Design study of a G-band FEL amplifier for application to cyclotron resonant heating in magnetic fusion reactors

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Nuclear Instruments and Methods in Physics Research A 358 (1995) 163-166

s.j I7 ELSEVIER

NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH SectIonA

Design study of a G-band FEL amplifier for application to cyclotron resonant heating in magnetic fusion reactors H.P. Freud

a** ,‘, M.E. Read a, R.H. Jackson b, D.E. Pershing b32,J.M. Taccetti b33 a Physical Sciences, Inc., Alexandria, VA 22314. USA h Nal,al Research Laboratory, Washington, DC 20375, USA

Abstract A G-band (140-150 GHz) free-electron laser is described using a coaxial hybrid iron (CHI) wiggler. The CHI wiggler is produced by insertion into a solenoid of a central rod and an outer ring composed of alternating ferrite and nonferrite spacers. The position of the spacers is such that the ferrite (nonferrite) spacers on the central rod are opposite the nonferrite (ferrite) spacers on the outer ring. The field is cylindrically symmetric and exhibits minima in the center of the gap providing for enhanced beam focusing. We describe a tapered wiggler amplifier for plasma heating applications. Preliminary design studies using a nonlinear simulation indicates that output powers of 3.5 MW are possible using a 690 kV/40 A electron beam for a total efficiency of 13%. It is important to note that no beam loss was observed even for realistic values of beam energy spread.

1. Introduction Auxiliary sources of plasma heating for currentlyplanned thermonuclear fusion reactors employ both ion and electron cyclotron schemes. The electron cyclotron heating schemes necessitate approximately 20 MW of CW power at frequencies ranging from 140 to 280 GHz depending upon whether it is desired to use the fundamental or second harmonic resonance [l]. At the present time no source under consideration, or even anticipated, is expected to produce the full power requirement in a single module, and a system composed of several similar sources is envisioned. In this paper, we describe the design and operation of a G-band (140-150 GHz) free-electron laser (FELI amplifier based upon a coaxial hybrid iron (CHI) wiggler [2-41 which can meet these requirements. The CHI wiggler is produced by insertion into a solenoid of a central rod and an outer ring composed of alternating ferrite and nonferrite spacers. A schematic representation

* Corresponding author. Tel. + 1 703 734 5840, fax + 1 703 821 1134, e-mail [email protected]. ’ Permanent address: Science Applications International Corp., McLean, VA 22102, USA. ’ Permanent address: Mission Research Corp., Newington, VA 22122, USA. ’ Permanent address: University of Maryland, College Park, MD 20742, USA. 0168.9002/95/%09.50 Q 1995 Elsevier Science B.V. All rights reserved SSDI 0168.9002(94)01561-9

of the structure is shown in Fig. 1. The position of the spacers is such that the ferrite (nonferrite) spacers on the central rod are opposite the nonferrite (ferrite) spacers on the outer ring. The field is cylindrically symmetric and exhibits minima in the center of the gap providing for enhanced beam focusing. Since high fields at short wiggler periods can be achieved with this design by the relatively simple expedient of using narrow spacers and a ferromagnetic material with a high saturation level in a strong solenoid, a CHI wiggler-based FEL is capable of producing power at the required wavelengths using a relatively low energy electron beam. The analysis and design of a CHI-wiggler FEL herein is based upon a 3-D slow-time-scale nonlinear simulation. Interested readers are referred to Refs. [3,4] in which the formulation is described in detail. In this formulation a set of second order nonlinear differential equations is derived for the evolution of the amplitudes and phases of an arbitrary ensemble of the TE, TM, and TEM modes of a coaxial waveguide. These equations are simultaneously integrated with the complete 3-D Lorentz force equations for an ensemble of electrons using an analytic model of the CHI wiggler [2,3]. The orbit equations are not averaged over a wiggler period; hence, we model the adiabatic injection of the beam into the wiggler self-consistently, and can specify the initial conditions of the beam prior to injection. This is advantageous since the design codes for electron guns and beam diagnostics generally give information on the beam conditions outside the wiggler.

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The wiggler amplitudes and periods which can be achieved have been determined using the POISSON/SUPERFISH group of codes [s]. To this end, we have specified vanadium permendur spacers and found that a 4 kG solenoid would saturate the ferrite for spacers with inner and outer radii of Ri, = 0.7 and I?,,, = 1.5 cm, and a wiggler period of A, = 1.5 cm. For convenience, we shall also assume that Ri, and R,,, are also the inner and outer radii of the coaxial waveguide. Using these wiggler dimensions, we choose to operate with a 10 kG solenoid which provides a wiggler amplitude of N 2 kG at the center of the gap (corresponding to a maximum of the periodic field amplitude of - 4 kG at the pole faces) and a uniform axial field component of = 6 kG to provide for additional focusing. Note that a magneto-resonant enhancement in the gain and efficiency is also present when the Larmor period associated with the uniform axial field component is close to the wiggler period. We also assume an entry taper region of h(+,= 5 wiggler periods in length. This is found to be sufficiently long to preserve the initial electron beam quality through the injection process. Since the performance of an FEL is critically dependent upon the electron beam quality, we must design an electron gun which produces an annular beam with a low energy spread. The design tool we used for this is the EGUN code [6]. In designing the electron beam, we first need to specify the energy, current, and inner and outer radii of the beam. Bearing in mind that the wiggler period is 1.5 cm and that operation in G-band is desired, we choose an electron beam voltage in the neighborhood of 690 kV and a current of 40 A. Assuming that the inner and outer radii of the beam at the exit of the gun were 1.05 cm and 1.15 cm respectively, it was found to be possible to design a gun which produced a beam with an axial energy spread of substantially less than 0.1%.

Solenoid

Dielectric

Fig. 1. Schematic

illustration of the CHI wiggler configuration.

Mode (a = 0.7 cm; b = 1.5 cm; P,” = IT3.0 L’ -I 1 ‘- T---‘F’

TEoI

2.5

1 kW) 70

I

0.0 __-I 135

1~/1 145

140

150

’ 40 155

Frequency (GHz) Fig. 2. Efficiency kV.

and saturation

distance versus frequency

at 690

Finally, throughout the paper we shall deal with the TE,,, mode and an injected power level of 1 kW.

2. Uniform wiggler case We first address the interaction for the case of a uniform wiggler, and consider the above-mentioned wiggler, waveguide and beam parameters for the case of an ideal beam in which the axial energy spread Ayz = 0. The first issue to be addressed is the frequency tuning for these parameters. To this end, the efficiency and saturation distance is plotted in Fig. 2 versus frequency. It is clear from the figure that the efficiency decreases with frequency over this entire band from 140 to 150 GHz. Since the saturation distance is relatively constant over the range of 142-147 GHz, this implies that the peak gain is found in the vicinity of 142 GHz for an efficiency of = 2.2%. As such, we consider the highest gain and efficiency possible and assume a frequency of 142.5 GHz in the remainder of the paper. Note that this type of tuning is expected to occur at all beam voltages and wiggler periods. Thus, it should be possible to retune to 150 GHz just as readily if you are willing to go to higher beam voltages or shorter wiggler periods. The interaction is sensitive to the beam position. In the first place, we hold the cross-sectional beam area fixed at that used in Fig. 2 and vary the mean beam radius R,,. The results of this study are shown in Fig. 3 in which the variation in efficiency and saturation distance is plotted versus R,. As seen in the figure, a beam center of 1.10 cm (which is that used previously) seems to be the optimum. Although the efficiency is somewhat higher at R,, = 1.12 cm, this is near the edge of a steep decrease in efficiency with increasing R,. Therefore, we use the more conservative choice of R, = 1.10 cm henceforth. In the second place, the interaction is sensitive to the thickness of the beam. In order to illustrate this, consider

165

H.P. Freund et al. / Nucl. Instr. and Meth. in Phys. Res. A 358 (1995) 163-166 TE,, Mode (a = 0.7 cm; b = 1.5 cm; f = 142.5 GHz; P,” = 1 kW)

TEo, Mode (a = 0.7 cm; b = 1.5 cm; f = 142.5 GHz)

2.2

2.25 -,~I-’

2.1

2.20 P

,

I

_I

2.15 ig

2.0

6 G .$

1.9

3

1.8

g -

6 5

2.10 2.05

‘Z rF1 2.00 ;ri 1.95

1.7

1.90

1.6 1.07

1.09

1.10

1.11

1.12

1.13

B, = 4.0 kG Bo ert= 6.0 kG hw’ = 1.5 cm !

NW=5

1

F 0.00

1,85

1.08

1

1.14

I

0.05

R,, (cm) Fig. 3.

I

L-_-d 0.15 L

,

0.10 “r,lr,,

Efficiency and saturation distance versus R,,

Fig. 5. Variation beam thickness.

the variation in the efficiency as a function of beam thickness AR for a mean beam radius fixed at R, = 1.10 cm. The efficiency and saturation distance are shown in Fig. 4 as a function of beam thickness. It is clear from the figure that the gain remains relatively constant for AR I 0.6 cm and that the efficiency decreases with increasing AR over the entire range surveyed. Since it is difficult to focus the beam down to an extremely narrow thickness, we make a conservative choice of AR = 0.4 cm which maximizes the gain and still yields a respectively high efficiency. This is the value of the beam thickness which we shall use for the remainder of the paper. Before proceeding to the study of the tapered wiggler interaction, we turn to the effect of the axial beam energy spread. The variation in the efficiency as a function of A y, is shown in Fig. 5. Observe that the efficiency falls from about 2.24% to 2.10% as the axial energy spread increases to 0.10%. This is a relatively modest decrease in efficiency, and a beam quality within this range has been demonstrated with the gun design code.

TE,, Mode (a = 0.7 cm; b = 1.5 cm; f = 142.5 GHz; P,” = 1 kW)

in the efficiency

0.20

0.25

(%I

and saturation

distance

versus

Finally, since CW operation is required, the amount of beam loss during the course of the interaction is an important consideration. Since the total beam power is in the neighborhood of 28 MW, even 1% beam loss could pose an insurmountable problem. As a result of the favorable focusing properties of the CHI wiggler, however, no beam loss was found in the simulation prior to saturation for the uniform wiggler cases studied.

3. Tapered wiggler case Turning to the case of a tapered wiggler, it should be remarked that there is an optimum both in the start-taper point and in the slope of the taper for the efficiency enhancement process. We have optimized both of these parameters and found that for a 1 kW input power that the optimal start-taper point is given by z,/h,., = 46 and the optimal slope of the taper is E, = - 0.001 (where E, =

TEoI Mode (a = 0.7 cm; b = 1.5 cm; Pin = 1 kW)

3.0 2.5 1

1.5 52

\

A-1

0.0

0.5

1.0

1.0 i-

;:;

1, ,L 0

1.5

, 50

100

, ‘I=y, _

150

200

,I 250

AR (mm) Fig. 4. Variation the beam.

in efficiency

versus the axial energy

spread of

Fig. 6. Evolution of the power with axial position for two choices of the energy spread.

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166

H.P. Freurd rt al. / Nucl. Instr. and Met/t in Plqs. Rcs. i-2358

TE,,, Mode (a = 0.7 cm; b = 1.5 cm; P,” = 1 kW)

’ lb-= 40 A R_” = I .06 cm RInax= 1.14cm Ayr=O

B, = 4.0 kG Ba ef, = 6.0 kG hw’=

1.5cm

NW=5

Frequency (GHz) Fig. 7. The bandwidth for the tapered wiggler interaction.

k,‘d In B,/dz). The evolution of the power with axial distance for this choice is shown in Fig. 6 for the cases of an ideal beam with A yZ = 0 and for AyZ/yo = 0.2%. Note that the interaction is shown over a length of = 200h, which represents the length required to taper the wiggler amplitude to zero for this choice of the taper. It is clear from the figure that the efficiency does not change a great deal with the decrease in beam quality over this range, and that the efficiency rises to a value over 13% for an output power of better than 3.5 MW. This represents a substantial improvement over the uniform wiggler efficiency, and occurs due to the relatively high wiggler field strength. We now turn to the bandwidth of the tapered wiggler interaction, and find that the bandwidth can be quite large. Consider the case in which we start with the optimum parameters for the interaction at 142.5 GHz including the total length of the system. The bandwidth will then be determined by the response of the identical system to different drive frequencies. The result of this study is shown in Fig. 7 in which the efficiency at the end of the interaction region is plotted as a function of frequency. As is evident from the figure, the efficiency remains high over a frequency range of approximately 142.5 GHz through 160 GHz, which represents a rather large instantaneous bandwidth. This is in accord with an earlier study made using a simpler FEL model [7]. Finally, it should be noted that despite the extended interaction length for the tapered wiggler cases shown, no beam loss was found in simulation for any of these parameters.

4. Summary The results of this study of a G-band amplifier based upon the CHI wiggler can be summarized rather simply. In the first place, no beam loss was found to occur for either

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the uniform or tapered wiggler runs. This is a requirement from the standpoint of designing a CW device. In the second place, the efficiencies were found to be fairly high. In the uniform wiggler case, efficiencies are in the neighborhood of 2-3s for the chosen parameters, while the tapered wiggler interaction produced efficiencies of 1314% at 143 GHz. These conclusions hold for both an ideal beam and for one with the more realistic beam energy spread of less than or of the order of 0.2%. It should be remarked here that beam qualities of this order are quite reasonable with careful gun design. We also observe that, given the sensitivity of the interaction to the beam dimensions, careful gun design is required. The principal source of concern with the above-mentioned design is the length of the tapered wiggler interaction. At 200 wiggler periods in length, the support of the central rod becomes a serious design issue. However, we feel that it is not insurmountable. Most importantly, a vertical mount would be preferable. Secondly, it is not necessary to taper the wiggler to saturation. A shorter tapered wiggler would sacrifice some output power but facilitate the support of the central rod. Lastly. it should be emphasized that this study represents an initial design only. On the basis of this work, we can now undertake to optimize the design for higher gain and shorter interaction length. This might include several variations in the parameters. Shorter wiggler periods and lower beam voltages would help to shorten the overall interaction length. In addition, operation closer to the magneto-resonance can also enhance the gain. Finally, it should be noted that a 1 kW source at these frequencies might require the design of a gyrotron oscillator as a source of the drive power.

Acknowledgement This work was supported by the Department and the Office of Naval Research.

of Energy

References [ll V.L. Granatstein

and R. Colestock (eds.1, Wave Heating in Plasmas (Gordon & Breach, New York, 1986). 121R.H. Jackson, H.P. Freund. D.E. Pershing and J.M. Taccetti. Nucl. Instr. and Meth. A 341 (1994) 454. [31 H.P. Freund, R.H. Jackson. D.E. Pershing and J.M. Taccetti, Phys. Plasmas 1 (1994) 1046. 141 H.P. Freund, R.H. Jackson, D.E. Pershing and J.M. Taccetti, these Proceedings (16th Int. Free Electron Laser Conf.. Stanford CA, USA, 1994) Nucl. Instr. and Meth. A 358 (1995) 139. [51 A.M. Winslow, J. Comp. Phys. 2 (1967) 149. [d W.B. Herrmannsfeldt, SLAC Report No. 226 (1979). [71 B. Levush, H.P. Freund and T.M. Antonsen, Jr.. Nucl. Instr. and Meth. A 341 (1994) 234.