Estes R. D.

G. Bekefi

R. E. Shefer

W. W. Destler

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Millimeter wave emission from a rotating electron ring in a rippled magnetic field

Bekefi, G.

Shefer, R.E.

Destler, W.W.

DSpace@MIT

Preprint PFC/JA-83-38MILLIMETER WAVE EMISSION FROM A ROTATING ELECTRONRING IN A RIPPLED MAGNETIC FIELDG. Bekefi and R.E. SheferPlasma Fusion Center andResearch Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridge, MA. 02139W.W. DestlerDepartment of Electrical EngineeringUniversity of MarylandCollege Park, Maryland 20742September 1983- 1 -MILLIMETER WAVE EMISSION FROM A ROTATING ELECTRON RINGIN A RIPPLED MAGNETIC FIELDG. Bekefi and R.E. SheferDepartment of Physics and Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridge, Massachusetts 02139andW.W. DestlerDepartment of Electrical EngineeringUniversity of MarylandCollege Park, Maryland 20742ABSTRACTWe report measurements of millimeter wave emission from a rotating rela-tivistic electron ring (2MV, 1kA) in which electrons move in quasi-circularorbits under the combined action of a uniform axial magnetic field and an azi-muthally periodic wiggler magnetic field. We observe radiation at frequenciesbetween 91 and 170GHz, at power levels in excess of 200kW.- 2 -There have been many theoretical' and experimental2 studies of free elec-tron lasers (FEL's) in linear geometry with spatially periodic transverse',2or longitudinal 3-6 magnetic wiggler fields. Such configurations have gainlimitations imposed by the finite length of the interaction region. Recently,a novel circular version of the free electron laser has been explored boththeoretically 7',8 9 and experimentally'" in which a rotating, relativistic elec-tron stream is subjected to an azimuthally periodic wiggler field. The poten-tial advantages of circular FEL's as compared with the conventional linear formare several. First, the beam circulates continuously through the wiggler fieldresulting in a long effective interaction region. Secondly, because of the re-circulation of the growing electromagnetic wave, the device provides its owninternal feedback, and is in essence an oscillator rather than an ampliflier,as is the case in linear FEL's. Thus, external mirrors are not required. Andthirdly, because the electron motion is primarily circular the system'" tendsto be very compact.There are several ways of producing a rotating relativistic electronstream. One is to subject the electrons to orthogonal DC electric and magnet-ic fields as is typical in magnetron-like devices. Here, the electrons under-go a v*(r)=Uo(r)xio/IBo12 drift in a radial electric field rEo(r) and a uniformaxial magnetic field zBo. Addition of an azimuthally periodic magnetic fieldBw(e,r) then results in the sought-after circular FEL. This scheme has beenexplored previously,7'8,10 and though the experimental results " are encourag-ing, it may have a potential drawback in that the electron velocity v(r) varieswith radial distance r. This velocity shear may lead to some degradation ofthe spectral purity of the emitted electromagnetic radiation, and a reductionin gain and efficiency of the device.In this letter we describe initial experiments on a circular FEL whichuses a monoenergetic rotating electron ring and thereby circumvents the problem- 3 -of velocity shear mentioned above. Moreover, in the device discussed below onehas better control over the circulating current than in a magnetron-like schemewhere the anode-cathode gap is partl0 of the magnetic wiggler interaction region.A high quality (energy spread s 1%) rotating electron ring is produced byinjecting a hollow nonrotating beam into a narrow magnetic cusp. ,12 The hol-low beam is generated by field emission from an annular graphite cathode ener-gized by a pulsed, high voltage, high current accelerator (2MV, 20kA, 30ns).The resulting rotating electron ring is guided downstream from the cusp by auniform axial magnetic field of %J.4kG. The ring is 6cm in radius, has a dura-tion of %5ns, and carries an axial current of %1.5kA. The electron rotationvelocity v=0.96c, and the electron axial velocity vz=0.2c. Thus, in the ab-sence of the wiggler magnetic field, the electron orbits form fairly tight he-lices.A schematic of the device is illustrated in Fig. 1. It comprises twosmooth coaxial stainless steel cylinders of radii r,=6.58 and r =5.25cm, re-spectively. The electron ring propagates within the gap formed by the two cyl-inders. Superimposed on the axial guiding magnetic field (produced by a sole-noid) is an azimuthally periodic magnetic wiggler field Bw. Subject to the re-quirement that v-Bw=vxBw=O, the field in the vacuum gap is calculated to be,B r ~N-1 +rN+1 (N2-1)/2NB =r cos(NO) +w 2 Tr rB r N-1 rN+1 (N21)/2N-w sino(N) -2 r0 irwhere r and ^ are unit vectors in the radial and azimuthal directions, respec-tively. N=7(r +r )/k is the number of spatial periods and t is the linear- 4 -periodicity defined midway in the gap. Bow is the amplitude of the radial com-ponent of the field at a distance r=RE(rN- r +1)1/( 2N) where the azimuthalfield component vanishes (which is roughly midway between the two cylinders).We see that near the center of the gap the wiggler field is primarily radialand is thus transverse to the electron flow velocity, as is the case in conven-tional linear free electron lasers. The undulatory force -evxBw is along the±z axis. A single particle computer simulation program has been generated forthe purpose of studying the electron motion in the combined axial and wigglermagnetic fields. Figure 2a shows the projection of the electron trajectory inthe absence of the wiggler, and Fig. 2b shows the trajectory in the presenceof a wiggler field of 1.3kG strength (see below). We see that the trajectoryis not perturbed too strongly: it remains quasi-helical, the radial displace-ments are small, and the electron does not strike the cylinder walls.In our device, the wiggler magnetic field is produced by an assembly of384 samarium-cobalt bar magnets,10 1" each of 0.40cm x 0.40cm cross sectionand 4.8cm long. Each magnet has a residual induction of %9.OkG. The magnetsare positioned behind the grounded stainless steel cylinders and held in placein grooved aluminum holders. Therefore, the electrons see only smooth metal-lic boundaries.To achieve a given periodicity Z, the dipole axes of the magnets are ar-ranged as illustrated in Fig. 3. Because the magnets are discrete, harmonicsof the fundamental period cos(NO) are present. However, use of four or eightmagnets per period as shown in the second and third diagrams greatly reducesthe harmonic content:" all even harmonics are absent and the third harmonicalso vanishes. As a result, the magnetic field closely resembles that givenby Eq. (1). The lower part of Fig. 3 shows a Hall-probe measurement of theradial component of the wiggler field at the center of the vacuum gap for thecase of the longest period k=6.28cm. The measured wiggler field amplitude,- 5 -Bow of Eq. (1), equals 1.31kG. The axial length of the wiggler is 20cm. Thislength is achieved by stacking end-to-end four rows of bar magnets. At thepresent time, all of the radiation measurements described below were made witha wiggler having 6 spatial periods (N) and a periodicity z=6.28cm. Shorterperiodicities are expected to give radiation at frequencies which lie above therange of our detection equipment.The electromagnetic radiation generated in the interaction region is al-lowed to leak out from the gap formed by the two coaxial metal cylinders. Itis then received by means of a small horn antenna, and is guided through vari-ous waveguide cut-off filters to a crystal detector where it is rectified anddisplayed on a fast oscilloscope. Figure 4c illustrates the time history of atypical radiation burst as measured in the 91-170GHz frequency range (T-band).The accompanying beam voltage and axial beam current are shown in Figs. 4a and4b, respectively. When the magnetic wiggler field is turned off (by removingthe samarium-cobalt magnets from their grooved aluminum cylinders) the emitiedpower falls to a level too small to be distinguished from background noise.This is illustrated in Fig. 4d. We thus conclude that the observed radiationis produced only in the presence of the wiggler field.We point out that we have as yet not addressed the problem how best tocouple out the available radiation. Our horn antenna shown in Fig. 1 merelyprobes the radiation field and receives only a small fraction of the availablepower. Using the crystal calibration of our detector, and assuming that atthe high frequencies in question quasi-optical arguments are applicable, (wave-length is small compared with relevant dimensions), the total power radiatedfrom the device at frequencies between 91 and 170GHz is calculated to be nosmaller than 200kW. We also note that although we have as yet not determinedthe radiation spectrum, the observed frequencies are in the range expectedfrom the familiar free electron laser formula' 2- 6 -W ~ (1 + e) y 2 kO/K (2)Here a, = v0/c, y=1+eV/mOc 2 is the total relativistic energy factor with V asthe beam voltage; k0=2r/k is the wiggler wave number with k as its period.Qw=eBOW/mO is the nonrelativistic cyclotron frequency in the wiggler field ofamplitude BOW, and K=1+(Qw/koc)2 . Inserting experimental parameters into Eq.(2) yields a radiation frequency w/2f=143GHz.In addition to the high frequency T-band (91-170GHz) range of frequen-cies, we alsoexplored emission at lower frequencies including Ka-band (21-40GHz), V-band (40-75GHz), E-band (48-90GHz), R-band (59-110GHz) and N-band (73-140GHz). In these lower frequency bands we find that some emission occurseven in the absence of the wiggler magnetic field. The cause of this radia-tion is the negative mass instability which has been fully documented in earli-er studies. 4- 7 It is noteworthy that as a result of the proximity of thetwo grounded, concentric metal cylinders the level of this radiation is greatlyreduced compared to that observed in earlier work 1,1 5 on the negative massinstability, where the conducting boundaries were not in such close proximityto the beam. This points to the fact that considerable stabilization isachieved, as expected,'" by use of the closely spaced (1.3cm gap width) systemof cylinders. When the azimuthal wiggler magnetic field is introduced (by in-serting the samarium-cobalt magnets) the level of the low frequency emissionremains eitherunchanged or in some cases, it is in fact diminished. Thisshows that the presence of the wiggler field does not enhance the negative massinstability, which has been a worrisome possibility.In conclusion, we have observed radiation in the millimeter wavelengthrange (1.8-3.3mm) from a novel type of circular FEL which uses a high quality,high current relativistic electron ring rotating in an azimuthally periodicwiggler magnetic field. The emitted power attributed to the FEL instability- 7 -is at least 200kW. Detailed spectral measurement using a calibrated microwavegrating spectrometer",0 19 will be carried out in the near future. In addition,by rearranging the magnets as illustrated in Fig. 3, we will be able to shortenthe wiggler periodicity 2 and thereby study emission at wavelenghs rangingfrom 0.05 to 1.0mm.ACKNOWLEDGEMENTSThis work was supported in part by the United States Air Force Office ofScientific Research, in part by the Department of the Air Force AeronauticalSystems Division, and in part by the National Science Foundation. We grate-fully acknowledge the assistance of A. Bromborsky in performing the orbit cal-culations.- 8 -REFERENCES1. N.M. Kroll and W.A. McMullin, Phys. Rev. A17, 300 (1978); P. Sprangle andR.A. Smith, Phys. Rev. A21, 293 (1980) and references therein.2. P.A. Sprangle, R.A. Smith, and V.L. Granatstein in "Infrared and Submil-limeter Waves", K. Button editor (Academic Press, N.Y. 1979) Vol. 1, page279 and references therein.3. W.A. McMullin and G. Bekefi, Appl. Phys. Lett. 39, 845 (1981).4. W.A. McMullin and G. Bekefi, Phys. Rev. A25, 1826 (1982).5. R.C. Davidson and W.A. McMullin, Phys. Rev. A26, 1997 (1982).6. R.C. Davidson and W.A. McMullin, Phys. Fluids 26, 840 (1983).7. G. Bekefi, Appl. Phys. Lett. 40, 578 (1982).8. R.D. Estes, A. Palevsky, and A.T. Drobot, Bull. Am. Phys. Soc. 27, 1075(1982); also R.E. Shefer, G. Bekefi, R.D. Estes, C-L. Chang, E. Ott, T.M.Antonson, and A. T. Drobot, Proceedings Fifth International Topical Con-ference High Power Electron and Ion-Beam Research and Technology, SanFrancisco 1983.9. R. C. Davidson and W.A. McMullin, Massachusetts Institute of Technology,Cambridge, Massachusetts, Plasma Fusion Center Report No. PFC/JA-82-33(1982).10. G. Bekefi, R.E. Shefer, and B.D. Nevins, Massachusetts Institute ofTechnology, Cambridge, Massachusetts, Plasma Fusion Center Report No.PFC/JA-83-3 (1983); also Lasers '82, Society for Optical and Quantum Elec-tronics, SOQUE (1982) (to be published).11. M.J. Rhee and W. W. Destler, Phys. Fluids 17, 1574 (1974).12. W.W. Destler, P.K. Misra, and M.J. Rhee, Phys. Fluids 18, 1820 (1975).- 9 -13. K. Halbach, Lawrence Berkeley Laboratory, University of California Accel-erator and Fusion Research Division Report No. LBL11393, August 1980;also IEEE Trans. Nucl. Sci. NS-26, 3882 (1979).14. W.W. Destler, H. Romero, C.D. Striffler, R.L. Weiler, and W. Namkung, J.Appl. Phys. 52, 2740 (1981).15. W.W. Destler, D.W. Hudgins, M.J. Rhee, S. Kawasaki, and V.L. Granatstein,J. Appl. Phys. 48, 3291 (1977).16. H. Uhm and R.C. Davidson, J. Appl. Phys. 49, 593 (1978).17. Y. Goren, H. Uhm, and R.C. Davidson, J. Appl. Phys. 49, 3789 (1978).18. L.J. Laslett, IEEE Trans. N.S.20, 271 (1973).19. J.A. Pasour and S.P. Schlesinger, Rev. Scient. Instr. 48, 1355 (1977);also R.E. Shefer, Ph.D Thesis, Department of Physics, M.I.T. (1981).(Unpublished).- 10 -FIGURE CAPTIONSFig. 1. General experimental configuration.Fi-g. 2. Calculated particle orbits in the r-e and r-z planes for an electroninjected with vz=0.20c,ve=0.96c into the interaction space with(a) BOZ=1.4kG, B W=O, and (b) BOZ=1.4kG, B ,=1. 3kG.Fig. 3. Arrangement of bar magnets (top); Hall probe measurement of the radialmagnetic field at a radial position r=5.92cm, as a function of azi-muthal angle (bottom).Fig. 4. Oscilloscope waveforms of (a) diode voltage, (b) axial current col-lected by a 2.24mm 2 collector located in the center of the interactionregion, (c) microwave signal in T-band (91-170GHz) with wiggler mag-nets, and (d) microwave signal without wiggler magnets.Outerinteraction ConductingSpace Boundary-rBoz r.-InnerConductingBoundaryEmbeddedPermanentMagnetsEmbeddedPermanent MagnetsAnode Plate Iron PlateOilVacuumCathode StemDetectorDownstream CoilsDiode Coils Wave GuideFig. 1Bekefi, Shefer, Destleri tt ..t... ..........(b)Fig. 2Bekefi, Shefer, Destler..... ....------ - -7c-3.14 cm-,-6.28 cmI I I I1.0~ow0wz6.28 cm-1.0I| I I I I0 60 120 180 240 300ANGULAR DISPLACEMENT (DEGREES)Fig. 3Bekefi, Shefer, DestlerI(a)50 ns0. 2 A (b)200 mV (c)200 mV (d)Fig. 4Bekefi, Shefer, Destler

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Millimeter wave emission from a rotating electron ring in a rippled magnetic field

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