Induction-linac based free electron laser amplifier for fusion applications

Nuclear Instruments and Methods in Physics Research A285 (1989) 387-394 North-Holland, Amsterdam

387

INDUCTION-LINAC BASED FREE ELECTRON LASER AMPLIFIER FOR FUSION APPLICATIONS R.A . JONG and R.R. STONE Lawrence Livermore National Laboratory, University of California, Livermore, California 94550, USA

We describe an induction-linac based free electron laser amplifier design for producing multm-megawatt levels of microwave power for electron cyclotron resonance heating of tokamak fusion devices such as the Compact Ignition Tokamak or the International Thermonuclear Experimental Reactor. The wiggler design strategy incorporates a tapering algorithm suitable for FEL systems with moderate space charge effects and minimizes spontaneous noise growth at frequencies below the fundamental, while enhancing the growth of the signal at the fundamental . In addition, engineering design considerations of the waveguide wall loading and electron beam fill factor in the waveguide set limits on the waveguide dimensions, the wiggler magnet gap spacing, the wiggler period, and the minimum magnetic field strength in the tapered region of the wiggler. This FEL ms designed to produce an average power of about 10 MW at frequencies in the range from 280 to 560 GHz. The achievement of this average power at a reasonable cost requires a high duty factor, which affects some component design . In addition, the desire to obtain a high extraction efficiency pushes the beam energy up and requires magnetic field strengths in the wiggler that are near or possibly larger than the Halbach limit. We used a methodology for our system study that had been developed earlier. We considered several FEL configurations and selected one that minimized total cost . We determined that increasing the beam energy requires that the wiggler use vanadium-permendur as the pole material . We discuss the basic design of the selected configuration and give the expected performance . 1. Introduction In recent years, the induction-linac based free electron laser (IFEL) amplifier has become a viable source of high power coherent radiation, demonstrating high gain and efficiency at 34 .6 and 140 GHz [1-4] in the Electron Laser Facility (ELF) at the Lawrence Livermore National Laboratory (LLNL) . The success of these experiments and the demonstrated ability of numerical simulations in calculating the experimental results [1-5] has encouraged the use of these computational tools to predict the expected performance of free electron laser (FEL) amplifiers at the higher frequencies suitable for controlled fusion applications [6-9]. Electron cyclotron resonance heating (ECRH), current drive, and profile control in tokamak fusion devices are examples of such applications where a tunable source of high power microwave radiation could be used . Earlier predictions [6-9] of FEL performance at 250 GHz were based on a design goal of 2 MW of average power for heating pulse durations of about 0.5 s. This power was to be used in plasma heating experiments in the Microwave Tokamak Experiment (MTX) at LLNL. The FEL portion of this experiment has been named the Intense Microwave Prototype (IMP). Preparations for the MTX and IMP * Work performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under W-7405-ENG-48 0168-9002/89/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

experiments are currently under way, and an experimental test of the utility of the IFEL as a source of microwave power for plasma heating will take place over the next several years . In the meantime, we have begun to study the use of IFEL amplifier systems to produce coherent microwave radiation at higher average power levels, up to about 10 MW, for heating pulse durations of up to 10 s, at frequencies ranging from 280 to 560 GHz [10] . These parameter values would be suitable for a heating system for use with proposed advanced tokamak devices such as the Compact Ignition Tokamak (CIT) and the International Thermonuclear Experimental Reactor (ITER) . For these studies, we used the two-dimensional version of the LLNL free electron laser simulation code, FRED [2,5,11], and the simulation code for sideband calculations, GINGER. The methodology for this study was developed for the design of the IMP wiggler [8,9], where moderate space-charge effects were important. The tapering algorithm enhances the gain at the design frequency while suppressing noise growth at other frequencies and thus extends the parameter range over which we can taper effectively. We used the performance predictions from FRED to select a baseline configuration to produce the required average power. We consider the performance of various IFEL assemblies and traded various designs off against cost . Since the accelerator is about 50% of the total system value, minimizing its costs will also minimize the X. APPLICATIONS

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system cost . After selecting the accelerator configuration, we sized and costed other assemblies of the system. In section 2, we briefly discuss the engineering and physics constraints that determine the waveguide size, the wiggler gap spacing and wtggler period, and the beam energy range of interest for our FEL design . Section 3 summarizes the calculations for a typical design at 280 and 560 GHz, and includes the effects on FEL performance of realistic electron beam displacements, beam energy sweep, current variation, and random wtggler errors . In section 4, we discuss the methodology used to select a baseline configuration to produce 10 MW of average power. The effect on accelerator design as a result of assumed FEL performance is shown. In section 5, we present the baseline configuration and discuss its expected performance . We also show one variation on the system configuration that illustrates the flexibility of an IFEL-based ECRH system. A summary of the results is presented in section 6. 2. Design constraints on the allowed parameter range 2.1 . Engineering constraints

Unlike the earlier design for the IMP wiggler [9], wall loading due to the microwave power for a smoothwalled waveguide is a problem. At the higher average power levels and longer pulse lengths (5-10 s) required for the new designs, the estimated temperature rise per pulse (about 85'C [12]) for a smooth-walled copper waveguide is large enough to produce fatigue cracks on the waveguide wall . Consequently, the expected lifetime of a smooth-walled copper waveguide is too short to be considered practical . Therefore, for the current FEL designs, we have modeled a corrugated, circular waveguide and have calculated the power gain in the HE,, mode [13] . Since the HE,, mode has a spatial distribution that is more peaked about the axis of the waveguide (when compared to the TE ii mode in a smooth-walled circular waveguide), it produces less dissipation in the walls of the waveguide. Estimates of the wall loading [14] with the corrugated circular waveguide give dissipation factors for the HE,, mode that are nearly three orders of magnitude smaller than for the corresponding circular TE,I mode . We expect the temperature rise to be lower by two orders of magnitude, and consequently, the fatigue life of the waveguide to be no longer an issue. Using the corrugated waveguide and the HE,, mode appears to have another advantage over using a smooth-walled waveguide. Because the spatial distribution is more peaked on axis, the FEL interaction is stronger, we can trap more electrons in the ponderomotive well, the gam in the exponential region is higher, than the required wiggler length is shorter .

C7 a U

ä

cm period 0 6 .5 cm period O 8 .0 cm period " 10 cm period 12 cm period

Fig. 1. (a) Plot of Halbach relationship showing the peak wiggler magnetic flux density in kG for a REC hybrid wiggler as a function of gap spacing for various wiggler periods ; and (b) plot of magnetic field at FEL synchronism as a function of electron beam energy for various wiggler periods and a frequency of 280 GHz. The beam linear fill factor in the waveguide, however, is still important in determining the required waveguide size and the wiggler gap spacing. We define the linear fill factor as the ratio of the beam linear dimension to the waveguide linear dimension in the same plane, and we require that this fill factor in both the wiggle and non-wiggle planes be <_ 50% for our baseline design before wiggler errors and beam displacement degradations are included. This constraint leads us to consider circular waveguides with an inner diameter of about 3 .5 cm . Using the Halbach limit [15] as a measure of difficulty in achieving a prescribed magnetic flux density in the permanent-magnet-laced electromagnetic wiggler [16], the choice of the waveguide size determines the gap spacing and wiggler period that are optimal for the design, and sets a practical upper limit on the magnetic flux density. For the 3.5 cm diameter waveguide we are considering, we choose a 4 cm gap spacing and a 10 cm wiggler period . This gives a suggested maximum magnetic flux density of about 5 kG, as shown in fig . la . 2.2. Physics constraints

The 5 kG magnetic field limit determines the maximum usable electron beam energy that will satisfy the

R.A . Jong, R.R . Stone / Induction-bnac based FEL amplifier

FEL synchronism condition [171 . The free-space FEL synchronism condition is plotted in fig. 1(b) for a frequency of 280 GHz and is given by the expression

=

Z ( I+aW~,

2y

(1)

where X is the wavelength of the radiation, X w is the wiggler period, aw is the normalized vector potential due to the wiggler magnetic field, and y is the usual Lorentz factor . This approximate form of the synchronism relation neglects waveguide corrections and betatron motion effects but is sufficiently accurate for our estimates. From fig. lb, the 5 kG magnetic field limit gives a maximum beam energy of about 11 .5 MeV. (The corresponding maximum beam energy at 560 GHz is 16 MeV.) By choosing a beam energy of 10 MeV, we will operate at a synchronous magnetic field of about 4 kG, a comfortable 80% of the Halbach limit. In section 4, we shall return to this discussion of the maximum usable beam energy for magnetic flux densities larger than the Halbach limit. The lower limit on the electron beam energy is set by one of two considerations. First, longitudinal spacecharge effects become more pronounced as the beam energy is decreased for fixed values of beam current and brightness . These space-charge effects lower the peak gain at the desired frequency will enhancing the relative gain at a lower frequency, shift the peak gain away from FEL synchronism, and make it more difficult to trap electrons in the ponderomotiv well when tapering the magnetic field. While the new Raman tapering algorithm [8] can extent the parameter range over which we can taper effectively, there is a point at which it becomes impossible to capture a large fraction of the electrons in the ponderomotive well . At this point, tapering becomes ineffective, with a corresponding decrease in extraction efficiency and output power for the FEL. The second consideration in setting a lower limit on the beam energy is expected overall efficiency of the FEL in combination with the desired output power. We assume that the electron beam repetition rate, pulse length, and current are set by the accelerator design limits, and hence are fixed at their optimum (i .e., maximum) values for our calculations. If we further assume that the extraction efficiency will be in the 35-40% range (typical experimental values achieved with a tapered wiggler [3]), then the lower beam-energy limit follows from the desired output power level. In practice, it is this second consideration that sets the practical (i .e ., largest) value on the lower beam energy limit . If we assume typical parameters such as a 50 ns pulse length and a 20 kHz repetition rate, then the resulting duty factor of 0.001 combines with the assumed 3 kA beam current and the expected efficiency range to produce a minimum beam energy of about 9 or 10 MeV .

389

3. Representative IFEL design 3.1 . IFEL design with no errors

The methodology for optimizing the wiggler taper when space-charge effects are important has been described in detail previously [8-10] . The goal is to choose the value of the initial magnetic field and a length for the untapered wiggler section which puts the peak gain at the desired signal frequency, minimizes the gain at other frequencies to produce a sufficiently large signalto-noise ratio at the end of the untapered section, and to begin tapering when there is sufficient bunching in the phase, ,,, before there is significant spreading in energy (i.e . y), and also before synchrotron oscillations begin . The profile for the magnetic flux density in the tapered section of the wiggler is determined using the usual synchronous tapering scheme in FRED, suitable for FELs operating in the Compton regime . Because the electron beam radius can grow as the magnetic field strength is decreased, the beam linear fill factor can increase as we taper the magnetic field. We stop tapering when the beam linear fill factor grows to about 50% in either the wiggle or non-wiggle plane. This value for the linear fill factor in both planes corresponds to about a 25% area fill factor. We chose such a conservative value because the linear fill factor will grow when beam displacements and wiggler errors are included in the calculation, as will be described in section 3 .2 . With the wiggler optimized as described above, the predicted axial profile of the HE,, power is shown in fig. 2. With a beam energy of 10 MeV and a beam current of 3 kA, the HE,, power grows from the input level of 500 W at a rate of about 46 dB/m in the exponential gain region and attains a level of about 12 .8 GW at the end of the 3 m long wiggler. This corresponds to an extraction efficiency of 43%, with 73% of the electrons trapped in the bucket . The tapered wiggler

d a â

0

z Z (in)

Fig. 2. Axial profile of the HE,, output power at a frequency of 280 GHz for a 3 IcA, 10 MeV electron beam . X. APPLICATIONS

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m c ç.

70 66

3.0

2

ô ô

62 58 54 50

N N

46

z0 0

L_-

0

42 1

z (m)

2

3

Fig. 3. Axial profile of the tapered wiggler for the FEL operating at 280 GHz for a 3 kA, 10 MeV electron beam .

profile predicted by FRED is shown in fig. 3. The constant (and peak) magnetic field is 4.1 kG, and the minimum field at the end of the wiggler is 1 .4 kG . 3.2 . Effect of parameter oariations on IFEL design The FEL performance calculated in section 3.1 assumes that the FEL parameters are all at their optimum values, with no alignment or wiggler errors, no beam displacements, no energy sweep, and the full rated beam current. Such a situation is highly unlikely in an experiment . A series of simulations in which errors were systematically introduced was used to determine acceptable ranges for these errors . These errors will lower the output HE,, power and also cause the linear beam fill factor to grow . Hence, the limit on the variation of any particular parameter is determined when the output power degrades sufficiently, or, as is usually the case, the beam fill factor gets too large. Using the wiggler profile determined above and shown in fig. 3, we considered the effect on the HE,, output power and linear beam fill factor of variations in the beam current and energy, master oscillator power, beam displacement, and random wiggler errors . The calculations thus simulated an experimental situation where the wiggler was tuned for the baseline case and where some or all of the electron beam, input laser, or wiggler parameters did not equal their baseline values on a particular experimental shot . Variations in the electron beam current and master oscillator power affected only the output power. A 20% decrease in HE,, output power was produced by a 10% decrease in the beam current. The dependence of output power on the master oscillator power was weak . While the nominal master oscillator power is 500 W, it appears that input power levels ranging from 200 W up to at least 1 .5 kW will produce HE,, power levels in excess of 80% of the baseline value, without requiring wiggler taper modifications .

0

0.2

0 .4

0 .6

0.8

1 .0

rms wlggler error (%)

Fig. 4. Effect of rms wiggler errors on the linear beam fill factor m the wiggle and non-wiggle planes . Variations in the electron beam energy, electron beam displacements, and random wlggler errors lowered the output power and also increased the beam linear fill factor by increasing the beam centroid, the beam radius, or the amplitude of the electron wiggle motion . For example, the growth of the wiggle plane linear fill factor with rms random wiggler errors can be seen in fig. 4. The wiggle plane fill factor is less than 52% for rms wiggle errors up to 0.1%, is about 54% for rms wiggler errors of 0.2%, and grows rapidly above 0.2%. In contrast, the non-wiggle plane linear fill factor is independent of the rms wiggler errors because the errors cause the beam to move in the wiggle plane. For comparison, we show in fig. 5, the dependence of the output HE,, power on the random wiggler errors . The power is still within 80% of the baseline value for wiggler errors as large as 0.75% . Clearly the limit on the allowed random wiggler errors is set by the growth of the beam fill factor. 3.3. IFEL design with combined errors In the preceding section, we discussed the HE,, power and linear fill factor dependence on various parameters when one parameter was varied at a time . However, in the actual system, all the parameters may be varied together . We determined that with combined

12 .5

3

C7

d 3 â w x

11 .5 10.5 9 .5 8 .5

0

0 .2

0 .4

0 .6

0 .8

rms wlggler error (%)

1 .0

Fig. 5. HE,, power at 280 GHz at the end of the wiggler as a function of rms wiggler errors.

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R .A . Jong, R R . Stone / Induction-Irnac based FEL amplifier

errors, the allowed tolerances that form our "standard error" set are a beam displacement of 0.1 cm, rms wiggler errors of 0.1%, and a beam energy sweep of +_ 1% . We assume that the beam current can be kept at the 3 kA level and the master oscillator power is 500 W. With these standard errors, and a 10 MeV beam with a brightness of 10 8 A/(m rad) 2, the calculated peak output HE,, power at 280 GHz is about 10 .4 GW . This corresponds to an extraction efficiency of 34%, with an electron trapping efficiency of 55%. The corresponding wiggle plane fill factor is about 62%, and the non-wiggle plane linear fill factor is 50%. At 560 GHz with a 14 MeV beam, the peak output power is 13 .4 GW, with an extraction efficiency of 32% and a trapping efficiency of 55% . The wiggle plane fill factor is about 60%, and the non-wiggle plane linear fill factor is 46% . While the above performance is adequate for our present design goals, if we assumed smaller error limits that would be typical of the error limit goals for the next generation of accelerator technology, we could expect even better FEL performance . The beam energy sweep would change from ±1% to ±0 .4%, and the beam displacement limits would change from 0.1 cm to 200 gm . The random wiggler error remains at the 0.1% level. With these smaller, the average HE,, output at 250 (560) GHz would be 12 .5 (15 .4) GW, only a 2 (1)% decrease from the "no error" base case . This compares with the 19 (10)% decrease with the larger errors . With these smaller errors, the growth in the linear fill factors is also less, about 5% smaller than the corresponding large error cases.

4 .2. Components and subassembly limits

4. Systems studies

We have found that, although the use of permanent magnets, electromagnets and normal iron in the wiggler poles (in a laced wiggler design) allows us to exceed the Halbach limit, this limit is an excellent indication of degree of difficulty in obtaining the high fields . If normal iron is used, we assume the upper limit on wiggler field to be the Halbach limit value. If other materials are used, the upper field value is taken to be the Halbach limit values times the ratio of maximum allowed field in the material over the maximum allowed field in normal iron (14 kG). As discussed earlier, the maximum magnetic field determines the maximum electron energy that will meet the synchronism conditions defined by eq . (1). At a field that is 1 .5 times the Halbach limit, the maximum usable beam energy nses to about 17 MeV. Using this higher beam energy and magnetic field limit in the FRED calculations would result in higher gain and larger predicted peak power levels . We have an ongoing study to select the operating conditions for the next generation of IFELs. We use these conditions, where possible, as our baseline parameters to minimize design costs and risks. We have determined that the power conditioning chain should operate at a maximum pulse rate frequency (PRF) of 10 kHz, the maximum pulse width should be < 70 ns, and the maximum energy per pulse of the magnetic compressor [18] (MAG) should be < 1200 J. We have completed an analysis that indicates that the temperature rise per pulse on copper surfaces should be limited to 30 ° C. This limit will ensure that the life of these surfaces will be long, even when pulsed at a 10 kHz rate.

4 .1 . Methodology

4 .3 . Effect of limits on configuration selection

We have developed algorithms that calculate the size and cost of components as a function of various input or calculated parameters . The top level requirements for the FEL are the initial input for our systems studies. As shown by the examples in section 3 we made a series of calculations to determine peak output power as a function of beam energy, current, and wiggler length . We have validated the component costs against vendor bid responses and our experience with similar items. We run spreadsheets which size and cost components for the various subassemblies . These costs are summed and a system cost is determined. When a configuration is selected, a risk assessment is completed that may modify the design . For this study, we used the basic parameters for components and subassemblies that have been selected for IFELs planned for other projects . This will minimize the design costs for our system as well as reduce the risks.

We show in fig. 6 the effect on the accelerator pulse power chain when the above limits are used . With a

Fig. 6. Number of MAGs (pulsed power chains) required per cell as a function of PRF, pulse width, and microwave peak power. X . APPLICATIONS

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PRF of 10 kHz, a pulse width of 70 ns, and 1200 J/pulse in the MAG, the peak power must be about 14 GW or above to eliminate the requirement for multiplexing two pulse power chains into each cell . The most efficient method of obtaining increased peak power in the FEL is to increase the initial electron beam energy . This increase will cause the accelerator costs to go up ; however, if the gain increases sufficiently, only one pulsed power chain/cell is required and the costs would decrease . From an examination of the FRED calculation data base, we find that at a peak power of about 14 GW, the costs of the accelerator are minimum and that beam energy required to obtain the 14 GW is about 13 MeV (for 280 GHz) . Fig. 1 shows that we must exceed the Halbach limit in order to use an initial electron beam energy of 13 MeV at 280 GHz. We have chosen to use vanadium-permendur as the wiggler pole material . With an allowed maximum field of 22 kG, versus 14 kG for normal iron, the obtainable field should allow the initial electron energy to be as high as 15 MeV. 5. System configuration We show in fig. 7 the basic configuration for the 280 GHz, 10 MW FEL. The accelerator has four pulse power chains, no multiplexing, a pulse width of 70 ns, and a PRF of 10 kHz . Within the accelerator, the ferrite heats up during the run time. We have calculated that with a 360 J/m3/pulse energy generation rate in the ferrite and a PRF of 10 kHz, our run time can be about 30 s without cooling. Between bursts, we must cool the ferrite back to its initial temperature. We have calculated the cool-down time for a 1 .27 cm (0 .5 in .) thick disk of ferrite . Using a reasonable film coefficient, we find that a 30 s burst can be allowed about four times an hour . Future FELs may have to run continuously . We show in fig. 8 the results of calculations for the steady state temperature using different thicknesses of ferrite

16m

39M

Accelerator E=13M'V 1=3kA L-16m PRF=10kHZ

7.

14m

4m

014 4. T

Master oscillator BWO gyrotron 10kW Tunable +3% In msec

Accelerator

Fig.

35M

Fig. 8. Maximum steady state temperature in the center of the ferrite when cooled with Freon for various thicknesses (L) of ferrite and PRE [19] . At 10 kHz, a 0 .95 cm (0 .375 in .) thickness of ferrite will remain below the maximum allowed temperature of 70 ° C when cooled with Freon. The microwave transport from the FEL to the fusion machine appears to be similar to that planned for the MTX experiment at LLNL . We have determined that a mirror with a diameter of about 40 cm (16 in .) will transport the 10 MW of microwave power without exceeding the 30'C limit for the copper surfaces and will provide very low diffraction loss over the longest path we envision [14] . The 560 GHz FEL configuration is almost the same at that for 280 GHz. We have determined that the 560 GHz system requires a higher initial energy of about 15 MeV, a slightly longer wiggler, and a marginally lower wiggler magnetic field. In fig. 9 we show a configuration that offers flexibility in frequency and power for a fusion machine. The two wigglers can be tuned to different frequencies with the initial energy being the same. By selecting the switching profile of the kicker magnet, one can obtain a different power at each frequency. We show an example of using 280 GHz and 560 GHz master oscillators with similar wiggler designs. If the pulses are alternately sent to each wiggler, we would expect to obtain about 5 MW at 280 GHz and about 4 MW at 560 GHz. The reduc280GH.

"I

.beam diagnostics & matching section

moi

.beam tuning absorber

M02 560 GH .

Wiggler B o =57kG 10 cm L=3m Vanadium permendur

Basic configuration for a 10 MW, 280 GHz system.

Add - $8 M

Microwave diagnostic load tank

Fig 9. FEL configuration that produces high power at two frequencies. Cost increase is small since one accelerator is used .

R.A . Jong, R.R. Stone / Induction-linac based FEL amplifier

tion at 560 GHz occurs because of the reduced extraction efficiency at the higher frequency. 6. Summary In this study we have shown that IFEL technology can be used to produce microwave power for electron cyclotron resonance heating in a tokamak fusion device, providing average power levels in the 10 MW range at 280 and 560 GHz with basically the same machine. From the systems analysis we have determined that the lowest cost FEL system should produce a peak power of about 14 GW . In table 1, we summarize the parameters necessary for IFEL systems to operate at 280 and 560 GHz and produce the required 14 GW peak power. The beam energy is 2 MeV higher and the wiggler is 1 m longer for the 560 GHz case compared the 280 GHz case ; also, the 280 GHz case requires a higher wiggler magnetic field. Otherwise, the two IFEL systems are quite similar. In table 2, we summarize the calculated performance of the 280 and 560 GHz IFEL systems for the parameters of table 1. The standard errors are 0.1 cm beam displacement, 0.1 % rms wiggler errors, and ± 1% beam energy sweep . The results in table 2 indicate that the peak power requirements for an IFEL source suitable for CIT or ITER can be achieved at 280 GHz with the Table 1 FEL input parameter summary

393

current standard errors . The use of improved error limits, especially on the beam energy sweep, will result in improved FEL performance and is required for minimum cost operation at 560 GHz. The proposed CIT or ITER IFEL configurations use components that are similar to those planned for use in advanced systems at LLNL . This reduces the design costs and risks. We have chosen as our baseline a 10 kHz design that nunimizes the total system costs, since only one pulsed power chain is required per cell . We achieve the required duty factor by using a 70 ns pulse width and by increasing the electron beam energy to 13 MeV for the 280 GHz case, therefore improving the extraction efficiency . We must use vanadium-permendur as the wiggler pole material because of this higher beam energy . The run time for the accelerator can be about 30 s without cooling, with about four shots per hour allowed, and if thin ferrite is used, do operation is possible . The IFEL configuration can be modified to provide several different frequencies with only one accelerator required . Acknowledgements We are pleased to acknowledge many useful discussions with R.D . Scarpetti, E.T . Scharlemann, B.W . Stallard, A.L . Throop and J.H van Sant. References

Parameter

Frequency (GHz)

Beam energy (MeV) Current (kA) Brightness [108 A/(m rad) zl Input power (W) Diameter of waveguide (cm) Wiggler period (cm) Wiggler length (m) Gap spacing (cm) Constant magnetic field (kG) Minimum magnetic field (kG)

15 3 I 500 3.5 10 4.0 4.0 4.3 1.7

560

280

13 3 1 500 3.5 10 3.0 4.0 5.4 2.6

[2]

[4]

Table 2 Design summary showing FEL performance. Values in parentheses show performance with combined standard errors Parameter

Frequency (GHz)

HE I , output power (GW) Extraction efficiency (%) Trapping efficiency (%) Linear beam fill factor (%)

17(10) 37(23) 65(28) 50(60)

560

280

16(14) 40(35) 74(61) 50(55)

[6]

[8]

T.J . Orzechowski, B. Anderson, W.M . Fawley, D. Prosnitz, E.T . Scharlemann, S. Yarema, D. Hopkms, A.C . Paul, A.M . Sessler and J. Wurtele, Phys . Rev. Lett . 54 (1985) 889. T.J. Orzechowski, E.T . Scharlemann, B. Anderson, V.K . Neil, W.M . Fawley, D. Prosmtz, S.M . Yarema, D.B . Hopkms, A.C . Paul, A.M . Sessler and J.W . Wurtele, IEEE J. Quantum Electron . QE-21 (1985) 831 . T.J. Orzechowski, B.R . Anderson, J.C . Clark, W.M . Fawley, A.C . Paul, D Prosmtz, E.T . Scharlemann, S.M . Yarema, D.B . Hopkins, A.M . Sessler and J.W . Wurtele, Phys . Rev. Lett . 57 (1986) 2172. A.L . Throop, T.J . Orzechowski, B. Anderson, F.W. Chambers, J.C . Clark, W.M . Fawley, R.A. Jong, A.C . Paul, D. Prosnitz, E.T. Scharlemann, R.D . Stever, G.A . Westenskow, S.M . Yarema, K. Halbach, D.B . Hopkins and A.M . Sessler, Lawrence Livermore National Laboratory, Livermore, Calif., UCRL-95670, 1987 . E.T. Scharleman, W.M . Fawley, B R. Anderson and T.J . Orzechowski, Nucl. Instr. and Meth. A250 (1986) 150. R .A . Jong and E.T . Scharlemann, Nucl . Instr. and Meth . A259 (1987) 254. R.A . Jong, Lawrence Livermore National Laboratory, Livermore, Calif., UCID-21075, 1987 . R.A . Jong, E.T . Scharlemann and W.M . Fawley, Nucl . Instr. and Meth . A272 (1988) 99 . X . APPLICATIONS

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[9] R.A Jong, A.L . Throop and E.T. Scharlemann, Rev. Sci. Instr. 60 (1989) 186. [10] R.A. Jong and R.R. Stone, Lawrence Livermore National Laboratory, Livermore, Calif., UCRL-99595, 1988 . [11] E.T . Scharlemann and W.M . Fawley, Modeling and Simulation of Optoelectronic Systems, ed . J. Dugan O'Keefe, Proc . SPIE 642 (1986) 2 . [12] M Makowski, TRW, private communication (1988) . [13] J.L . Doane, Infrared and Millimeter Waves, Vol 13, ed . K.J . Button (Academic Press, New York, 1985) p. 123. [14] B.W . Stallard, Lawrence Livermore National Laboratory, private communication (1988) .

[15] K. Halbach, J. Physique Coll . Cl, 44 (1983) 44 . [16] T.C . Christensen, M.J . Burns, G.A . Deis, C.D. Parkinson, D Prosmtz and K. Halbach, IEEE Trans. Mag. 24 (1988) 1094 . [17] N.M . Kroll, P.L . Morton, and M.N . Rosenbluth, IEEE J. Quantum Electron . QE-17 (1981) 1436 . [18] B.L . Birx, S.A. Hawkins, S.E. Poor, L.L . Reginato and M.W. Smith, IEEE Trans. Nucl . Sci. NS-32 (1985) 2743 . [191 J.H . Van Sant, Lawrence Livermore National Laboratory, private communication (1988).