Notes on study of a neutrino source with no cooling I note first that the muon beam after phase rotation is too large to fit in an 800 MHz linac. 30 cm rad at 1.25 T would require 17.5 T to squeeze it into the maximum 8 cm rd of the linac. It must first be cooled, or emittance exchanged. In this study, I look at my standard phase rotation in a 60 cm diameter 1.25 T solenoid , 40 m long (see below). This is followed by a second phase rotation in an even lower field (.3 T) larger solenoid (120 cm diameter, 500 m long. If I do not further lower the field then differences in cos theta wreck this second phase rotation. This is a very long drift, and I lose almost 50% of the muons to decay, but at the end I have 0.85 \% energy spread and a bunch now 200 m long: chosen to fit in the final storage ring. The rf used at the end of the drift needs a rise time of over 600 nsec and is, presumably, an induction linac. I would then emittance exchange, reducing the transverse emittance, say by a factor of 3 and allowing the dE/E to rise to 7.6 \%. The solenoid field required is now down to 10 T (B \propto \sqrt{\epsilon}: still high, but a bit more reasonable. We now fit the beam into the 800 MHz linac and capture the bunches, allowing the momentum spread to rise to about 15 \% . Now we accelerate from the initial 200 MeV to 2 GeV. The momentum spread drops to 1.5 \% and we can phase rotate again to reduce the emittance further and reduce the needed apertures and focus fields. The inital rms transverse emittance was 17000 pi mm mrad. It is reduced to about about 5000 after the first exchange, and could be down to 2000 at 20 GeV. Not bad. Note that the different positions along the 200 m unch, and thus in the bunches formed, vary from over + \60% at one end , to - \30% at the other. Figures ------- Figures are given in top draw and tex format: .td or .tex lowba gives bunch at end of first phase rotation nu2a gives it after the long 500 m drift but before the induction linac nu2b shows it after the induction linac, ie after the second rotation. Polarizations are broken into those -1 to -1/3, -1/3 to + 1/3, and + 1/3 to 1. nu2c shows the same thing cut off at ct < 60 m and enl;arged vertically. Projections are also given. Statistics etc -------------- original capture and phase rotation: p at 24 GeV rms rad 4 mm skew Cu target r=1cm th=.15 y0= -1.5 cm len=45 cm Bz=20 T Taper1 len 3m Bz 20-2 T rad 8-24 cm no rf taper2 len 3m Bz 2-1.25 rad 24-30 cm rf 60 MHz 5 Mv/m rf len 29m Bz 1.25 T rad 30 cm 30 MHz 4 MV/m rf len 5m " rad 30 cm 60 MHz 4 MV/m ----------------------------------- added new stages: taper3 + rf len 13m Bz 1.25-.31 T rad 30-60 cm rf 3 MHz 5 MV/m note 1 drift len 500m Bz .31 T rad 60 cm Ind rf len 40m " " rf 5MV/m note 2 ------------------------------------ at end from 10000 p's 1503 muons mean E 205 MeV rms E 21 MeV (but see below in table: all but the first are \approx 17 MeV) rms ct 32 m emit t 18,000 pi mm mrad Bz .31 T r max 60 cm rms r 20 cm rms th .031 pol .30 ------------------------------------- polarization vs bunch at end from 5000 p's: ct - ct n dE/E pol 60 110 169 1.3 .63 110 135 296 .85 .37 135 160 187 .85 .07 160 210 97 .85 -.13 210 300 20 .85 -.36