Rf System Modeling for the High Average Power Fel at Cebaf

High beam loading and energy recovery compounded by the use of superconducting cavities, which requires tight control of microphonic noise, place stringent constraints on the linac rf system design of the proposed high average power FEL at CEBAF. Longitudinal dynamics imposes off–crest operation, which in turn implies a large tuning angle to minimize power requirements. Amplitude and phase stability requirements are consistent with demonstrated performance at CEBAF. A numerical model of the CEBAF rf control system is presented and the response of the system is examined under large parameter variations, microphonic noise and beam current fluctuations. Studies of the transient behavior lead to a plausible start–up and recovery scenario. I. RF SYSTEM OVERVIEW The driver accelerator for the high average power FEL, proposed for construction at CEBAF, is a recirculating energy– recovering 200 MeV, 5 mA cw superconducting rf (SRF) electron accelerator. The accelerator consists of a 10 MeV injector, a 96 MV SRF linac with a two–pass recirculation transport which accelerates the beam to 200 MeV, decelerates it for energy recovery through two passes, and transports it to a ∼10 MeV dump [1]. Matching of the longitudinal phase space for bunching going into the wiggler and debunching going out of the wiggler and into energy recovery, implies a fairly restrictive set of constraints on the rf voltage, phases of the four beams (two accelerating and two decelerating) with respect to the crest of the rf wave, and arc compaction factors (M56). Phasing of the four beams is such that the resultant beam vector has a strong reactive component; therefore the rf cavities must be operated off resonance to minimize the required generator power. With energy recovery, the generator power that must be supplied to the cavities is greatly reduced to approximately 1.5 kW per cavity, despite accelerating 5 mA by 4 MV. The rf system provides power for acceleration of the electron beam, and control of the phase and amplitude of the accelerating field. High beam loading, energy recovery and the use of superconducting cavities, which require tight control of microphonic noise, place stringent constraints on the linac rf system design. A dedicated klystron, power amplifier and regulation system for each rf accelerating cavity is required because of the large influence of microphonic noise parametrically modulating the resonant frequency of the superconducting cavity. This modulation is not coherent over the many cavities, and results in random errors in phase and amplitude that can best be corrected by the use of individual rf cavity control systems. To minimize cost and risk it has been proposed that the CEBAF rf control system [2] be used for the FEL driver accelerator. To ∗Supported by the Virginia Center for Innovative Technology and DOE Contract # DE-AC05-84ER40150. Table I RF system requirements Parameter Requirement RF power to beam per cavity 1.34 kW Klystron power per cavity 5 kW Phase stability (rms) 0.140 Phase stability (long term) 30 Gradient stability (rms) 2.8 × 10−4 Gradient stability (long term) 1.4 × 10−3 Gradient 8 MV/m Accelerating phases 1.80, -13.50, 195.30, 1800 Loaded Q 6.6×106 Tuning angle -61.50 test the control system capabilities and its robustness under the FEL operating conditions, we developed a model of the control system using SIMULINK [3], which numerically integrates the equations of motion of the system. This paper describes the model and presents results of the simulations. We start with a summary of the FEL rf system requirements for the linac. The cavity equation is presented next and power requirements for the linac at steady–state are derived. RF amplitude and phase control is addressed next. We describe the rf model, discuss its validity and present simulation results which include transient behavior, regulation of microphonics, response to large parameter variation and a start–up/recovery scenario. II. RF SYSTEM REQUIREMENTS Table I summarizes the rf system requirements for the linac. III. STEADY–STATE: POWER REQUIREMENTS The rf cavity powered by an rf source (klystron) can be represented by a resonant LCR circuit [4]. The beam in the cavity is represented by a current generator. The dynamics of this system can be described, to a very good approximation, by the following first order differential equation, d ṽc dt + ω0 2QL (1− i tan9)ṽc = ω0 RL 4QL (ĩg − ĩb) (1) whereω0 is the cavity resonant frequency, QL is the loaded Q of the cavity and RL is the loaded shunt impedance RL = (r/Q)QL . For CEBAF cavities (r/Q)=480 Ä per cavity. In arriving at (1) we assume that the cavity voltage, generator and beam current vary as eiωt , where ω is the rf frequency, and ṽc, ĩg and ĩb are the corresponding complex amplitudes, varying slowly with time. For short bunches, ib ≈ 2I0, where I0 is the average beam current, and ib denotes the magnitude of ĩb. In this equation 9 is the tuning angle defined by tan9 = −2QL(ω − ω0)/ω0. 2735 © 1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. The current source ĩb is the vector sum of the four beams present in the linac cavities each with an average current of I0 = 5mA and phases with respect to the crest of the rf wave, φk, k = 1, 2, 3, 4. Therefore ĩb = 2I0 ∑4 k=1 e iφk or ĩb = 2Ibei9b where 2Ib is the magnitude and 9b the phase of ĩb. Similarly we write ṽc = vcei9c . For convenience the reference phase is taken in the direction of ṽc, therefore9c=0. In steady–state the generator power is given by Pg = (1+ β) 16β i g RL , (2) where β is the cavity coupling coefficient. Using eq. (1) we can express the generator power in terms of 9, Ib, 9b and β, and obtain the condition for optimum tuning, tan9opt = (Ib RL/vc) sin9b. The generator power at optimum tuning is Pg0 = v 2 c RL (1+ β) 4β [ 1+ Ib Ra Vc cos9b ]2 . (3) For the accelerating phases given in Table I, Ib = 2.33 mA and 9b = −890. For QL = 6.6× 106, Q0 = 5× 109, and vc=4 MV, the optimum tuning angle is −61.50, and the required generator power is equal to 1.34 kW per cavity. IV. RF AMPLITUDE AND PHASE CONTROL Several designs exist to control the rf fields in superconducting cavities. The “classical” approach, employed by CEBAF, uses separate control of amplitude and phase. In the CEBAF system the cavity signal at 1497 MHz is downconverted to an IF frequency of 70 MHz where the phase detector and the controllers for amplitude and phase are operated. The amplitude of the accelerating field is determined by a Schottky detector which is operated in its linear range; i.e., the output voltage is proportional to the accelerating field. The fast phase detector uses an analog multiplier. The output signal is proportional to the sin (1φ), where1φ is the phase difference between the rf reference (at 70 MHz) and the frequency–converted field probe (rf signal). Amplitude and phase modulators use analog multipliers at 70 MHz. The gains and the frequency response of the feedback loops have to be optimized to minimize the residual amplitude and phase noise under steady–state conditions. During tune–up of the accelerator the field stability requirements can be relaxed but the control system must be stable for a wide range of beam loading conditions. The stability over a wide range of parameters determines the robustness of the rf control system. The coupling between the amplitude and phase loop should be minimal for maximum stability (robustness) and minimum residual noise. Microphonic noise modulates the resonance frequency, which results in the uncontrolled (no feedback) case in rms phase variations of up to 70 and amplitude fluctuations of 0.5% rms (average tuning angle zero) or 8.7% rms (average detuning angle 450). For the required stability a minimum gain of 40 dB for the phase loop and 50 dB for the amplitude loop is required. The typical microphonic noise frequency range is from 1 Hz to 200 Hz for the CEBAF accelerator.