Bekefi, B.

Fajans, J.

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PFC/JA-85-4FREE ELECTRON LASER ORCYCLOTRON MASER INSTABILITY?G. BekefiJ. FajansPlasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USAJanuary 1985- 1 -FREE ELECTRON LASER OR CYCLOTRON MASER INSTABILITY?G. Bekefi and J. FajansDepartment of Physics and the Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139ABSTRACTAn analysis of recent free electron laser experiments in combined wiggler andstrong axial magnetic fields shows that near resonance, Q,,=kwv,,, the proximityof the cyclotron maser instability precludes an unambiguous identification ofthe radiation mechanism ( 2,, is the cyclotron frequency in the axial field, kwis the wiggler wavenumber, and v,, the axial electron velocity).- 2 -Experiments carried out several years ago' have shown that extreme cau-tion in data interpretation must be exercised when the electrons of a freeelectron laser are subjected simultaneously to a periodic wiggl.er magneticfield and a strong axial guide magnetic field. The reason is that in theneighborhood of the resonance Q2i=kwv., the free electron laser 2 ,3 ,4,5 (FEL)and cyclotron maser6 (CM) instabilities have similar radiation frequencies;consequently they may coexist and they may be difficult to separate. Indeed,the two instabilities could well be coupled, leading to complicated spectralcharacteristics. In the above ,,=eB/moy is the relativistic cyclotron fre-quency in the guide field; y=(1-3-1)~ is the total relativistic energyfactor; ,=v,/c with v, as the axial electron velocity and 8s=v,/c with v1 asthe transverse velocity induced by the wiggler magnetic field; kw= 21r/t is thewiggler wave number with i as the wiggler period.In this note we examine the spectral characteristics of two recent FELexperiments. We find that in the parameter regime where Q, is near butslightly above the value kwv", the proximity of the FEL and CM instabilitiesprecludes an unambiguous identification of the radiation mechanism, unlessvery careful mapping of relevant parameters is undertaken. In making thisassessment we compare experimental radiation characteristics with those pre-dicted by FEL and CM theories.In the first experiment,7 8 shown in Fig. 1, the radiation characteristicsare studied near resonance by determining the beam energy y, necessary to ob-serve radiation of a given fixed frequency (12.33 GHz) as a function of B,, withthe wiggler field strength Bw held constant (190 G). The solid dots and thevertical lines are from measurements. The vertical lines indicate that inthis region of B,, and y, a given frequency is emitted over a broad band ofelectron energies. This implies that for a given fixed beam energy the radia-tion would be emitted over a wide frequency band, in accordance with theoret-- 4 -However, we prefer the former. It'0 takes cognizance of the fact that thestrength of the wiggler field increases radially with distance from the wig-gler axis, and that it has an axial component. However, it assumes that allelectrons enter the wiggler exactly on axis, and that they then spiral out tohelical, axis encircling orbits. Although this model does not take into ac-count the finite electron beam thickness, and non-axis encircling orbits, ex-periments' and computer simulations'3 indicate that it yields better agreementwith experiment than does id theory which neglects radial variations of thewiggler field and its axial field component. The authors of Ref. 11 preferthe id theory:" to simulate 3d effects, they increase the on-axis wigglerfield strength by 8%, a correction which is said' 4 to represent the field seenby the average, off-axis situated electron.Figure 3 illustrates frequency tuning obtained by variation of the wig-gler field amplitude, observed for six different values of the radiation fre-quency. The solid curves represent experimental observations." Next to eachresonant maximum are shown four solid dots, each representing a theoreticalprediction. For purposes of clarity, and in order to illustrate generaltrends, corresponding points are joined by straight lines.,-The,-,amily of points labelled 1 and 2 represent 3d and Id FEL theory re-spectively, for the case of TE,1 mode excitation. The,cross (x) on the bottomspectrum stands for Id FEL theory of the TMO, mode of excitation. The familyof points labelled 3 and 4 denote 3d CM Theory, for TMO, and TE,, mode of ex-citation, respectively. It is clear from Fig. 3 that in the parameter rangeexplored the predictions of the FEL and CM theories are quite close to oneanother. The proximity of the two instabilities, combined with the large ex-perimental widths of the resonances makes identification of the radiationmechanism very difficult.In conclusion then, we find that in a strong axial guide magnetic field- 6 -REFERENCES1. R.E. Shefer and G. Bekefi, Int. J. Electronics 51, 569 (1981).2. L. Friedland, Phys. Fluids 23, 2376 (1980).3. L. Friedland and A. Fruchtman, Phys. Rev. A. 25 , 2693 (1982).4. H.P. Freund and P. Sprangle, Phys. Rev. A. 28, 1835 (1983).5. W. McMullin, and R.C. Davidson, Phys. Rev. A 25, 3130 (1982).6. P. Sprangle and A.T. Drobot, IEEE Trans. Microwave Theory and Tech.MTT-25, 528 (1977), and references therein.7. J. Fajans, G. Bekefi, Y.Z. Yin, and B. Lax, Phys. Rev. Lett. 53, 246(1984).8. J. Fajans, G. Bekefi, Y.Z. Yin, and B. Lax, M.I.T. Plasma Fusion CenterReport No. PFC/JA-84-41 (1984); accepted for publication in Phys.Fluids.9. H.P. Freund, P. Sprangle, D. Dillenburg, E.H. da Jornata, R.S. Schneider,and B. Liberman, Phys. Rev. A. 26, 2004 (1982).10. H.P. Freund, S. Johnston, and P. Sprangle, IEEE J. Quant. Elect. QE-19,322 (1983).11. S.H. Gold, W.M. Black, H.P. Freund, V.L. Granatstein, R.H. Jackson, P.C.Efthimion, and A.K. Kinkead, Phys. Fluids. 26, 2683 (1983).12. In Ref. 11 the predicted radiation frequency corresponding to the param-eters of Fig. 2a was erroneously calculated from Eqs. (5), (6), and (7)to occur at 67 GHz. Similarly, the predicted frequencies of the twospectra of Fig. 2b were erroneously calculated to be at 78 GHz and 96 GHzrespectively. The two spectra in Fig. 2c were incorrectly predicted tooccur at the same frequencies as the corresponding spectra of Fig. 2b.- 8 -CAPTIONS TO FIGURESFig. 1. Beam energy required for radiation of frequency 12.33GHz as a func-tion of the axial magnetic field.7, Solid curves are from 3d FELtheory, and dashed line is from 3d CM theory, both for the TE,, mode;kw=1.904cm-1 ; BW=190G; TE,, mode cutoff frequency = 6.92GHz.Fig. 2. Emission spectra." (a) TE,, mode; (b) TMO, mode at left and TE,,mode at right; (c) TMOI mode at left and TE,, mode at right. Solidvertical arrows are from 3d FEL theory, and dashed arrows from ld FELtheory; y=3.40 ; kw=2.094cm-1. TE,, mode cutoff frequency = 16.27GHz; TMO, mode cutoff frequency = 21.25GHz.Fig. 3. Frequency tuning by variation of B w. Solid curves are experiment."Points 1 : 3d FEL Theory for TE,, mode. Points 2 : ld FEL theoryfor TE,, mode... Points 3: 3d CM theory for TMO, mode. Points 4 : 3dCM theory for TE,, mode. x : ld FEL theory for TMO, mode. y=3.40kw=2.094cm-1.-jU 0ea0000a0000 000'I3LLI'.)OA9 +1(nLL.4-*-Cii000I'O000000C\i0000AU)Li)00000In 0aI I(b) Bz = 13.12 kGB = 630G*'-0I t I itt, I |(c) Bz =16.0 kGBw =1.4 kG* I . | .+|60 70 80 90 10000RADIATION FREQUENCY (GHz)Fig. 2Bekefi & Fajans6040200(a) * BzI= 3.2kG-Bw = 910 G---- ' 'Icl)I-zcrw0C-0-02010060402004063.9 GHz 1 23 40- -070.7 GHz0- -0zD 75.2 GHzc6 0 - 0wS79.5 GHza.0LD84.2 GHz0- 095.0 GHz0 ,0.2 0.4 0.6 0.8 1.0 1.2WIGGLER FIELD AMPLITUDE Bw (kG)Fig. 3Bekefi & Fajans

Free electron laser or cyclotron maser instability?

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Free electron laser or cyclotron maser instability?

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