Design and Characterization of the DC Acceleration and Transport System Required for the IMW Free Electron Maser Experiment

Transcription

1 UCRL-JC-2833 Design and Characterization of the DC Acceleration and Transport System Required for the MW Free Electron Maser Experiment M. Caplan C. Van Der Geer M. Valentini W. Urbanus This paper was prepared for submittal to the 7th nternational Free Electron Laser Conference New York City,NY August 2-25,995 * August 995 Thisisa preprintofa paperintendedforpublicationin ajoumalorproeeedingasince changes may be made before publication, this preprint is made available with the undemhnding that it will not be cited or reproduced without the permission of the rutha. Y '

2 DSCLAMER This document was prepared as an account of work sponsored by an agency of the United States Government. NeithertheUnitedStates GovernmentaortheUniversity of California n o r any oftheiremployees, makes any warranty, express o r implied, or assmesanylegalliabilityor responsibilityforthe accuracy, cornpleteness,or usefulness ofanyinfoxmation,apparatus,product, orproeess.~sdosed,orrepresentsthatitsuse wouldnotinfringeprivatelyowned lights. Referencehe& toany specificcommercial produds,process, o r service by trade name, trademark, manufacturer, or d e m i s e, doesnotaecessvily constituteorimply its endorsement,recommendation,orfavoriug by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for adveriisiig or product endorsementpurposes.

3 Design and Characterization of the DC Acceleration and TransDort System Required for the MW Free Electron Maser ExDeriment* M. Caplan Lawrence Livermore National Laboratory P.O. BOX88, L-637 Livermore, CA 9455 U.S.A. Fax (5) C. Van Der Geer, M. Valentini, W. Urbanus FOM nstituut voor Plasma Fysica Rijnhuizen, Nieuwegein, The Netherlands Abstract A Free Electron Maser (FEW has been constructed and is soon to be tested at the FOM nstitute (Rijnhuizen) Netherlands with the ultimate goal of producing MW long pulse to CW microwave output in the range 3 GHz to 25 GHz. The DC acceleration and beam transport systems is eventually to be used in a depressed collector configuration requiring 99.8% beam transmission in order that the High Voltage 2MV supply be required only to supply 2 milliamps of body current. A relativistic version of the Herrmann optical theory originally developed for microwave tube beams is used to take in account thermal electrons far out on the gaussian distribution tail which can translate into beam current well outside the ideal beam edge. This theory is applied to the FOM beamline design and predicts that the beam envelope containing 99.8% of the current can be successfully transported to the undulator for a wide range of assumed emittance values. *Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-745-Eng-48. Page

4 (). ntroduction A Free Electron Maser (FEM) has been designed and constructed at the FOM nstitute (Rijnhuizen) Netherlands with the ultimate goal of producing MW long pulse to CW microwave output in the range 3 GHz to 25 GHz. The overall FEM design concept has been discussed elsewhere () and consists of using a 2MeV 2 ampere DC beam system that can eventually be'used in a depressed collector configuration allowing for high overall wall plug efficiency. Operation using a depressed collector requires that the high voltage power supply (- 2MV) provides for the body interception current while the 2 ampere beam current is supplied by the -25 kv collector supplies. The beam transport system is thus required to have 99.8% transmission in order to keep the body current in the range 2 milliamps. Some of the design features, which were incorporated to ensure low interception current are: () DC beam.inline transport and accelerator system, (2) emittance conserving solenoid focusing system, (3) halo suppression at the cathode using an edge emission suppression ring, (4) low beam fill factor (< 3%) Table gives the main design parameters for the FEM beam transport system. (2). Short Pulse Test Configuration The FEM will first be tested short pulse ( psec) in order to verify the beam transport characteristics and microwave output. Figure shows the FEM in the inverse set up without depressed collector with the undulator at ground potential. There are two air core solenoids, which focus the beam from the 8 kv gun into the 2MV accelerator and 2 air core solenoids, which catch the beam just after the accelerator. The radial fields from the accelerator provide additional focusing. There are then 4 iron clad solenoids, which transport the beam through the mm-wave feedback systems to the undulator. The step-tapered undulator provides beam focusing in both the wiggle and non-wiggle plane. There is great care to minimize the flux leaking into the gun and undulator. All diameters Page 2

5 have been kept large compared with the beam size in order to ensure linear focusing, thus conserving emittance. Figure 2 illustrates the solenoid magnetic fields and Accelerator electric fields, which make up the beamline design. The initial conditions of the beam upon emerging from the gun have been determined using the beam analyzer at Varian [23. Current density profiles were determined over a 3 inch distance allowing the emittance to be determined from free beam expansion. t was also verified that the cathode edge suppression ring eliminated halo current. This is illustrated in Figure 3. The predicted beam transport using a 3D particle code GPS starting from measured initial beam conditions is shown in Figure 4 and indicates % beam transmission. However, particle codes have statistical difficulties in taking. into account thermal electrons far out on the gaussian tail, which can translate into small percentages of beam current outside the nominal beam edge. The importance of ensuring 99.8% transmission (2 ma body current) for future depressed collector application motivated the development of a relativistic version [3] of the Herrmann optical theory of thermal velocity effects [4,5] which determines current distribution functions semi-analytically everywhere along the beam allowing the determination of beam envelopes containing up to 99.9% of the beam. This theory is applied to the FEM beamline design in an attempt to accurately account for thermal electrons far out on the gaussian tail.. (3). Hermann ODtical Theory The equations of motion of an electron in the Larmor frame is given by: 3 where: w = (x + iy)exp[-iw,,] Page 3

6 The general trajectory for any electron can be constructed from two linearly independent solutions Re(t) and &(t) where: Re(t) = non-thermal electron emitted from cathode edge with zero thermal velocity. &o(t)=thermal electron emitted from cathode centre with RMS thermal velocity. The equations for Re and o are coupled through space charge since charge density p is defined by: (current)) - ( current) = vzn[r, vznr~~ -4 where RH= = Henmann radius A single equation for rh= RH@ w=--e N fh2 is obtained as follows: (E, is normalized emittance = R,v, / c) Since all possible trajectories are known in terms of Re ando, the current density at any position z can be derived analytically in terms of R e / o assuming an initial gaussian distribution in velocity space, uniform distribution in real space, and initial current density J,. Page. 4

7 The current density is given by: J(r,z) = J, ( R, ~/ R:)exp[-r2 / 2 4 J x exp[-x2 / 2],[rx / o]dx Rd, The total current enclosed at some radius R is determined by integrating the current density and is given by a function T(R/ a, R / a). This function is numerically tabulated so that for a given value R J o, the radius at which a given percent transmission occurs can be determined. (4). Predictions of Herrmann ODtical Theory for FEM Beam Transmission The main predictions of the Herrmann theory are that there are positions along the transport system where the initial beam profile is imaged. At these locations, all thermals from the same initial point are focused at the same image point. Figure 5 shows the predicted radii vs distance at which 99.9%, 99.8%, 99.5% and 95% of the beam is contained. One observes a well defined image plane at the mirror location and at the entrance to the wiggler. Figure 6 shows the current profiles at various locations along the beamline transforming from a uniform distribution (Re / cr+ -) to a gaussian (Re/a+O) and back to a uniform distribution at the image planes. Finally, Figure 7 show the radius containing 99.9% of the beam for various values of RMS Emittance ranging from 7 to 35 n-mm-mrad (with corresponding range of RMS thermal velocities.) (5). Conclusion Careful investigations of the thermal electrons far out on the gaussian tail using the Herrmann theory shows that 99.8% transmission should be achievable over a wide range of emittance due to the oversized pipe diameters as well as the optimized design, which places the cathode image planes at the location of the mirror and entrance to the wiggler. Future long pulse operation using the depressed collector configuration should be possible. Page 5

8 References. W. H. Urbanus, et al, "Design of the MW 2 GHz FOM Fusion FEM, Nuclear nstruments and Methods, A33 (993) 235 North Holland C. Cattelino, J. Atkinson, "Low Emittance Electron Gun for FOM MW 2 GHz CW FEM," Final Technical Report, Varian Associates, Palo Alto, January, 994. C. Thorington, K. Amboss, Private Communication, Hughes Aircraft, Torrance, El Segundo, 995. CC. Cutler, M. Hines, "Thermal Velocity Effects in Electron Guns," Proc. nst. Radio Engineers, 43, 37 (995).. G. Herrmann, "Optical Theory of Therm4 Velocity Effects in Cylindrical Electron Beams," Journal of Applied Physics Volume 29 NO.'^, 958. Page 6

9 Table Beamline Design Parameters for MW FOM FEM Electron Gun Voltage... 8 kv DC Beam Current... 2 amperes Accelerator Voltage... nitial Beam radius... 9mm Final Beam radius mm RMS Emittance (xx') E-mm-mad Beamline Length meters Current Pulse Length... Desired Body nterception Current... 2 milliamp (.2%).35 MeV+2. MeV psec+ OOmillisecond+C W Page 7

10 Pressure Hiah Accelerator tank - v voltage tube terminal mm-wave -2 MV cavity. Solenoid - lens Undulator mm-wave output Beam dump FOM FEM Beamline and Undulator Configuration in the inverse set up.

11 6C Axial electric field (.3 MWmeter) n v) v) 2 = Q tn - w ' yl a, 8 DC accelerator (2 MV) J Air ron Radial electric fields 4 Solenoid magnetic lenses 2 3 Axial distance (cm) 4 Accelerator Electric Fields and Solenoid Magnetic Fietds for the FOM FEM Beamline design. 5 L 6

12 *.26iv x-axis Measured C-nt Density Profile 3 inches from gun showing absence of halo due to cathode edge emission suppression ring. Least squares fit of R(z) with ERYS= 4 x-mm-mrad n.2 Rs(z) with (space charge only)' loexperimental data.o 2. 2 (inches) 3. Emittance determined from free expansion of beam after electron gun. ERMS (xx') = /2 ERMs (measured) = 2 x-mm-mrad.

13 ._ E U 9 a. 5 Q) E m E (D a m Q L E OF w- L., N 4 8 b co v) w m cu

14 5. 4. \+Accelerator + - E mm-wave system 2.,Mirror m Axial distance (cm) Predicted current envelopes at 99.9%. 99.8%. 99.5% and. 95% beam transmission. ERMS(xx') =2 C m - m d -

15 z = 25 cm.o 2 7.o 2 7 i Radius (cm) - Radius (cm) Normalrzed current density profiles at various positions dong the beamiine.

16 5. 4. tn 'b 3. U 3 E mm-wave system 2. Mirror.o 2 w 3 4 Axial distance (cm) Predicted current envelopes at 99.9% transmission for various values of Qvs (xx') ranging from 7 to 35 x-mm-mrad 5 6

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