The beam time structure in the CW linac. The linac beam current has a periodic time structure (at 10 Hz) with two major components, one for injection to the pulse linac (4.3 msec), and the other for the 3-GeV program. 

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... a multi-MW proton source, is under development at Fermilab. It enables a Long Baseline Neutrino Ex- periment via a new beam line pointed to DUSEL in Lead, South Dakota, and a broad suite of rare decay experiments. The initial acceleration is provided by a 3-GeV 1-mA CW superconducting linac. In a second stage, about 5% of the H − beam is accelerated up to 8 GeV in a 1.3 GHz SRF pulsed linac and injected into the Recycler/Main Injector complex. In order to mitigate problems with stripping foil heating during injection, higher current pulses are accelerated in the CW linac in conjunction with the 1 mA beam which is separated and further accelerated in the pulsed linac. The optimal current in the pulsed linac is discussed as well as the constraints that led to its selection. A con- ceptual design which covers optics and RF stability analysis is presented. Finally, the need for HOM damping is discussed. Project-X, a multi-MW proton source, is under development at Fermilab [1]. It enables a world-leading program in neutrino physics and a broad suite of rare decay experiments. The facility is based on 3-GeV 1-mA CW superconducting linac [2]. In a second stage, about 5-9% of the H- beam is accelerated up to 8 GeV in a SRF pulsed linac for injection into the Recycler/Main Injector synchrotron complex. This fraction is directed from the CW to the to the 8 GeV linac using a pulsed dipole. The overall configuration is shown in Fig. 1 The 3-8 GeV pulsed linac must be capable of deliver- ing correctly formatted beam for injection into the Recycler Ring (or Main Injector) with a total charge per cycle of 26 mA-msec within less than 0.75 s. The bunch structure fed to the pulsed linac must incorporate the Recycler synchrotron RF bucket (52.8 MHz) structure to facilitate pseudo bunch-to-bucket transfer as well as the Recycler revolution (90.3 kHz) structure to provide a 200-ns extrac- tion gap. This results in the removal of 33% of bunches during the beam pulse. The beam in the 8 GeV linac has a pulse duration of 4.3 msec with a 10 Hz repetition rate. Details of the beam structure and timing are presented in Fig. 2. The beam velocity = 0 97 at the pulsed linac input al- lows for efficient acceleration in 1.3 GHz, ILC-type β g = 1 superconducting acceleration cavities [3]. Standard ILC- type cryo-modules containing 8 cavities and one focusing element will be used . A conservative accelerating gradient of 25 MeV/m is chosen so as to provide reliable opera- tion in pulsed regime. The ILC cavity has R/Q = 1036 Ohms [3], leading to an optimal loaded Q of 2 . 5 × 10 7 and a bandwidth of 53 Hz. This narrow bandwidth creates a po- tential problem with microphonics. In addition, the filling time is 4.2 msec and the entire RF pulse is 8.5 msec, which may increase the effect of frequency detuning from Lorentz forces. Experiments done at Fermilab [4] show that it is possible to provide active compensation of Lorentz forces and operate the cavity with a pulse width up to 10 msec at a loaded Q up to 10 7 . To mitigate both Lorentz force and microphonics, the cavity is to be over-coupled. The loaded Q is chosen to be 1 . 0 × 10 7 corresponding to a bandwidth of 130 Hz. Filling time in this case is 3 msec, and entire RF pulse is 7.3 msec and the input pulse power is 32 kW per cavity (20% higher than for optimal coupling). If one klystron excites two cryomodules, it should provide pulsed power of about 615 kW and average power of 45 kW, tak- ing into account 20 % overhead for control and losses in the power distribution system. If the klystron feeds three cryomodules, the pulse power becomes 923 kW and the average power 67.5 kW. The klystron is to be ordered from the industry. Note that the cryogenic load in the cavities is close to the one envisioned for the ILC (20 W/CM). This load is what permits the use long cryomodule strings in the ILC design (the ILC rf pulse is shorter, but additional load of up to 16 W/CM takes place because of HOM excita- tion). A standard TTF3 coupler, designed for the DESY XFEL and ILC for 250 kW of peak power and 4 kW of the average power [3] would likely work for Project-X parameters as well, but it looks complicated and expensive. For the 8-GeV Project X linac one only need 30 kW of peak power and 2.3 kW of average power. Accordingly, a simple 1.3 GHz coupler compatible with the Type-IV ILC cryomodule is being designed for the Project X linac parameters [5]. The coupler design with flat window and no internal bellows is shown in Fig. 3. The lattice has a simple regular FODO structure, with 8 cavities in the open space between quadrupoles. One cryomodule encompasses a quadrupole and 8 cavities, a quadrupole in the center, 4 cavities upstream and 4 cavities downstream of the quadrupole. It is assumed that cryomodules would be assembled in a single cryogenic string cooled by one cryo-plant, similarly to the XFEL and ILC designs. Synchronous rf phases in cavities vary along the linac from − 16 ◦ at the linac entrance to − 10 ◦ at the end of linac to accept bunches emerging from a 50 m transfer line downstream of the CW linac. The design of this transport line will be discussed elsewhere. The beam is accelerated from 3 to 8 GeV in a total of 28 cryomodules. Both lattice design and beam tracking were performed using the CEA TraceWin/Partran code. The beam rms envelopes and phase advances in the pulsed linac are shown in Fig. 4. Space charge is a small perturbation in the 3-8 GeV energy range; emittances are well-preserved an no special issue arises in the error-free nominal lattice. While a de- tailed analysis of the impact of misalignments and rf errors has not yet been done, no major problem is anticipated. The most serious issues are microphonics and Lorentz force detuning (LFD) in long pulses ( 8ms) given the high loaded Q of the cavities. As mentioned above, the baseline ap- proach for the Project-X pulsed linac is to use one rf source for a few cryomodules (16, 24 or 32 cavities per rf station) in conjunction with feed-forward compensation for LFD and microphonics and feedback control of the cavity voltages vector-sum . The required hardware components, algorithms and software are under development at ...