed, because of the requirement for fast phase and amplitude control, best done in the drive stages. The sources must, of course, have a common oscillator. The proposed structure presents an impedance to the electron beam and so gives beam loading over the whole macropulse. Therefore, RF power must be supplied to the structure in addition to the extra power needed to keep the energy constant during lasing. Clearly, there must be appropriate feedback systems. After extensive MAFIA investigations, previously reported [6], it was clear that the optimum structure for FELs in the indicated energy range was a n-mode structure with a 40 nm aperture (see Fig. 1). A smaller aperture could not be tolerated because of waveguide cut-off problems. The use of a n/2 mode structure to go to shorter wavelengths was also ruled out. MAFIA investigations showed that the structure investigated could give a shunt impedance, in real
478
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
Fig. 4. Overall layout of present proposal.
ohms, of about 26 M)/m at S-band frequencies. A model of the structure, investigated by perturbation techniques at Daresbury Laboratory confirmed a shunt impedance of 26 M)/m. Allowing for surface finish, etc., it seems that one can estimate performance on the basis of 20 M)/m. R. Miller [7], for instance, gives the energy gain in a resonant RF structure as (1#b) I R¸ 1 P " »# 15 4R ¸b (1#b) 1 where » is the voltage gain, R is the impedance in 1 real )/m, b is the coupling factor to the feeder, I is the average current during the pulse and ¸ is the structure length. If one chooses a beam current of 0.2 A and a b of 2 and assumes a linac length of 1 m, then one can find the RF power needed for an energy gain of 5 MeV in 1 m. For the parameters listed, this turns out to be 2.25 MW, assuming electrons to be riding at the peak of the wave. However, it may be desirable to offset the phase to obtain, for instance, a smaller energy spread. This would require a small increase in power, to say 2.7 MW. One must not overlook the power required to overcome beam loading even before lasing takes off; about 0.27 MW for a 0.2 A beam.
3. A new structure for short infra-red wavelengths It is clear that, in order to obtain FEL wavelengths in the 10—20 lm regime, then not only must the electron energy be increased but the undulator period must be reduced and the minimum
magnet gap must be small enough to obtain suitable K-values. For instance, with an electron energy in the range 25—30 MeV, then a tuning range with an undulator period of 50 mm can be as shown in Fig. 5 for K-values up to 1.5. A suitable magnet and interleaved RF structure is shown in Fig. 6. This allows the magnet gap to close down to about 30 mm. The question arises as to the nature of this RF structure and how power is to be coupled into it. The proposed solution uses half-wavelength resonant rectangular waveguide cavities in the TE 011 mode. Such a cavity could have the dimensions given in Fig. 7. The height of the cavities is determined by the space available between the magnet poles (12.5 mm) so that a cavity internal height of 10 mm seems feasible. Then one can choose the other two dimensions for the cavity, e.g. 60 mm width and 90 mm length. In order to feed this train of cavities, it is proposed to couple them to a parallel coaxial line via a slot in the wall of each cell (see Fig. 6). A similar system was used by Sundelin et al. [8] at Cornell, but at much longer wavelengths. It would seem beneficial to employ a variable short-circuit at the end of the coaxial line so that a standing-wave exists along its length. This has two advantages: the first is that it equalises the coupling to each cell (for equal voltages) and the second more important advantage is that by moving the short-circuit one can control the phase of bunches riding through the whole structure. This can be used, for instance, to minimise energy spread. There are, of course, small holes at the centre of each cavity allowing for the transmission of the electron and optical beams. They are too small to
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
479
Fig. 5. Output tuning range with 50 mm period.
affect the microwave coupling. From the text books, the Q-value and dimensions of the cavities are readily calculable, although MAFIA estimates have also been made [6]. These suggest an R/Q value of 118 ) at 3 GHz. If the Q-value is 5000, then R is 590 k) (in real ohms). In linac ohms (peak field squared with respect to power) this gives 1.18 M), but allowing for imperfections a more realistic estimate is 0.95 M). This is the shunt impedance of the unloaded cavity, but a coupling factor must be allowed to accomodate for the feeder impedance as well as the beam loading. Note that beam loading must be allowed for whether one is accelerating or not. A coupling factor of b"2 would allow for beam currents up 0.4 A, although one is only considering 0.2 A in the present proposal. With a b-value of 2, the effective shunt impedance is 0.315 M). One would like to achieve a peak field across each cavity of 100 kV. This represents a gradient across the 10 mm gap of 10 MV/m which seems acceptable. To produce this field in a non-beam loaded cavity would require a power of 21.5 kW. However, allowing for beam loading, the power demand per cell would be 38 kW at 0.2 A loading and 59 kW at 0.4 A.
Let us suppose that there are 60 cells, occupying 1.5 m, then for a 0.2 A beam, the total power demand would be 2.3 MW to give an energy gain of about 5.7 MeV. The assumption here is that electrons would not be riding at the crest of the wave but would have an energy gain of 95 keV per cell. One is looking at RF sources giving 3 MW over a long pulse length at S-band. Such sources are available. The RF regime which would be needed for this project would include a separate low power source from the injector linac, but, of course, at the same frequency. This would allow for phase and amplitude control appropriate to the project. During the formative period when optical compression of the beam is occurring, power must still be applied to the structure to overcome beaminduced loading. Once lasing takes off then increased power is needed. The way in which this is controlled needs further study, once a definitive scheme is proposed. With the parameters outlined, the ideal small signal gain with a structure of length 1.5 m can be calculated as 120% per pass at 10 lm. However, broadening effects must reduce this, by a factor of 0.675 for energy spread, 0.98 for emittance and
480
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
Fig. 6. Magnet/RF structure.
a larger figure for pulse slippage. One might end up with a gain of 64% per pass at 20 lm. Clearly this is adequate for lasing. The assumed peak injected current is 70 A as achieved at FELIX.
4. Conclusion
Fig. 7. Waveguide cavity dimensions.
An argument has been presented for a possible future for FEL facilities using beams from electron linacs with FEL outputs in the infra-red region. The advantages are not so much in higher ‘efficiency’ (FELs are never efficient in energy terms) as in enhancing the output power by at least an order of magnitude and this at not very high cost.
G. Saxon/Nucl. Instr. and Meth. in Phys. Res. A 418 (1998) 476 — 481
There is the further intriguing possibility that, since the electron energy is maintained constant, then the output beam could be used in some other way (possibly another FEL!). I hope that some FEL enthusiasts will try it. Clearly further work is needed e.g. with regard to the optical bunching of the beam before injection into the combined structure. This has not formed part of the present study, but, clearly, should be pursued. Acknowledgements The author is indebted to his collaborators at Daresbury Laboratory for their contribution to
481
these ideas, particularly, P.A. McIntosh for his analysis of the RF structures using both MAFIA and perturbation methods. M.W. Poole has been a constant source of encouragement for the project and has contributed in the area of magnet design.
References [1] [2] [3] [4] [5] [6] [7] [8]
R.W. Warren et al., J. IEEE QE 19 (1983) 391. Ho, Pantell et al., J. IEEE QE 23 (1987) 1545. Ho, Pantell et al., Nucl. Instr. and Meth. A 296 (1990) 631. Ho, Pantell et al., J. IEEE QE 27 (1991) 2650. M.W. Poole et al., EPAC (Sitges) (1996) 77. M.W. Poole, P.A. McIntosh, EPAC (Sitges) (1996) 1958. R.H. Miller, LA Conf. Proc., Stanford, 1986, p. 200. R. Sundelin et al., Nucl. Instr. and Meth. (1997) 558.