1. Experimental modeling of a Magnetron Transmitter for Superconducting Intensity Frontier Linacs Technical notes G. Kazakevich, V. Yakovlev, R. Pasquinelli, B. Chase, G. Flanagan, F. Marhauser and D. Wolff 11/25/2012

2. ► The RF average power required for the CW proton and ion GeV-scale intensity frontier superconducting linacs for High Energy, HE, physics investigations and for Accelerator Driven System, ADS, projects is within the range of several MW to tens of MW. Traditional CW RF sources as klystrons, IOTs, solid state amplifiers for such power are a significant fraction of the cost of these projects. ► The concept most applicable for the proton and ion accelerators is the powering of each Superconducting Cavity, SC, by an individual Low Level RF (LLRF) vector controlled RF source. The vector control includes a management of the SC feeding power and phase to keep optimized the phase and the amplitude of the accelerating field, [1-3] in each individual cavity to prevent the beam emittance growth, [4]. The CW power per cavity is within the range of tens kW to hundreds kW depending on the beam current. ► The CW magnetrons based on commercial prototypes are potentially less expensive than the above-listed RF sources the more so since the CW magnetrons with power of tens to hundreds kW are well within current manufacturing capabilities. ► A 2.45 GHz model of high-power RF transmitter based on injection-locked CW 1 kW magnetrons demonstrated features necessary for the vector control by a LLRF system.

3. Courtesy of R.J. Pasquinelli; 2012 Fall Project X Collaboration Meeting, 11.27-28.2012, FNAL, Batavia, IL

4. ► The principle of the vector control in magnetrons assuming a control in power and phase is realized by control in phase based on a concept of operation of a magnetron, injection-locked by a signal with varying (slowly in the magnetron frequency domain) frequency/phase in assumption that the injection-locked magnetron phase response is quite linear and fast. ► The concept of operation of a magnetron locked by a wave with slowly-varying frequency has been considered and well verified, [5-7], in numerical modelling and in experiments. ► In the presented work we have verified experimentally that the phase response of the magnetrons injection-locked by a signal with slowly varying frequency/phase is quite linear and fast to suppress parasitic phase modulation in superconducting cavities through a LLRF vector control. ► We performed experimental modelling demonstrating proof of principle of the proposed magnetron transmitter based on two 2-cascade injection-locked magnetrons applicable to utilize the vector control necessary for powering of the superconducting cavities with electronic damping of parasitic phase modulations.

5. A CONCEPT OF THE MAGNETRON TRANSMITTER CONTROLLED IN PHASE AND POWER ► This transmitter configuration allows for the wideband phase and magnitude control following from accelerator RF vector regulation requirements. ► The transmitter consists of two 2-cascade injection-locked magnetrons with outputs combined by a 3-dB hybrid. The phase management is provided by a control of phase in both channels simultaneously, while the power management is provided by a control of phase difference on the inputs of the 2-cascade magnetrons, [8]. ► The 2-cascade injection-locked magnetrons are proposed to decrease the locking power by -40 to -30 dB relatively the combined output power, [9]. Fig. 1. Block diagram of the CW magnetron transmitter based on 2-cascade injection-locked magnetrons with a control in power and phase.

6. TECHNIQUES MODELLING THE MAGNETRON TRANSMITTER ► All features of the transmitter were modelled using two CW 2.45 GHz magnetrons with output power up to 1 kW. The magnetrons were chosen to be locked at the same frequency. Both magnetrons were powered by a single pulse modulator with partial discharge of storage capacitor of 200  F commutated by HTS 101-80-FI IGBT switch, Figs. 2, 3. Fig. 2. Simplified scheme of the modulator HV module ► The lower voltage magnetron is powered from a compensated divider shown in Fig. 2. Fig. 3. Photo of the modulator HV module

7. The modulator operating parameters: Output voltage: U Out = 1-5 kV Repetition rate: 0.25 Hz Pulse duration: 2.5-15 ms Output current: I Out = 0.3-1.0 A Fig. 4. Pulse shapes of voltages of magnetrons operating simultaneously To protect the magnetrons and the modulator components from arcs the modulator has an interlock chain that rapidly interrupts the HV if the modulator load current exceeds 3.5 Amps.

8. ► Features of the transmitter based on injection-locked CW magnetrons have been modelled using two magnetron modules, Figs. 5, 6. Fig. 5. The magnetron experimental module in which a CW magnetron operates as an injection-locked oscillator. Fig. 6. Photo of a single CW magnetron module intended to work in injection-locked mode ► The CW magnetrons were mounted on the WR430 waveguide sections coupled with a waveguide-coax adapters. The adapter and the section designs were optimized using CST Studio model to minimize reflection and maximize transmittance in the magnetron-adapter system. Accordingly the CST Studio modelling for the optimized designs the parameters S 11 and S 21 values are: -26.3 dB and -0.102 dB respectively.

9. ► Verification of operation of the each CW magnetron in injection-locked mode was performed in pulsed regime while each magnetron was pre-excited by CW TWT amplifier driven by N5181A Agilent synthesizer as it is shown in Fig. 7, [9]. The setup was used to measure intrapulse phase variations of the injection-locked magnetron, Fig. 8a-b, utilizing an interferometer including a trombone φ (a phase shifter), and a double balanced mixer. Fig. 7. Setup with the interferometer to measure phase variations of the injection-locked magnetron.

10. FIG. 8a. Typical measured phase variations of the injection-locked CW magnetron operating in pulsed mode at pulse duration of 8 ms at P Out /P Lock ≈19-20 dB. Inset b shows zoomed in time phase variation during first 1.0 ms of the pulse. ► The presented in Fig. 8 traces show phase variation of  φ~ 43 deg. at pulse width of  t~ 8 ms. The value corresponds to parasitic frequency modulation of the injection-locked magnetron with effective amplitude of 15 Hz. ► Approximately same phase variation with the injection- locked magnetron was measured in [10, 11], when the phase control was OFF. ► The transient process of phase modulation in the injection-locked magnetron takes of ~ 200 ns. This implies that a Low Level RF controller may have a closed loop band- width of < 100 kHz and will be able to suppress all expected system disturbances suppressing the parasitic frequency/phase modulation with the frequency as low as tens of Hz, as it was demonstrated in [10, 11] for magnetron operating in CW mode with a superconducting cavity in the feedback loop.

11. EXPERIMENTAL VERIFICATION OF THE MAGNETRON TRANSMITTER MODEL ► The setup modelling the power control of the injection-locked CW 2.45 GHz low- power magnetrons with 3-dB 180 degrees hybrid combiner is shown in Fig. 9. Fig. 9. Experimental modelling of the power control concept and power combining with the CW, 2.45 GHz, 1 kW injection-locked magnetrons. ► A phase shifter (trombone) φ II was used to vary the power combined on port “  ” of the 3-dB 180 degrees hybrid by variation of the phase difference in RF signals locking the magnetrons; the spectrum analyser E4445A was used to measure the combined power. ► Measured power levels shown in Fig. 9 correspond to ratios of the output power to the locking power of 17.6 dB and 14.9 dB, respectively.

12. ► Results of the power combining vs. the phase difference caused by variation of the phase shift φ II by the trombone φ II are plotted in Fig. 10 showing measured power on the combiner outputs “  ”, curve B, and “  ”, curve C, considering the hybrid insertion losses of 0.4 dB and 0.7 dB, respectively. Curve E shows fit of the curve B by a sin(φ II ) function. ► Good agreement of the measured combined power, curve B, with the fit trace, curve E, demonstrates quite good linearity of the phase response of the injection-locked magnetrons with power combining since the sin(φ II ) function is linear at low value of argument and the phase control in magnetrons assumes just such a control using an appropriate LLRF vector system generating the slowly-varying controlling signal. Fig. 10. Plot of control of combined power by phase difference in the combined injection-locked magnetrons.

13. ► Bandwidth of the combined in power injection-locked magnetrons was measured with setup shown in Fig. 9, using phase modulation with amplitude of 20 degrees in the synthesizer. The trombone φ II length at the measurement was chosen to provide maximum power in the “  ” combiner output. Signal from the combiner output “  ” has been compared in phase with the synthesizer signal by the interferometer. The phase response of the injection-locked magnetrons with power combining measured with the interferometer at the frequency of phase modulation of 30 kHz is shown in Fig. 11. Fig. 11. Trace of phase modulation measured for the magnetrons with power combining, injection-locked at phase modulation of the locking signal. The modulation amplitude is 20 degrees and the modulating frequency is 30 kHz.

14. ► Varying frequency of the phase modulation we measured the phase response of the injection-locked magnetrons with power combining by the 3-dB hybrid vs. frequency of the phase modulation of the locking signal, Fig. 12. The Bode plot demonstrates linearity and bandwidth of the injection-locked magnetron response on the phase control by the forcing signal. Maximum frequency of the phase modulation responded by the magnetron as it follows from Fig. 12 is at least of 1 MHz. This value is a bandwidth for phase control in the injection-locked magnetrons with power combining at ratio of the output power to the locking power of ~16 dB. The bandwidth of the phase response is acceptable to suppress the phase modulation of the accelerating field in the SC caused by mechanical noises or/and the magnetron power supplies ripples. ► The measured linearity of the phase response, Fig. 10, and the transfer characteristic of the phase control, Fig. 12, prove principle of phase control of injection- locked magnetron by a slowly varying signal. ► Since the power control in the proposed transmitter is reduced to phase control, the vector control in the transmitter with power combining was proven in the experiments. Fig. 12. Measured with interferometer transfer characteristic of the phase control for injection- locked magnetrons with power combining.

15. ► Phase variation of the injection-locked magnetrons with the power combining has been measured using setup shown in Fig. 9. At the measurements the trombone φ II length has been chosen to provide maximum signal on the hybrid port “  ”. Main part of the trace measured with calibrated interferometer, Fig. 13, has a smooth shape with instantaneous phase noise of few degrees. ► The increase of the modulation index in comparison with the value obtained with single injection-locked magnetron results most likely from more noticeable discharge of the modulator charging capacitor loaded by two magnetrons that causes larger deviation of the magnetron current. Noticeable phase variations measured on the leading edge of the modulator pulse look like the phase variations measured with single injection-locked magnetrons operating in pulsed mode. They may result from multipactoring in magnetrons, when pulsed voltage is applied, or/and variation of the magnetron cathode emitting properties because of back-streaming electrons cleaning the emitting surface. Fig. 13. Interferometer trace on the output “  ” of the hybrid ► The measured frequency variation at t ≥ 50-100 ms corresponds to parasitic frequency modulation in the injection-locked magnetron with effective amplitude of 22 Hz.

16. ► Operation of the 2-cascade injection-locked magnetron has been modelled combining two the magnetron modules in series through an attenuator to provide injection-locking in the second magnetron by lowered (in the attenuator) signal from the first injection-locked magnetron, [12], as it is shown in Fig. 14. Both of the injection- locked magnetrons were fed simultaneously by the pulse modulator at pulse duration of ≈ 5 ms. Fig. 14. Experimental setup to measure phase variation of the 2-cascade injection-locked magnetron Fig. 15. Experimental setup to study 2-cascade injection-locked magnetron

17. Fig. 16. Phase deviations of the 2-cascade injection-locked magnetron measured for pulse duration of≈ 5 ms at various values of the attenuator. Curves B and D show measured traces at 20 dB and 13 dB attenuator values, respectively. ► The traces of phase variation of the 2-cascade injection-locked magnetron look as the measured trace of the injection-locked magnetrons with power combining, The phase deviations measured at ratio of the output power to locking power of 26.5 dB correspond to parasitic modulation with modulating effective frequency of 34 Hz. At the ratio of the output power to locking power of 33.5 dB the phase deviations of the 2- cascade magnetron correspond to parasitic modulation with modulating frequency of 40 Hz.

18. ► The phase response of the 2-cascade injection-locked magnetron model on the fast 180 degrees phase flip has been measured using setup shown in Fig. 14, [ibid.]. The 180 degree phase flip in the TWT drive signal is accomplished, Fig. 17, with a pulse generator and double balanced mixer on the TWT amplifier input. Fig. 17. Response of the frequency-locked 2- cascade magnetron on a fast 180 degrees phase flip measured at ratio of the output power to locking power of 33.5 dB. ► The transient process in the phase flip response, Fig. 16, takes of ~200 ns. This value is in good agreement with results obtained in [11] and corresponds to measurements with phase modulation. The trace in Fig. 14 shows that the 2-cascade injection-locked magnetron is applicable for a phase control at the bandwidth in MHz range. References [1] H. Padamsee, J. Knobloch, T. Hays in RF Superconductivity for Accelerators, 1998 [2] J. R. Delayen, PAC01 Proceed., 2001. [3] T.L. Grimm, et al., Linac04 Proceed., 2004. [4] N. Solyak et al., LINAC10 Proceed., 2010. [5] G.Kazakevitch at al., NIM A 528, (2004), 115. [6] G. Kazakevich et al., PRST-AB, 12, 040701, 2009. [7] G. Kazakevich et al., NIM A 647, 10-16, 2011. [8] G. Kazakevich, V. Yakovlev,” Magnetron option for a pulse linac of the Project X”, Project X document 896, http://projectx-docdb.fnal.govhttp://projectx-docdb.fnal.gov [9] G. Kazakevich et al., WEPPC059, IPAC12 Proceed., 2012. [10] H. Wang et al., IPAC10 Proceed., 2010. [11] A.C. Dexter et al., PRST-AB, 14, 032001, 2011. [12] G. Kazakevich et al., WEPPC060, IPAC12 Proceed., 2012.

19. ► In the presented work we have verified experimentally that the phase response of the magnetrons with a power combining, injection-locked by a signal with slowly varying frequency/phase is quite linear and fast to suppress parasitic phase modulation in superconducting cavities through a LLRF vector control. ► We performed experimental modelling demonstrating proof of principle of the proposed magnetron transmitter based on two 2-cascade injection-locked CW magnetrons with power combining applicable to provide the vector control necessary to power the superconducting cavities with electronic damping of parasitic phase modulations caused by mechanical noises and ripples from magnetrons power supplies. ► We have verified applicability of the proposed CW injection-locked magnetron transmitter to power superconducting cavities in pulsed intensity frontier linacs accelerating long trains of bunches utilizing a vector control to suppress instabilities of the accelerating field. Summary